From ae97c7dcc31d0d8a35268336e31f9cdebb8dafb5 Mon Sep 17 00:00:00 2001
From: DaZuiZui <y51288033@outlook.com>
Date: Wed, 26 Aug 2026 11:51:32 +0800
Subject: [PATCH 1/3] docs: document FFT table function

---
 .../SQL-Manual/Featured-Functions_apache.md   | 91 ++++++++++++++++--
 .../User-Manual/User-defined-function.md      |  6 ++
 .../SQL-Manual/Featured-Functions_apache.md   | 92 +++++++++++++++++--
 .../User-Manual/User-defined-function.md      |  6 ++
 .../SQL-Manual/Featured-Functions_apache.md   | 92 +++++++++++++++++--
 .../User-Manual/User-defined-function.md      |  6 ++
 6 files changed, 270 insertions(+), 23 deletions(-)

diff --git a/src/UserGuide/Master/Table/SQL-Manual/Featured-Functions_apache.md b/src/UserGuide/Master/Table/SQL-Manual/Featured-Functions_apache.md
index d0b771fee..b6b71587a 100644
--- a/src/UserGuide/Master/Table/SQL-Manual/Featured-Functions_apache.md
+++ b/src/UserGuide/Master/Table/SQL-Manual/Featured-Functions_apache.md
@@ -321,7 +321,84 @@ WHERE device_id = '100';
 +-----------------------------+-----------+-----------+-----------+
 ```
 
-## 3 Timeseries Windowing Functions
+## 3. `FFT` Function
+
+### 3.1 Function Description
+
+`FFT` is a table-valued function that calculates the complex discrete Fourier transform of one or more numeric columns. It processes each partition independently and returns one row for every frequency bin.
+
+### 3.2 Function Definition
+
+```sql
+FFT(
+  DATA => table_reference
+    [PARTITION BY partition_column [, ...]]
+    ORDER BY time_column,
+  [SAMPLE_INTERVAL => duration],
+  [N => positive_integer],
+  [NORM => 'backward' | 'forward' | 'ortho'],
+  [TIMECOL => 'time_column_name']
+)
+```
+
+`DATA` is a set-semantic table argument. Its `ORDER BY` clause is required and must contain exactly the time column in ascending order. `PARTITION BY` is optional; without it, all input rows are processed as one partition.
+
+### 3.3 Parameters
+
+| Parameter | Type | Default | Description |
+|-----------|------|---------|-------------|
+| `DATA` | Table | Required | Input table or query. The input must contain a `TIMESTAMP` column and at least one numeric column. |
+| `SAMPLE_INTERVAL` | Duration | Inferred | Sampling interval. If omitted, IoTDB infers the average interval from the first and last timestamps in each partition. |
+| `N` | Positive integer | Number of input rows | FFT transform length. If `N` is greater than the number of rows, the input is zero-padded; if it is smaller, only the first `N` rows are transformed. `N` cannot exceed 65,536. |
+| `NORM` | String | `'backward'` | Normalization mode: `backward` (no scaling), `forward` (divide by `N`), or `ortho` (divide by `sqrt(N)`). Values are case-insensitive. |
+| `TIMECOL` | String | `'time'` | Name of the timestamp column in `DATA`. |
+
+### 3.4 Input Requirements and Limitations
+
+* Supported FFT input types are `INT32`, `INT64`, `FLOAT`, and `DOUBLE`. Other non-partition columns are ignored.
+* Every numeric input value must be non-`NULL`.
+* Timestamps must be strictly ascending within each partition.
+* If `SAMPLE_INTERVAL` is omitted, each partition must contain at least two rows. For regularly sampled data, explicitly specifying the interval is recommended.
+* FFT assumes equally spaced samples. For irregular timestamps, the implementation uses the average interval (or the supplied interval), so the frequency axis is an approximation.
+
+### 3.5 Returned Results
+
+The result contains the following columns in order:
+
+1. Columns listed in `PARTITION BY` (if any).
+2. `frequency_index` (`INT64`): frequency-bin index from `0` to `N - 1`.
+3. `frequency` (`DOUBLE`): signed frequency in hertz; the upper half of the bins represents negative frequencies.
+4. For every numeric input column `value`, two `DOUBLE` columns: `value_real` and `value_imag`.
+
+The magnitude of a bin can be calculated as `sqrt(value_real * value_real + value_imag * value_imag)`.
+
+### 3.6 Usage Example
+
+The following query calculates a four-point FFT for each stock. The `price` values are sampled every minute and are normalized with the orthogonal convention.
+
+```sql
+SELECT *
+FROM FFT(
+  DATA => bid PARTITION BY stock_id ORDER BY time,
+  SAMPLE_INTERVAL => 1m,
+  N => 4,
+  NORM => 'ortho'
+);
+```
+
+For a table with a timestamp column named `event_time`, specify `TIMECOL` explicitly:
+
+```sql
+SELECT *
+FROM FFT(
+  DATA => (SELECT event_time, device_id, temperature FROM sensor_data)
+    PARTITION BY device_id ORDER BY event_time,
+  SAMPLE_INTERVAL => 1s,
+  TIMECOL => 'event_time'
+);
+```
+
+## 4 Timeseries Windowing Functions
 
 The sample data is as follows:
 
@@ -344,7 +421,7 @@ CREATE TABLE bid(time TIMESTAMP TIME, stock_id STRING TAG, price FLOAT FIELD);
 INSERT INTO bid(time, stock_id, price) VALUES('2021-01-01T09:05:00','AAPL',100.0),('2021-01-01T09:06:00','TESL',200.0),('2021-01-01T09:07:00','AAPL',103.0),('2021-01-01T09:07:00','TESL',202.0),('2021-01-01T09:09:00','AAPL',102.0),('2021-01-01T09:15:00','TESL',195.0);
 ```
 
-### 3.1 HOP
+### 4.1 HOP
 
 #### Function Description
 
@@ -410,7 +487,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM HOP(DAT
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 3.2 SESSION
+### 4.2 SESSION
 
 #### Function Description
 
@@ -463,7 +540,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM SESSION
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 3.3 VARIATION
+### 4.3 VARIATION
 
 #### Function Description
 
@@ -517,7 +594,7 @@ IoTDB> SELECT first(time) as window_start, last(time) as window_end, stock_id, a
 +-----------------------------+-----------------------------+--------+-----+
 ```
 
-### 3.4 CAPACITY
+### 4.4 CAPACITY
 
 #### Function Description
 
@@ -570,7 +647,7 @@ IoTDB> SELECT first(time) as start_time, last(time) as end_time, stock_id, avg(p
 +-----------------------------+-----------------------------+--------+-----+
 ```
 
-### 3.5 TUMBLE
+### 4.5 TUMBLE
 
 #### Function Description
 
@@ -624,7 +701,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM TUMBLE(
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 3.6 CUMULATE
+### 4.6 CUMULATE
 
 #### Function Description
 
diff --git a/src/UserGuide/Master/Table/User-Manual/User-defined-function.md b/src/UserGuide/Master/Table/User-Manual/User-defined-function.md
index 4213a7f9c..6afdba01a 100644
--- a/src/UserGuide/Master/Table/User-Manual/User-defined-function.md
+++ b/src/UserGuide/Master/Table/User-Manual/User-defined-function.md
@@ -448,6 +448,12 @@ The result set of a table function consists of two parts:
    * If no pass-through but PARTITION BY is specified: Only partition columns are included.
    * If neither is specified: No additional columns are added.
 
