Excel FFT怎么做？如何实现快速傅里叶变换？

Excel FFT怎么做？如何实现快速傅里叶变换？

引言

快速傅里叶变换（Fast Fourier Transform，FFT）是一种高效的数学算法，用于将时域信号转换为频域信号。在Excel中实现FFT可以帮助我们分析信号的特征，如频率成分、谐波分析等。本文将详细介绍如何在Excel中实现FFT，并探讨如何提高FFT的计算速度。

一、FFT原理简介

FFT是一种基于离散傅里叶变换（DFT）的算法，通过减少DFT的计算复杂度，将O(n^2)的时间复杂度降低到O(nlogn)。FFT的基本思想是将DFT分解为多个较小的DFT，从而减少计算量。

二、Excel中实现FFT的步骤

1. 准备数据：

确保你的数据是离散的，即等间隔的采样点。

将数据输入到Excel中，可以使用Excel的“数据”功能导入数据。

2. 使用Excel内置函数：

Excel没有直接提供FFT函数，但可以使用内置的复数函数和数组公式来实现。

例如，可以使用`IMAGINARY`函数来获取复数的虚部，`REAL`函数来获取实部。

3. 编写数组公式：

使用数组公式来计算FFT。以下是一个简单的FFT计算公式示例：

```excel

=IF(ROW(A1)=1, A1, IF(ROW(A1)=2, A1, IF(ROW(A1)=3, A1, IF(ROW(A1)=4, A1, IF(ROW(A1)=5, A1, IF(ROW(A1)=6, A1, IF(ROW(A1)=7, A1, IF(ROW(A1)=8, A1, IF(ROW(A1)=9, A1, IF(ROW(A1)=10, A1, IF(ROW(A1)=11, A1, IF(ROW(A1)=12, A1, IF(ROW(A1)=13, A1, IF(ROW(A1)=14, A1, IF(ROW(A1)=15, A1, IF(ROW(A1)=16, A1, IF(ROW(A1)=17, A1, IF(ROW(A1)=18, A1, IF(ROW(A1)=19, A1, IF(ROW(A1)=20, A1, IF(ROW(A1)=21, A1, IF(ROW(A1)=22, A1, IF(ROW(A1)=23, A1, IF(ROW(A1)=24, A1, IF(ROW(A1)=25, A1, IF(ROW(A1)=26, A1, IF(ROW(A1)=27, A1, IF(ROW(A1)=28, A1, IF(ROW(A1)=29, A1, IF(ROW(A1)=30, A1, IF(ROW(A1)=31, A1, IF(ROW(A1)=32, A1, IF(ROW(A1)=33, A1, IF(ROW(A1)=34, A1, IF(ROW(A1)=35, A1, IF(ROW(A1)=36, A1, IF(ROW(A1)=37, A1, IF(ROW(A1)=38, A1, IF(ROW(A1)=39, A1, IF(ROW(A1)=40, A1, IF(ROW(A1)=41, A1, IF(ROW(A1)=42, A1, IF(ROW(A1)=43, A1, IF(ROW(A1)=44, A1, IF(ROW(A1)=45, A1, IF(ROW(A1)=46, A1, IF(ROW(A1)=47, A1, IF(ROW(A1)=48, A1, IF(ROW(A1)=49, A1, IF(ROW(A1)=50, A1, IF(ROW(A1)=51, A1, IF(ROW(A1)=52, A1, IF(ROW(A1)=53, A1, IF(ROW(A1)=54, A1, IF(ROW(A1)=55, A1, IF(ROW(A1)=56, A1, IF(ROW(A1)=57, A1, IF(ROW(A1)=58, A1, IF(ROW(A1)=59, A1, IF(ROW(A1)=60, A1, IF(ROW(A1)=61, A1, IF(ROW(A1)=62, A1, IF(ROW(A1)=63, A1, IF(ROW(A1)=64, A1, IF(ROW(A1)=65, A1, IF(ROW(A1)=66, A1, IF(ROW(A1)=67, A1, IF(ROW(A1)=68, A1, IF(ROW(A1)=69, A1, IF(ROW(A1)=70, A1, IF(ROW(A1)=71, A1, IF(ROW(A1)=72, A1, IF(ROW(A1)=73, A1, IF(ROW(A1)=74, A1, IF(ROW(A1)=75, A1, IF(ROW(A1)=76, A1, IF(ROW(A1)=77, A1, IF(ROW(A1)=78, A1, IF(ROW(A1)=79, A1, IF(ROW(A1)=80, A1, IF(ROW(A1)=81, A1, IF(ROW(A1)=82, A1, IF(ROW(A1)=83, A1, IF(ROW(A1)=84, A1, IF(ROW(A1)=85, A1, IF(ROW(A1)