+#### 3.4.7 Built-in FFT Table Function
+
+IoTDB provides the built-in `FFT` table function for computing a fast Fourier transform of numeric columns in a table argument. The `DATA` argument must specify an ascending `ORDER BY` on the time column; `PARTITION BY` can be used to calculate each device or tag independently. See [FFT in Featured Functions](../SQL-Manual/Featured-Functions_apache.md#3-fft-function) for the complete parameter list, output schema, and examples.
+
+`FFT` supports `INT32`, `INT64`, `FLOAT`, and `DOUBLE` value columns. Numeric values cannot be `NULL`, and timestamps must be strictly ascending within each partition. FFT treats input as equally spaced samples; when `SAMPLE_INTERVAL` is omitted, the interval is inferred from the average span of each partition, so irregular timestamps produce an approximate frequency axis.
+
 ### 3.5 Complete Maven Project Example
 
 For Maven-based implementations, refer to the sample project: [udf-example](https://github.com/apache/iotdb/tree/master/example/udf).
diff --git a/src/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md b/src/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
index fd91d58ef..b6b71587a 100644
--- a/src/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
+++ b/src/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
@@ -321,7 +321,84 @@ WHERE device_id = '100';
 +-----------------------------+-----------+-----------+-----------+
 ```
 
-## 3 Timeseries Windowing Functions
+## 3. `FFT` Function
+
+### 3.1 Function Description
+
+`FFT` is a table-valued function that calculates the complex discrete Fourier transform of one or more numeric columns. It processes each partition independently and returns one row for every frequency bin.
+
+### 3.2 Function Definition
+
+```sql
+FFT(
+  DATA => table_reference
+    [PARTITION BY partition_column [, ...]]
+    ORDER BY time_column,
+  [SAMPLE_INTERVAL => duration],
+  [N => positive_integer],
+  [NORM => 'backward' | 'forward' | 'ortho'],
+  [TIMECOL => 'time_column_name']
+)
+```
+
+`DATA` is a set-semantic table argument. Its `ORDER BY` clause is required and must contain exactly the time column in ascending order. `PARTITION BY` is optional; without it, all input rows are processed as one partition.
+
+### 3.3 Parameters
+
+| Parameter | Type | Default | Description |
+|-----------|------|---------|-------------|
+| `DATA` | Table | Required | Input table or query. The input must contain a `TIMESTAMP` column and at least one numeric column. |
+| `SAMPLE_INTERVAL` | Duration | Inferred | Sampling interval. If omitted, IoTDB infers the average interval from the first and last timestamps in each partition. |
+| `N` | Positive integer | Number of input rows | FFT transform length. If `N` is greater than the number of rows, the input is zero-padded; if it is smaller, only the first `N` rows are transformed. `N` cannot exceed 65,536. |
+| `NORM` | String | `'backward'` | Normalization mode: `backward` (no scaling), `forward` (divide by `N`), or `ortho` (divide by `sqrt(N)`). Values are case-insensitive. |
+| `TIMECOL` | String | `'time'` | Name of the timestamp column in `DATA`. |
+
+### 3.4 Input Requirements and Limitations
+
+* Supported FFT input types are `INT32`, `INT64`, `FLOAT`, and `DOUBLE`. Other non-partition columns are ignored.
+* Every numeric input value must be non-`NULL`.
+* Timestamps must be strictly ascending within each partition.
+* If `SAMPLE_INTERVAL` is omitted, each partition must contain at least two rows. For regularly sampled data, explicitly specifying the interval is recommended.
+* FFT assumes equally spaced samples. For irregular timestamps, the implementation uses the average interval (or the supplied interval), so the frequency axis is an approximation.
+
+### 3.5 Returned Results
+
+The result contains the following columns in order:
+
+1. Columns listed in `PARTITION BY` (if any).
+2. `frequency_index` (`INT64`): frequency-bin index from `0` to `N - 1`.
+3. `frequency` (`DOUBLE`): signed frequency in hertz; the upper half of the bins represents negative frequencies.
+4. For every numeric input column `value`, two `DOUBLE` columns: `value_real` and `value_imag`.
+
+The magnitude of a bin can be calculated as `sqrt(value_real * value_real + value_imag * value_imag)`.
+
+### 3.6 Usage Example
+
+The following query calculates a four-point FFT for each stock. The `price` values are sampled every minute and are normalized with the orthogonal convention.
+
+```sql
+SELECT *
+FROM FFT(
+  DATA => bid PARTITION BY stock_id ORDER BY time,
+  SAMPLE_INTERVAL => 1m,
+  N => 4,
+  NORM => 'ortho'
+);
+```
+
+For a table with a timestamp column named `event_time`, specify `TIMECOL` explicitly:
+
+```sql
+SELECT *
+FROM FFT(
+  DATA => (SELECT event_time, device_id, temperature FROM sensor_data)
+    PARTITION BY device_id ORDER BY event_time,
+  SAMPLE_INTERVAL => 1s,
+  TIMECOL => 'event_time'
+);
+```
+
+## 4 Timeseries Windowing Functions
 
 The sample data is as follows:
 
@@ -344,7 +421,7 @@ CREATE TABLE bid(time TIMESTAMP TIME, stock_id STRING TAG, price FLOAT FIELD);
 INSERT INTO bid(time, stock_id, price) VALUES('2021-01-01T09:05:00','AAPL',100.0),('2021-01-01T09:06:00','TESL',200.0),('2021-01-01T09:07:00','AAPL',103.0),('2021-01-01T09:07:00','TESL',202.0),('2021-01-01T09:09:00','AAPL',102.0),('2021-01-01T09:15:00','TESL',195.0);
 ```
 
-### 3.1 HOP
+### 4.1 HOP
 
 #### Function Description
 
@@ -410,7 +487,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM HOP(DAT
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 3.2 SESSION
+### 4.2 SESSION
 
 #### Function Description
 
@@ -463,7 +540,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM SESSION
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 3.3 VARIATION
+### 4.3 VARIATION
 
 #### Function Description
 
@@ -517,7 +594,7 @@ IoTDB> SELECT first(time) as window_start, last(time) as window_end, stock_id, a
 +-----------------------------+-----------------------------+--------+-----+
 ```
 
-### 3.4 CAPACITY
+### 4.4 CAPACITY
 
 #### Function Description
 
@@ -570,7 +647,7 @@ IoTDB> SELECT first(time) as start_time, last(time) as end_time, stock_id, avg(p
 +-----------------------------+-----------------------------+--------+-----+
 ```
 
-### 3.5 TUMBLE
+### 4.5 TUMBLE
 
 #### Function Description
 
@@ -624,7 +701,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM TUMBLE(
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 3.6 CUMULATE
+### 4.6 CUMULATE
 
 #### Function Description
 
@@ -693,4 +770,3 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM CUMULAT
 |2021-01-01T09:00:00.000+08:00|2021-01-01T09:10:00.000+08:00|    AAPL|101.66666666666667|
 +-----------------------------+-----------------------------+--------+------------------+
 ```
-
diff --git a/src/UserGuide/latest-Table/User-Manual/User-defined-function.md b/src/UserGuide/latest-Table/User-Manual/User-defined-function.md
index 770151fd5..528fb8df4 100644
--- a/src/UserGuide/latest-Table/User-Manual/User-defined-function.md
+++ b/src/UserGuide/latest-Table/User-Manual/User-defined-function.md
@@ -448,6 +448,12 @@ The result set of a table function consists of two parts:
    * If no pass-through but PARTITION BY is specified: Only partition columns are included.
    * If neither is specified: No additional columns are added.
 
+#### 3.4.7 Built-in FFT Table Function
+
+IoTDB provides the built-in `FFT` table function for computing a fast Fourier transform of numeric columns in a table argument. The `DATA` argument must specify an ascending `ORDER BY` on the time column; `PARTITION BY` can be used to calculate each device or tag independently. See [FFT in Featured Functions](../SQL-Manual/Featured-Functions_apache.md#3-fft-function) for the complete parameter list, output schema, and examples.
+
+`FFT` supports `INT32`, `INT64`, `FLOAT`, and `DOUBLE` value columns. Numeric values cannot be `NULL`, and timestamps must be strictly ascending within each partition. FFT treats input as equally spaced samples; when `SAMPLE_INTERVAL` is omitted, the interval is inferred from the average span of each partition, so irregular timestamps produce an approximate frequency axis.
+
 ### 3.5 Complete Maven Project Example
 
 For Maven-based implementations, refer to the sample project: [udf-example](https://github.com/apache/iotdb/tree/master/example/udf).
diff --git a/src/zh/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md b/src/zh/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
index 20abca659..997412e37 100644
--- a/src/zh/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
+++ b/src/zh/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
@@ -323,7 +323,84 @@ WHERE device_id = '100';
 +-----------------------------+-----------+-----------+-----------+
 ```
 
-## 3. 时序分窗函数
+## 3. `FFT` 函数
+
+### 3.1 功能概述
+
+`FFT` 是一个表值函数，用于对一个或多个数值列计算复数离散傅里叶变换。函数会分别处理每个分区，并为每个频率箱返回一行结果。
+
+### 3.2 函数定义
+
+```sql
+FFT(
+  DATA => table_reference
+    [PARTITION BY partition_column [, ...]]
+    ORDER BY time_column,
+  [SAMPLE_INTERVAL => duration],
+  [N => positive_integer],
+  [NORM => 'backward' | 'forward' | 'ortho'],
+  [TIMECOL => 'time_column_name']
+)
+```
+
+`DATA` 是组语义表参数，必须指定 `ORDER BY`，且该子句只能包含升序排列的时间列。`PARTITION BY` 为可选项；未指定时，所有输入行作为一个分区处理。
+
+### 3.3 参数说明
+
+| 参数 | 类型 | 默认值 | 说明 |
+|------|------|--------|------|
+| `DATA` | 表 | 必填 | 输入表或查询。输入必须包含一个 `TIMESTAMP` 列以及至少一个数值列。 |
+| `SAMPLE_INTERVAL` | 时间间隔 | 自动推断 | 采样间隔。省略时，IoTDB 根据每个分区的首尾时间戳计算平均间隔。 |
+| `N` | 正整数 | 输入行数 | FFT 变换长度。`N` 大于输入行数时使用零填充；小于输入行数时只对前 `N` 行进行变换。`N` 不能超过 65,536。 |
+| `NORM` | 字符串 | `'backward'` | 归一化模式：`backward`（不缩放）、`forward`（除以 `N`）或 `ortho`（除以 `sqrt(N)`）。值不区分大小写。 |
+| `TIMECOL` | 字符串 | `'time'` | `DATA` 中时间戳列的名称。 |
+
+### 3.4 输入要求与限制
+
+* 支持的 FFT 输入类型为 `INT32`、`INT64`、`FLOAT` 和 `DOUBLE`，其他非分区列会被忽略。
+* 所有数值输入都不能为 `NULL`。
+* 每个分区内的时间戳必须严格递增。
+* 省略 `SAMPLE_INTERVAL` 时，每个分区至少需要两行数据。对于等间隔采样数据，建议显式指定采样间隔。
+* FFT 假设样本等间隔。对于时间戳不规则的数据，函数使用平均间隔（或用户提供的间隔），因此频率轴结果是近似值。
+
+### 3.5 返回结果
+
+返回列按以下顺序排列：
+
+1. `PARTITION BY` 中指定的列（如果指定）。
+2. `frequency_index`（`INT64`）：从 `0` 到 `N - 1` 的频率箱索引。
+3. `frequency`（`DOUBLE`）：以赫兹为单位的有符号频率，后半部分频率箱表示负频率。
+4. 对每个数值输入列 `value`，返回两个 `DOUBLE` 列：`value_real` 和 `value_imag`。
+
+频率箱的幅值可以通过 `sqrt(value_real * value_real + value_imag * value_imag)` 计算。
+
+### 3.6 使用示例
+
+以下查询按股票分别计算 4 点 FFT。`price` 每分钟采样一次，并使用正交归一化方式。
+
+```sql
+SELECT *
+FROM FFT(
+  DATA => bid PARTITION BY stock_id ORDER BY time,
+  SAMPLE_INTERVAL => 1m,
+  N => 4,
+  NORM => 'ortho'
+);
+```
+
+如果表中的时间戳列名为 `event_time`，可以显式指定 `TIMECOL`：
+
+```sql
+SELECT *
+FROM FFT(
+  DATA => (SELECT event_time, device_id, temperature FROM sensor_data)
+    PARTITION BY device_id ORDER BY event_time,
+  SAMPLE_INTERVAL => 1s,
+  TIMECOL => 'event_time'
+);
+```
+
+## 4. 时序分窗函数
 
 原始示例数据如下：
 
@@ -346,7 +423,7 @@ CREATE TABLE bid(time TIMESTAMP TIME, stock_id STRING TAG, price FLOAT FIELD);
 INSERT INTO bid(time, stock_id, price) VALUES('2021-01-01T09:05:00','AAPL',100.0),('2021-01-01T09:06:00','TESL',200.0),('2021-01-01T09:07:00','AAPL',103.0),('2021-01-01T09:07:00','TESL',202.0),('2021-01-01T09:09:00','AAPL',102.0),('2021-01-01T09:15:00','TESL',195.0);
 ```
 
-### 3.1 HOP
+### 4.1 HOP
 
 #### 3.1.1 功能描述
 
@@ -411,7 +488,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM HOP(DAT
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 3.2 SESSION
+### 4.2 SESSION
 
 #### 3.2.1 功能描述
 
@@ -464,7 +541,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM SESSION
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 3.3 VARIATION
+### 4.3 VARIATION
 
 #### 3.3.1 功能描述
 
@@ -518,7 +595,7 @@ IoTDB> SELECT first(time) as window_start, last(time) as window_end, stock_id, a
 +-----------------------------+-----------------------------+--------+-----+
 ```
 
-### 3.4 CAPACITY
+### 4.4 CAPACITY
 
 #### 3.4.1 功能描述
 
@@ -571,7 +648,7 @@ IoTDB> SELECT first(time) as start_time, last(time) as end_time, stock_id, avg(p
 +-----------------------------+-----------------------------+--------+-----+
 ```
 
-### 3.5 TUMBLE
+### 4.5 TUMBLE
 
 #### 3.5.1 功能描述
 
@@ -625,7 +702,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM TUMBLE(
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 3.6 CUMULATE
+### 4.6 CUMULATE
 
 #### 3.6.1 功能描述
 
@@ -694,4 +771,3 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM CUMULAT
 |2021-01-01T09:00:00.000+08:00|2021-01-01T09:10:00.000+08:00|    AAPL|101.66666666666667|
 +-----------------------------+-----------------------------+--------+------------------+
 ```
-
diff --git a/src/zh/UserGuide/latest-Table/User-Manual/User-defined-function.md b/src/zh/UserGuide/latest-Table/User-Manual/User-defined-function.md
index 288071f3f..5081c50d2 100644
--- a/src/zh/UserGuide/latest-Table/User-Manual/User-defined-function.md
+++ b/src/zh/UserGuide/latest-Table/User-Manual/User-defined-function.md
@@ -430,6 +430,12 @@ IoTDB 中的表函数为多态表值函数，支持参数类型如下所示：
    * 如果没有指定为列穿透但指定了 PartitionBy，则是 PartitionBy 的列；
    * 如果均未指定，则不根据表参数自动构建列。
 
+#### 3.4.7 内置 FFT 表函数
+
+IoTDB 内置 `FFT` 表函数，用于对表参数中的数值列计算快速傅里叶变换。调用时必须在 `DATA` 参数上指定按时间列升序排列的 `ORDER BY`，并可使用 `PARTITION BY` 对不同设备或标签分别计算。函数的参数、输出列和数据约束请参阅 [特色函数中的 FFT 说明](../SQL-Manual/Featured-Functions_apache.md#3-fft-函数)。
+
+`FFT` 支持 `INT32`、`INT64`、`FLOAT` 和 `DOUBLE` 数值列，数值列不能包含 `NULL`，每个分区内的时间戳必须严格递增。FFT 将输入视为等间隔采样；省略 `SAMPLE_INTERVAL` 时按分区首尾时间戳的平均间隔计算，因此不规则时间戳只能得到近似频率结果。
+
 
 
 ### 3.5 完整Maven项目示例

From bfe7d122dafd5faf9efa582741d56f1f6e942f70 Mon Sep 17 00:00:00 2001
From: DaZuiZui <y51288033@outlook.com>
Date: Wed, 26 Aug 2026 17:15:59 +0800
Subject: [PATCH 2/3] docs: preserve existing function numbering

---
 .../SQL-Manual/Featured-Functions_apache.md   | 170 +++++++++---------
 .../User-Manual/User-defined-function.md      |   2 +-
 .../SQL-Manual/Featured-Functions_apache.md   | 170 +++++++++---------
 .../User-Manual/User-defined-function.md      |   2 +-
 .../SQL-Manual/Featured-Functions_apache.md   | 170 +++++++++---------
 .../User-Manual/User-defined-function.md      |   2 +-
 6 files changed, 261 insertions(+), 255 deletions(-)

diff --git a/src/UserGuide/Master/Table/SQL-Manual/Featured-Functions_apache.md b/src/UserGuide/Master/Table/SQL-Manual/Featured-Functions_apache.md
index b6b71587a..cd3000ec4 100644
--- a/src/UserGuide/Master/Table/SQL-Manual/Featured-Functions_apache.md
+++ b/src/UserGuide/Master/Table/SQL-Manual/Featured-Functions_apache.md
@@ -321,84 +321,7 @@ WHERE device_id = '100';
 +-----------------------------+-----------+-----------+-----------+
 ```
 
-## 3. `FFT` Function
-
-### 3.1 Function Description
-
-`FFT` is a table-valued function that calculates the complex discrete Fourier transform of one or more numeric columns. It processes each partition independently and returns one row for every frequency bin.
-
-### 3.2 Function Definition
-
-```sql
-FFT(
-  DATA => table_reference
-    [PARTITION BY partition_column [, ...]]
-    ORDER BY time_column,
-  [SAMPLE_INTERVAL => duration],
-  [N => positive_integer],
-  [NORM => 'backward' | 'forward' | 'ortho'],
-  [TIMECOL => 'time_column_name']
-)
-```
-
-`DATA` is a set-semantic table argument. Its `ORDER BY` clause is required and must contain exactly the time column in ascending order. `PARTITION BY` is optional; without it, all input rows are processed as one partition.
-
-### 3.3 Parameters
-
-| Parameter | Type | Default | Description |
-|-----------|------|---------|-------------|
-| `DATA` | Table | Required | Input table or query. The input must contain a `TIMESTAMP` column and at least one numeric column. |
-| `SAMPLE_INTERVAL` | Duration | Inferred | Sampling interval. If omitted, IoTDB infers the average interval from the first and last timestamps in each partition. |
-| `N` | Positive integer | Number of input rows | FFT transform length. If `N` is greater than the number of rows, the input is zero-padded; if it is smaller, only the first `N` rows are transformed. `N` cannot exceed 65,536. |
-| `NORM` | String | `'backward'` | Normalization mode: `backward` (no scaling), `forward` (divide by `N`), or `ortho` (divide by `sqrt(N)`). Values are case-insensitive. |
-| `TIMECOL` | String | `'time'` | Name of the timestamp column in `DATA`. |
-
-### 3.4 Input Requirements and Limitations
-
-* Supported FFT input types are `INT32`, `INT64`, `FLOAT`, and `DOUBLE`. Other non-partition columns are ignored.
-* Every numeric input value must be non-`NULL`.
-* Timestamps must be strictly ascending within each partition.
-* If `SAMPLE_INTERVAL` is omitted, each partition must contain at least two rows. For regularly sampled data, explicitly specifying the interval is recommended.
-* FFT assumes equally spaced samples. For irregular timestamps, the implementation uses the average interval (or the supplied interval), so the frequency axis is an approximation.
-
-### 3.5 Returned Results
-
-The result contains the following columns in order:
-
-1. Columns listed in `PARTITION BY` (if any).
-2. `frequency_index` (`INT64`): frequency-bin index from `0` to `N - 1`.
-3. `frequency` (`DOUBLE`): signed frequency in hertz; the upper half of the bins represents negative frequencies.
-4. For every numeric input column `value`, two `DOUBLE` columns: `value_real` and `value_imag`.
-
-The magnitude of a bin can be calculated as `sqrt(value_real * value_real + value_imag * value_imag)`.
-
-### 3.6 Usage Example
-
-The following query calculates a four-point FFT for each stock. The `price` values are sampled every minute and are normalized with the orthogonal convention.
-
-```sql
-SELECT *
-FROM FFT(
-  DATA => bid PARTITION BY stock_id ORDER BY time,
-  SAMPLE_INTERVAL => 1m,
-  N => 4,
-  NORM => 'ortho'
-);
-```
-
-For a table with a timestamp column named `event_time`, specify `TIMECOL` explicitly:
-
-```sql
-SELECT *
-FROM FFT(
-  DATA => (SELECT event_time, device_id, temperature FROM sensor_data)
-    PARTITION BY device_id ORDER BY event_time,
-  SAMPLE_INTERVAL => 1s,
-  TIMECOL => 'event_time'
-);
-```
-
-## 4 Timeseries Windowing Functions
+## 3 Timeseries Windowing Functions
 
 The sample data is as follows:
 
@@ -421,7 +344,7 @@ CREATE TABLE bid(time TIMESTAMP TIME, stock_id STRING TAG, price FLOAT FIELD);
 INSERT INTO bid(time, stock_id, price) VALUES('2021-01-01T09:05:00','AAPL',100.0),('2021-01-01T09:06:00','TESL',200.0),('2021-01-01T09:07:00','AAPL',103.0),('2021-01-01T09:07:00','TESL',202.0),('2021-01-01T09:09:00','AAPL',102.0),('2021-01-01T09:15:00','TESL',195.0);
 ```
 
-### 4.1 HOP
+### 3.1 HOP
 
 #### Function Description
 
@@ -487,7 +410,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM HOP(DAT
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 4.2 SESSION
+### 3.2 SESSION
 
 #### Function Description
 
@@ -540,7 +463,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM SESSION
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 4.3 VARIATION
+### 3.3 VARIATION
 
 #### Function Description
 
@@ -594,7 +517,7 @@ IoTDB> SELECT first(time) as window_start, last(time) as window_end, stock_id, a
 +-----------------------------+-----------------------------+--------+-----+
 ```
 
-### 4.4 CAPACITY
+### 3.4 CAPACITY
 
 #### Function Description
 
@@ -647,7 +570,7 @@ IoTDB> SELECT first(time) as start_time, last(time) as end_time, stock_id, avg(p
 +-----------------------------+-----------------------------+--------+-----+
 ```
 
-### 4.5 TUMBLE
+### 3.5 TUMBLE
 
 #### Function Description
 
@@ -701,7 +624,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM TUMBLE(
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 4.6 CUMULATE
+### 3.6 CUMULATE
 
 #### Function Description
 
@@ -770,3 +693,82 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM CUMULAT
 |2021-01-01T09:00:00.000+08:00|2021-01-01T09:10:00.000+08:00|    AAPL|101.66666666666667|
 +-----------------------------+-----------------------------+--------+------------------+
 ```
++-----------------------------+-----------------------------+--------+------------------+
+```
+
+## 4. `FFT` Function
+
+### 4.1 Function Description
+
+`FFT` is a table-valued function that calculates the complex discrete Fourier transform of one or more numeric columns. It processes each partition independently and returns one row for every frequency bin.
+
+### 4.2 Function Definition
+
+```sql
+FFT(
+  DATA => table_reference
+    [PARTITION BY partition_column [, ...]]
+    ORDER BY time_column,
+  [SAMPLE_INTERVAL => duration],
+  [N => positive_integer],
+  [NORM => 'backward' | 'forward' | 'ortho'],
+  [TIMECOL => 'time_column_name']
+)
+```
+
+`DATA` is a set-semantic table argument. Its `ORDER BY` clause is required and must contain exactly the time column in ascending order. `PARTITION BY` is optional; without it, all input rows are processed as one partition.
+
+### 4.3 Parameters
+
+| Parameter | Type | Default | Description |
+|-----------|------|---------|-------------|
+| `DATA` | Table | Required | Input table or query. The input must contain a `TIMESTAMP` column and at least one numeric column. |
+| `SAMPLE_INTERVAL` | Duration | Inferred | Sampling interval. If omitted, IoTDB infers the average interval from the first and last timestamps in each partition. |
+| `N` | Positive integer | Number of input rows | FFT transform length. If `N` is greater than the number of rows, the input is zero-padded; if it is smaller, only the first `N` rows are transformed. `N` cannot exceed 65,536. |
+| `NORM` | String | `'backward'` | Normalization mode: `backward` (no scaling), `forward` (divide by `N`), or `ortho` (divide by `sqrt(N)`). Values are case-insensitive. |
+| `TIMECOL` | String | `'time'` | Name of the timestamp column in `DATA`. |
+
+### 4.4 Input Requirements and Limitations
+
+* Supported FFT input types are `INT32`, `INT64`, `FLOAT`, and `DOUBLE`. Other non-partition columns are ignored.
+* Every numeric input value must be non-`NULL`.
+* Timestamps must be strictly ascending within each partition.
+* If `SAMPLE_INTERVAL` is omitted, each partition must contain at least two rows. For regularly sampled data, explicitly specifying the interval is recommended.
+* FFT assumes equally spaced samples. For irregular timestamps, the implementation uses the average interval (or the supplied interval), so the frequency axis is an approximation.
+
+### 4.5 Returned Results
+
+The result contains the following columns in order:
+
+1. Columns listed in `PARTITION BY` (if any).
+2. `frequency_index` (`INT64`): frequency-bin index from `0` to `N - 1`.
+3. `frequency` (`DOUBLE`): signed frequency in hertz; the upper half of the bins represents negative frequencies.
+4. For every numeric input column `value`, two `DOUBLE` columns: `value_real` and `value_imag`.
+
+The magnitude of a bin can be calculated as `sqrt(value_real * value_real + value_imag * value_imag)`.
+
+### 4.6 Usage Example
+
+The following query calculates a four-point FFT for each stock. The `price` values are sampled every minute and are normalized with the orthogonal convention.
+
+```sql
+SELECT *
+FROM FFT(
+  DATA => bid PARTITION BY stock_id ORDER BY time,
+  SAMPLE_INTERVAL => 1m,
+  N => 4,
+  NORM => 'ortho'
+);
+```
+
+For a table with a timestamp column named `event_time`, specify `TIMECOL` explicitly:
+
+```sql
+SELECT *
+FROM FFT(
+  DATA => (SELECT event_time, device_id, temperature FROM sensor_data)
+    PARTITION BY device_id ORDER BY event_time,
+  SAMPLE_INTERVAL => 1s,
+  TIMECOL => 'event_time'
+);
+```
diff --git a/src/UserGuide/Master/Table/User-Manual/User-defined-function.md b/src/UserGuide/Master/Table/User-Manual/User-defined-function.md
index 6afdba01a..75ae5458d 100644
--- a/src/UserGuide/Master/Table/User-Manual/User-defined-function.md
+++ b/src/UserGuide/Master/Table/User-Manual/User-defined-function.md
@@ -450,7 +450,7 @@ The result set of a table function consists of two parts:
 
 #### 3.4.7 Built-in FFT Table Function
 
-IoTDB provides the built-in `FFT` table function for computing a fast Fourier transform of numeric columns in a table argument. The `DATA` argument must specify an ascending `ORDER BY` on the time column; `PARTITION BY` can be used to calculate each device or tag independently. See [FFT in Featured Functions](../SQL-Manual/Featured-Functions_apache.md#3-fft-function) for the complete parameter list, output schema, and examples.
+IoTDB provides the built-in `FFT` table function for computing a fast Fourier transform of numeric columns in a table argument. The `DATA` argument must specify an ascending `ORDER BY` on the time column; `PARTITION BY` can be used to calculate each device or tag independently. See [FFT in Featured Functions](../SQL-Manual/Featured-Functions_apache.md#4-fft-function) for the complete parameter list, output schema, and examples.
 
 `FFT` supports `INT32`, `INT64`, `FLOAT`, and `DOUBLE` value columns. Numeric values cannot be `NULL`, and timestamps must be strictly ascending within each partition. FFT treats input as equally spaced samples; when `SAMPLE_INTERVAL` is omitted, the interval is inferred from the average span of each partition, so irregular timestamps produce an approximate frequency axis.
 
diff --git a/src/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md b/src/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
index b6b71587a..cd3000ec4 100644
--- a/src/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
+++ b/src/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
@@ -321,84 +321,7 @@ WHERE device_id = '100';
 +-----------------------------+-----------+-----------+-----------+
 ```
 
-## 3. `FFT` Function
-
-### 3.1 Function Description
-
-`FFT` is a table-valued function that calculates the complex discrete Fourier transform of one or more numeric columns. It processes each partition independently and returns one row for every frequency bin.
-
-### 3.2 Function Definition
-
-```sql
-FFT(
-  DATA => table_reference
-    [PARTITION BY partition_column [, ...]]
-    ORDER BY time_column,
-  [SAMPLE_INTERVAL => duration],
-  [N => positive_integer],
-  [NORM => 'backward' | 'forward' | 'ortho'],
-  [TIMECOL => 'time_column_name']
-)
-```
-
-`DATA` is a set-semantic table argument. Its `ORDER BY` clause is required and must contain exactly the time column in ascending order. `PARTITION BY` is optional; without it, all input rows are processed as one partition.
-
-### 3.3 Parameters
-
-| Parameter | Type | Default | Description |
-|-----------|------|---------|-------------|
-| `DATA` | Table | Required | Input table or query. The input must contain a `TIMESTAMP` column and at least one numeric column. |
-| `SAMPLE_INTERVAL` | Duration | Inferred | Sampling interval. If omitted, IoTDB infers the average interval from the first and last timestamps in each partition. |
-| `N` | Positive integer | Number of input rows | FFT transform length. If `N` is greater than the number of rows, the input is zero-padded; if it is smaller, only the first `N` rows are transformed. `N` cannot exceed 65,536. |
-| `NORM` | String | `'backward'` | Normalization mode: `backward` (no scaling), `forward` (divide by `N`), or `ortho` (divide by `sqrt(N)`). Values are case-insensitive. |
-| `TIMECOL` | String | `'time'` | Name of the timestamp column in `DATA`. |
-
-### 3.4 Input Requirements and Limitations
-
-* Supported FFT input types are `INT32`, `INT64`, `FLOAT`, and `DOUBLE`. Other non-partition columns are ignored.
-* Every numeric input value must be non-`NULL`.
-* Timestamps must be strictly ascending within each partition.
-* If `SAMPLE_INTERVAL` is omitted, each partition must contain at least two rows. For regularly sampled data, explicitly specifying the interval is recommended.
-* FFT assumes equally spaced samples. For irregular timestamps, the implementation uses the average interval (or the supplied interval), so the frequency axis is an approximation.
-
-### 3.5 Returned Results
-
-The result contains the following columns in order:
-
-1. Columns listed in `PARTITION BY` (if any).
-2. `frequency_index` (`INT64`): frequency-bin index from `0` to `N - 1`.
-3. `frequency` (`DOUBLE`): signed frequency in hertz; the upper half of the bins represents negative frequencies.
-4. For every numeric input column `value`, two `DOUBLE` columns: `value_real` and `value_imag`.
-
-The magnitude of a bin can be calculated as `sqrt(value_real * value_real + value_imag * value_imag)`.
-
-### 3.6 Usage Example
-
-The following query calculates a four-point FFT for each stock. The `price` values are sampled every minute and are normalized with the orthogonal convention.
-
-```sql
-SELECT *
-FROM FFT(
-  DATA => bid PARTITION BY stock_id ORDER BY time,
-  SAMPLE_INTERVAL => 1m,
-  N => 4,
-  NORM => 'ortho'
-);
-```
-
-For a table with a timestamp column named `event_time`, specify `TIMECOL` explicitly:
-
-```sql
-SELECT *
-FROM FFT(
-  DATA => (SELECT event_time, device_id, temperature FROM sensor_data)
-    PARTITION BY device_id ORDER BY event_time,
-  SAMPLE_INTERVAL => 1s,
-  TIMECOL => 'event_time'
-);
-```
-
-## 4 Timeseries Windowing Functions
+## 3 Timeseries Windowing Functions
 
 The sample data is as follows:
 
@@ -421,7 +344,7 @@ CREATE TABLE bid(time TIMESTAMP TIME, stock_id STRING TAG, price FLOAT FIELD);
 INSERT INTO bid(time, stock_id, price) VALUES('2021-01-01T09:05:00','AAPL',100.0),('2021-01-01T09:06:00','TESL',200.0),('2021-01-01T09:07:00','AAPL',103.0),('2021-01-01T09:07:00','TESL',202.0),('2021-01-01T09:09:00','AAPL',102.0),('2021-01-01T09:15:00','TESL',195.0);
 ```
 
-### 4.1 HOP
+### 3.1 HOP
 
 #### Function Description
 
@@ -487,7 +410,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM HOP(DAT
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 4.2 SESSION
+### 3.2 SESSION
 
 #### Function Description
 
@@ -540,7 +463,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM SESSION
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 4.3 VARIATION
+### 3.3 VARIATION
 
 #### Function Description
 
@@ -594,7 +517,7 @@ IoTDB> SELECT first(time) as window_start, last(time) as window_end, stock_id, a
 +-----------------------------+-----------------------------+--------+-----+
 ```
 
-### 4.4 CAPACITY
+### 3.4 CAPACITY
 
 #### Function Description
 
@@ -647,7 +570,7 @@ IoTDB> SELECT first(time) as start_time, last(time) as end_time, stock_id, avg(p
 +-----------------------------+-----------------------------+--------+-----+
 ```
 
-### 4.5 TUMBLE
+### 3.5 TUMBLE
 
 #### Function Description
 
@@ -701,7 +624,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM TUMBLE(
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 4.6 CUMULATE
+### 3.6 CUMULATE
 
 #### Function Description
 
@@ -770,3 +693,82 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM CUMULAT
 |2021-01-01T09:00:00.000+08:00|2021-01-01T09:10:00.000+08:00|    AAPL|101.66666666666667|
 +-----------------------------+-----------------------------+--------+------------------+
 ```
++-----------------------------+-----------------------------+--------+------------------+
+```
+
+## 4. `FFT` Function
+
+### 4.1 Function Description
+
+`FFT` is a table-valued function that calculates the complex discrete Fourier transform of one or more numeric columns. It processes each partition independently and returns one row for every frequency bin.
+
+### 4.2 Function Definition
+
+```sql
+FFT(
+  DATA => table_reference
+    [PARTITION BY partition_column [, ...]]
+    ORDER BY time_column,
+  [SAMPLE_INTERVAL => duration],
+  [N => positive_integer],
+  [NORM => 'backward' | 'forward' | 'ortho'],
+  [TIMECOL => 'time_column_name']
+)
+```
+
+`DATA` is a set-semantic table argument. Its `ORDER BY` clause is required and must contain exactly the time column in ascending order. `PARTITION BY` is optional; without it, all input rows are processed as one partition.
+
+### 4.3 Parameters
+
+| Parameter | Type | Default | Description |
+|-----------|------|---------|-------------|
+| `DATA` | Table | Required | Input table or query. The input must contain a `TIMESTAMP` column and at least one numeric column. |
+| `SAMPLE_INTERVAL` | Duration | Inferred | Sampling interval. If omitted, IoTDB infers the average interval from the first and last timestamps in each partition. |
+| `N` | Positive integer | Number of input rows | FFT transform length. If `N` is greater than the number of rows, the input is zero-padded; if it is smaller, only the first `N` rows are transformed. `N` cannot exceed 65,536. |
+| `NORM` | String | `'backward'` | Normalization mode: `backward` (no scaling), `forward` (divide by `N`), or `ortho` (divide by `sqrt(N)`). Values are case-insensitive. |
+| `TIMECOL` | String | `'time'` | Name of the timestamp column in `DATA`. |
+
+### 4.4 Input Requirements and Limitations
+
+* Supported FFT input types are `INT32`, `INT64`, `FLOAT`, and `DOUBLE`. Other non-partition columns are ignored.
+* Every numeric input value must be non-`NULL`.
+* Timestamps must be strictly ascending within each partition.
+* If `SAMPLE_INTERVAL` is omitted, each partition must contain at least two rows. For regularly sampled data, explicitly specifying the interval is recommended.
+* FFT assumes equally spaced samples. For irregular timestamps, the implementation uses the average interval (or the supplied interval), so the frequency axis is an approximation.
+
+### 4.5 Returned Results
+
+The result contains the following columns in order:
+
+1. Columns listed in `PARTITION BY` (if any).
+2. `frequency_index` (`INT64`): frequency-bin index from `0` to `N - 1`.
+3. `frequency` (`DOUBLE`): signed frequency in hertz; the upper half of the bins represents negative frequencies.
+4. For every numeric input column `value`, two `DOUBLE` columns: `value_real` and `value_imag`.
+
+The magnitude of a bin can be calculated as `sqrt(value_real * value_real + value_imag * value_imag)`.
+
+### 4.6 Usage Example
+
+The following query calculates a four-point FFT for each stock. The `price` values are sampled every minute and are normalized with the orthogonal convention.
+
+```sql
+SELECT *
+FROM FFT(
+  DATA => bid PARTITION BY stock_id ORDER BY time,
+  SAMPLE_INTERVAL => 1m,
+  N => 4,
+  NORM => 'ortho'
+);
+```
+
+For a table with a timestamp column named `event_time`, specify `TIMECOL` explicitly:
+
+```sql
+SELECT *
+FROM FFT(
+  DATA => (SELECT event_time, device_id, temperature FROM sensor_data)
+    PARTITION BY device_id ORDER BY event_time,
+  SAMPLE_INTERVAL => 1s,
+  TIMECOL => 'event_time'
+);
+```
diff --git a/src/UserGuide/latest-Table/User-Manual/User-defined-function.md b/src/UserGuide/latest-Table/User-Manual/User-defined-function.md
index 528fb8df4..e70ce1604 100644
--- a/src/UserGuide/latest-Table/User-Manual/User-defined-function.md
+++ b/src/UserGuide/latest-Table/User-Manual/User-defined-function.md
@@ -450,7 +450,7 @@ The result set of a table function consists of two parts:
 
 #### 3.4.7 Built-in FFT Table Function
 
-IoTDB provides the built-in `FFT` table function for computing a fast Fourier transform of numeric columns in a table argument. The `DATA` argument must specify an ascending `ORDER BY` on the time column; `PARTITION BY` can be used to calculate each device or tag independently. See [FFT in Featured Functions](../SQL-Manual/Featured-Functions_apache.md#3-fft-function) for the complete parameter list, output schema, and examples.
+IoTDB provides the built-in `FFT` table function for computing a fast Fourier transform of numeric columns in a table argument. The `DATA` argument must specify an ascending `ORDER BY` on the time column; `PARTITION BY` can be used to calculate each device or tag independently. See [FFT in Featured Functions](../SQL-Manual/Featured-Functions_apache.md#4-fft-function) for the complete parameter list, output schema, and examples.
 
 `FFT` supports `INT32`, `INT64`, `FLOAT`, and `DOUBLE` value columns. Numeric values cannot be `NULL`, and timestamps must be strictly ascending within each partition. FFT treats input as equally spaced samples; when `SAMPLE_INTERVAL` is omitted, the interval is inferred from the average span of each partition, so irregular timestamps produce an approximate frequency axis.
 
diff --git a/src/zh/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md b/src/zh/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
index 997412e37..03909bfa8 100644
--- a/src/zh/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
+++ b/src/zh/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
@@ -323,84 +323,7 @@ WHERE device_id = '100';
 +-----------------------------+-----------+-----------+-----------+
 ```
 
-## 3. `FFT` 函数
-
-### 3.1 功能概述
-
-`FFT` 是一个表值函数，用于对一个或多个数值列计算复数离散傅里叶变换。函数会分别处理每个分区，并为每个频率箱返回一行结果。
-
-### 3.2 函数定义
-
-```sql
-FFT(
-  DATA => table_reference
-    [PARTITION BY partition_column [, ...]]
-    ORDER BY time_column,
-  [SAMPLE_INTERVAL => duration],
-  [N => positive_integer],
-  [NORM => 'backward' | 'forward' | 'ortho'],
-  [TIMECOL => 'time_column_name']
-)
-```
-
-`DATA` 是组语义表参数，必须指定 `ORDER BY`，且该子句只能包含升序排列的时间列。`PARTITION BY` 为可选项；未指定时，所有输入行作为一个分区处理。
-
-### 3.3 参数说明
-
-| 参数 | 类型 | 默认值 | 说明 |
-|------|------|--------|------|
-| `DATA` | 表 | 必填 | 输入表或查询。输入必须包含一个 `TIMESTAMP` 列以及至少一个数值列。 |
-| `SAMPLE_INTERVAL` | 时间间隔 | 自动推断 | 采样间隔。省略时，IoTDB 根据每个分区的首尾时间戳计算平均间隔。 |
-| `N` | 正整数 | 输入行数 | FFT 变换长度。`N` 大于输入行数时使用零填充；小于输入行数时只对前 `N` 行进行变换。`N` 不能超过 65,536。 |
-| `NORM` | 字符串 | `'backward'` | 归一化模式：`backward`（不缩放）、`forward`（除以 `N`）或 `ortho`（除以 `sqrt(N)`）。值不区分大小写。 |
-| `TIMECOL` | 字符串 | `'time'` | `DATA` 中时间戳列的名称。 |
-
-### 3.4 输入要求与限制
-
-* 支持的 FFT 输入类型为 `INT32`、`INT64`、`FLOAT` 和 `DOUBLE`，其他非分区列会被忽略。
-* 所有数值输入都不能为 `NULL`。
-* 每个分区内的时间戳必须严格递增。
-* 省略 `SAMPLE_INTERVAL` 时，每个分区至少需要两行数据。对于等间隔采样数据，建议显式指定采样间隔。
-* FFT 假设样本等间隔。对于时间戳不规则的数据，函数使用平均间隔（或用户提供的间隔），因此频率轴结果是近似值。
-
-### 3.5 返回结果
-
-返回列按以下顺序排列：
-
-1. `PARTITION BY` 中指定的列（如果指定）。
-2. `frequency_index`（`INT64`）：从 `0` 到 `N - 1` 的频率箱索引。
-3. `frequency`（`DOUBLE`）：以赫兹为单位的有符号频率，后半部分频率箱表示负频率。
-4. 对每个数值输入列 `value`，返回两个 `DOUBLE` 列：`value_real` 和 `value_imag`。
-
-频率箱的幅值可以通过 `sqrt(value_real * value_real + value_imag * value_imag)` 计算。
-
-### 3.6 使用示例
-
-以下查询按股票分别计算 4 点 FFT。`price` 每分钟采样一次，并使用正交归一化方式。
-
-```sql
-SELECT *
-FROM FFT(
-  DATA => bid PARTITION BY stock_id ORDER BY time,
-  SAMPLE_INTERVAL => 1m,
-  N => 4,
-  NORM => 'ortho'
-);
-```
-
-如果表中的时间戳列名为 `event_time`，可以显式指定 `TIMECOL`：
-
-```sql
-SELECT *
-FROM FFT(
-  DATA => (SELECT event_time, device_id, temperature FROM sensor_data)
-    PARTITION BY device_id ORDER BY event_time,
-  SAMPLE_INTERVAL => 1s,
-  TIMECOL => 'event_time'
-);
-```
-
-## 4. 时序分窗函数
+## 3. 时序分窗函数
 
 原始示例数据如下：
 
@@ -423,7 +346,7 @@ CREATE TABLE bid(time TIMESTAMP TIME, stock_id STRING TAG, price FLOAT FIELD);
 INSERT INTO bid(time, stock_id, price) VALUES('2021-01-01T09:05:00','AAPL',100.0),('2021-01-01T09:06:00','TESL',200.0),('2021-01-01T09:07:00','AAPL',103.0),('2021-01-01T09:07:00','TESL',202.0),('2021-01-01T09:09:00','AAPL',102.0),('2021-01-01T09:15:00','TESL',195.0);
 ```
 
-### 4.1 HOP
+### 3.1 HOP
 
 #### 3.1.1 功能描述
 
@@ -488,7 +411,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM HOP(DAT
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 4.2 SESSION
+### 3.2 SESSION
 
 #### 3.2.1 功能描述
 
@@ -541,7 +464,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM SESSION
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 4.3 VARIATION
+### 3.3 VARIATION
 
 #### 3.3.1 功能描述
 
@@ -595,7 +518,7 @@ IoTDB> SELECT first(time) as window_start, last(time) as window_end, stock_id, a
 +-----------------------------+-----------------------------+--------+-----+
 ```
 
-### 4.4 CAPACITY
+### 3.4 CAPACITY
 
 #### 3.4.1 功能描述
 
@@ -648,7 +571,7 @@ IoTDB> SELECT first(time) as start_time, last(time) as end_time, stock_id, avg(p
 +-----------------------------+-----------------------------+--------+-----+
 ```
 
-### 4.5 TUMBLE
+### 3.5 TUMBLE
 
 #### 3.5.1 功能描述
 
@@ -702,7 +625,7 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM TUMBLE(
 +-----------------------------+-----------------------------+--------+------------------+
 ```
 
-### 4.6 CUMULATE
+### 3.6 CUMULATE
 
 #### 3.6.1 功能描述
 
@@ -771,3 +694,82 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM CUMULAT
 |2021-01-01T09:00:00.000+08:00|2021-01-01T09:10:00.000+08:00|    AAPL|101.66666666666667|
 +-----------------------------+-----------------------------+--------+------------------+
 ```
++-----------------------------+-----------------------------+--------+------------------+
+```
+
+## 4. `FFT` 函数
+
+### 4.1 功能概述
+
+`FFT` 是一个表值函数，用于对一个或多个数值列计算复数离散傅里叶变换。函数会分别处理每个分区，并为每个频率箱返回一行结果。
+
+### 4.2 函数定义
+
+```sql
+FFT(
+  DATA => table_reference
+    [PARTITION BY partition_column [, ...]]
+    ORDER BY time_column,
+  [SAMPLE_INTERVAL => duration],
+  [N => positive_integer],
+  [NORM => 'backward' | 'forward' | 'ortho'],
+  [TIMECOL => 'time_column_name']
+)
+```
+
+`DATA` 是组语义表参数，必须指定 `ORDER BY`，且该子句只能包含升序排列的时间列。`PARTITION BY` 为可选项；未指定时，所有输入行作为一个分区处理。
+
+### 4.3 参数说明
+
+| 参数 | 类型 | 默认值 | 说明 |
+|------|------|--------|------|
+| `DATA` | 表 | 必填 | 输入表或查询。输入必须包含一个 `TIMESTAMP` 列以及至少一个数值列。 |
+| `SAMPLE_INTERVAL` | 时间间隔 | 自动推断 | 采样间隔。省略时，IoTDB 根据每个分区的首尾时间戳计算平均间隔。 |
+| `N` | 正整数 | 输入行数 | FFT 变换长度。`N` 大于输入行数时使用零填充；小于输入行数时只对前 `N` 行进行变换。`N` 不能超过 65,536。 |
+| `NORM` | 字符串 | `'backward'` | 归一化模式：`backward`（不缩放）、`forward`（除以 `N`）或 `ortho`（除以 `sqrt(N)`）。值不区分大小写。 |
+| `TIMECOL` | 字符串 | `'time'` | `DATA` 中时间戳列的名称。 |
+
+### 4.4 输入要求与限制
+
+* 支持的 FFT 输入类型为 `INT32`、`INT64`、`FLOAT` 和 `DOUBLE`，其他非分区列会被忽略。
+* 所有数值输入都不能为 `NULL`。
+* 每个分区内的时间戳必须严格递增。
+* 省略 `SAMPLE_INTERVAL` 时，每个分区至少需要两行数据。对于等间隔采样数据，建议显式指定采样间隔。
+* FFT 假设样本等间隔。对于时间戳不规则的数据，函数使用平均间隔（或用户提供的间隔），因此频率轴结果是近似值。
+
+### 4.5 返回结果
+
+返回列按以下顺序排列：
+
+1. `PARTITION BY` 中指定的列（如果指定）。
+2. `frequency_index`（`INT64`）：从 `0` 到 `N - 1` 的频率箱索引。
+3. `frequency`（`DOUBLE`）：以赫兹为单位的有符号频率，后半部分频率箱表示负频率。
+4. 对每个数值输入列 `value`，返回两个 `DOUBLE` 列：`value_real` 和 `value_imag`。
+
+频率箱的幅值可以通过 `sqrt(value_real * value_real + value_imag * value_imag)` 计算。
+
+### 4.6 使用示例
+
+以下查询按股票分别计算 4 点 FFT。`price` 每分钟采样一次，并使用正交归一化方式。
+
+```sql
+SELECT *
+FROM FFT(
+  DATA => bid PARTITION BY stock_id ORDER BY time,
+  SAMPLE_INTERVAL => 1m,
+  N => 4,
+  NORM => 'ortho'
+);
+```
+
+如果表中的时间戳列名为 `event_time`，可以显式指定 `TIMECOL`：
+
+```sql
+SELECT *
+FROM FFT(
+  DATA => (SELECT event_time, device_id, temperature FROM sensor_data)
+    PARTITION BY device_id ORDER BY event_time,
+  SAMPLE_INTERVAL => 1s,
+  TIMECOL => 'event_time'
+);
+```
diff --git a/src/zh/UserGuide/latest-Table/User-Manual/User-defined-function.md b/src/zh/UserGuide/latest-Table/User-Manual/User-defined-function.md
index 5081c50d2..82abfcc1b 100644
--- a/src/zh/UserGuide/latest-Table/User-Manual/User-defined-function.md
+++ b/src/zh/UserGuide/latest-Table/User-Manual/User-defined-function.md
@@ -432,7 +432,7 @@ IoTDB 中的表函数为多态表值函数，支持参数类型如下所示：
 
 #### 3.4.7 内置 FFT 表函数
 
-IoTDB 内置 `FFT` 表函数，用于对表参数中的数值列计算快速傅里叶变换。调用时必须在 `DATA` 参数上指定按时间列升序排列的 `ORDER BY`，并可使用 `PARTITION BY` 对不同设备或标签分别计算。函数的参数、输出列和数据约束请参阅 [特色函数中的 FFT 说明](../SQL-Manual/Featured-Functions_apache.md#3-fft-函数)。
+IoTDB 内置 `FFT` 表函数，用于对表参数中的数值列计算快速傅里叶变换。调用时必须在 `DATA` 参数上指定按时间列升序排列的 `ORDER BY`，并可使用 `PARTITION BY` 对不同设备或标签分别计算。函数的参数、输出列和数据约束请参阅 [特色函数中的 FFT 说明](../SQL-Manual/Featured-Functions_apache.md#4-fft-函数)。
 
 `FFT` 支持 `INT32`、`INT64`、`FLOAT` 和 `DOUBLE` 数值列，数值列不能包含 `NULL`，每个分区内的时间戳必须严格递增。FFT 将输入视为等间隔采样；省略 `SAMPLE_INTERVAL` 时按分区首尾时间戳的平均间隔计算，因此不规则时间戳只能得到近似频率结果。
 

From f0c397dbbc6894796108e0daf211d7ad38636d2c Mon Sep 17 00:00:00 2001
From: DaZuiZui <y51288033@outlook.com>
Date: Wed, 26 Aug 2026 17:18:45 +0800
Subject: [PATCH 3/3] docs: clarify FFT limits

---
 .../Master/Table/SQL-Manual/Featured-Functions_apache.md     | 5 ++---
 .../latest-Table/SQL-Manual/Featured-Functions_apache.md     | 5 ++---
 .../latest-Table/SQL-Manual/Featured-Functions_apache.md     | 5 ++---
 3 files changed, 6 insertions(+), 9 deletions(-)

diff --git a/src/UserGuide/Master/Table/SQL-Manual/Featured-Functions_apache.md b/src/UserGuide/Master/Table/SQL-Manual/Featured-Functions_apache.md
index cd3000ec4..8551c9647 100644
--- a/src/UserGuide/Master/Table/SQL-Manual/Featured-Functions_apache.md
+++ b/src/UserGuide/Master/Table/SQL-Manual/Featured-Functions_apache.md
@@ -693,8 +693,6 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM CUMULAT
 |2021-01-01T09:00:00.000+08:00|2021-01-01T09:10:00.000+08:00|    AAPL|101.66666666666667|
 +-----------------------------+-----------------------------+--------+------------------+
 ```
-+-----------------------------+-----------------------------+--------+------------------+
-```
 
 ## 4. `FFT` Function
 
@@ -730,11 +728,12 @@ FFT(
 
 ### 4.4 Input Requirements and Limitations
 
-* Supported FFT input types are `INT32`, `INT64`, `FLOAT`, and `DOUBLE`. Other non-partition columns are ignored.
+* Supported FFT input types are `INT32`, `INT64`, `FLOAT`, and `DOUBLE`. Other non-partition, non-time columns are ignored.
 * Every numeric input value must be non-`NULL`.
 * Timestamps must be strictly ascending within each partition.
 * If `SAMPLE_INTERVAL` is omitted, each partition must contain at least two rows. For regularly sampled data, explicitly specifying the interval is recommended.
 * FFT assumes equally spaced samples. For irregular timestamps, the implementation uses the average interval (or the supplied interval), so the frequency axis is an approximation.
+* The total number of spectrum values (`2 × N × number of numeric columns`) is limited to 16,777,216 in addition to the `N <= 65,536` limit.
 
 ### 4.5 Returned Results
 
diff --git a/src/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md b/src/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
index cd3000ec4..8551c9647 100644
--- a/src/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
+++ b/src/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
@@ -693,8 +693,6 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM CUMULAT
 |2021-01-01T09:00:00.000+08:00|2021-01-01T09:10:00.000+08:00|    AAPL|101.66666666666667|
 +-----------------------------+-----------------------------+--------+------------------+
 ```
-+-----------------------------+-----------------------------+--------+------------------+
-```
 
 ## 4. `FFT` Function
 
@@ -730,11 +728,12 @@ FFT(
 
 ### 4.4 Input Requirements and Limitations
 
-* Supported FFT input types are `INT32`, `INT64`, `FLOAT`, and `DOUBLE`. Other non-partition columns are ignored.
+* Supported FFT input types are `INT32`, `INT64`, `FLOAT`, and `DOUBLE`. Other non-partition, non-time columns are ignored.
 * Every numeric input value must be non-`NULL`.
 * Timestamps must be strictly ascending within each partition.
 * If `SAMPLE_INTERVAL` is omitted, each partition must contain at least two rows. For regularly sampled data, explicitly specifying the interval is recommended.
 * FFT assumes equally spaced samples. For irregular timestamps, the implementation uses the average interval (or the supplied interval), so the frequency axis is an approximation.
+* The total number of spectrum values (`2 × N × number of numeric columns`) is limited to 16,777,216 in addition to the `N <= 65,536` limit.
 
 ### 4.5 Returned Results
 
diff --git a/src/zh/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md b/src/zh/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
index 03909bfa8..7f9aa670c 100644
--- a/src/zh/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
+++ b/src/zh/UserGuide/latest-Table/SQL-Manual/Featured-Functions_apache.md
@@ -694,8 +694,6 @@ IoTDB> SELECT window_start, window_end, stock_id, avg(price) as avg FROM CUMULAT
 |2021-01-01T09:00:00.000+08:00|2021-01-01T09:10:00.000+08:00|    AAPL|101.66666666666667|
 +-----------------------------+-----------------------------+--------+------------------+
 ```
-+-----------------------------+-----------------------------+--------+------------------+
-```
 
 ## 4. `FFT` 函数
 
@@ -731,11 +729,12 @@ FFT(
 
 ### 4.4 输入要求与限制
 
-* 支持的 FFT 输入类型为 `INT32`、`INT64`、`FLOAT` 和 `DOUBLE`，其他非分区列会被忽略。
+* 支持的 FFT 输入类型为 `INT32`、`INT64`、`FLOAT` 和 `DOUBLE`，其他非分区、非时间列会被忽略。
 * 所有数值输入都不能为 `NULL`。
 * 每个分区内的时间戳必须严格递增。
 * 省略 `SAMPLE_INTERVAL` 时，每个分区至少需要两行数据。对于等间隔采样数据，建议显式指定采样间隔。
 * FFT 假设样本等间隔。对于时间戳不规则的数据，函数使用平均间隔（或用户提供的间隔），因此频率轴结果是近似值。
+* 除了 `N <= 65,536` 的限制外，频谱值总数（`2 × N × 数值列数`）不能超过 16,777,216。
 
 ### 4.5 返回结果