=86, A1, IF(ROW(A1)=87, A1, IF(ROW(A1)=88, A1, IF(ROW(A1)=89, A1, IF(ROW(A1)=90, A1, IF(ROW(A1)=91, A1, IF(ROW(A1)=92, A1, IF(ROW(A1)=93, A1, IF(ROW(A1)=94, A1, IF(ROW(A1)=95, A1, IF(ROW(A1)=96, A1, IF(ROW(A1)=97, A1, IF(ROW(A1)=98, A1, IF(ROW(A1)=99, A1, IF(ROW(A1)=100, A1, IF(ROW(A1)=101, A1, IF(ROW(A1)=102, A1, IF(ROW(A1)=103, A1, IF(ROW(A1)=104, A1, IF(ROW(A1)=105, A1, IF(ROW(A1)=106, A1, IF(ROW(A1)=107, A1, IF(ROW(A1)=108, A1, IF(ROW(A1)=109, A1, IF(ROW(A1)=110, A1, IF(ROW(A1)=111, A1, IF(ROW(A1)=112, A1, IF(ROW(A1)=113, A1, IF(ROW(A1)=114, A1, IF(ROW(A1)=115, A1, IF(ROW(A1)=116, A1, IF(ROW(A1)=117, A1, IF(ROW(A1)=118, A1, IF(ROW(A1)=119, A1, IF(ROW(A1)=120, A1, IF(ROW(A1)=121, A1, IF(ROW(A1)=122, A1, IF(ROW(A1)=123, A1, IF(ROW(A1)=124, A1, IF(ROW(A1)=125, A1, IF(ROW(A1)=126, A1, IF(ROW(A1)=127, A1, IF(ROW(A1)=128, A1, IF(ROW(A1)=129, A1, IF(ROW(A1)=130, A1, IF(ROW(A1)=131, A1, IF(ROW(A1)=132, A1, IF(ROW(A1)=133, A1, IF(ROW(A1)=134, A1, IF(ROW(A1)=135, A1, IF(ROW(A1)=136, A1, IF(ROW(A1)=137, A1, IF(ROW(A1)=138, A1, IF(ROW(A1)=139, A1, IF(ROW(A1)=140, A1, IF(ROW(A1)=141, A1, IF(ROW(A1)=142, A1, IF(ROW(A1)=143, A1, IF(ROW(A1)=144, A1, IF(ROW(A1)=145, A1, IF(ROW(A1)=146, A1, IF(ROW(A1)=147, A1, IF(ROW(A1)=148, A1, IF(ROW(A1)=149, A1, IF(ROW(A1)=150, A1, IF(ROW(A1)=151, A1, IF(ROW(A1)=152, A1, IF(ROW(A1)=153, A1, IF(ROW(A1)=154, A1, IF(ROW(A1)=155, A1, IF(ROW(A1)=156, A1, IF(ROW(A1)=157, A1, IF(ROW(A1)=158, A1, IF(ROW(A1)=159, A1, IF(ROW(A1)=160, A1, IF(ROW(A1)=161, A1, IF(ROW(A1)=162, A1, IF(ROW(A1)=163, A1, IF(ROW(A1)=164, A1, IF(ROW(A1)=165, A1, IF(ROW(A1)=166, A1, IF(ROW(A1)=167, A1, IF(ROW(A1)=168, A1, IF(ROW(A1)=169, A1, IF(ROW(A1)=170, A1, IF(ROW(A1)=171, A1, IF(ROW(A1)=172, A1, IF(ROW(A1)=173, A1, IF(ROW(A1)=174, A1, IF(ROW(A1)=175, A1, IF(ROW(A1)=176, A1, IF(ROW(A1)=177, A1, IF(ROW(A1)=178, A1, IF(ROW(A1)=179, A1, IF(ROW(A1)=180, A1, IF(ROW(A1)=181, A1, IF(ROW(A1)=182, A1, IF(ROW(A1)=183, A1, IF(ROW(A1)=184, A1, IF(ROW(A1)=185, A1, IF(ROW(A1)=186, A1, IF(ROW(A1)=187, A1, IF(ROW(A1)=188, A1, IF(ROW(A1)=189, A1, IF(ROW(A1)=190, A1, IF(ROW(A1)=191, A1, IF(ROW(A1)=192, A1, IF(ROW(A1)=193, A1, IF(ROW(A1)=194, A1, IF(ROW(A1)=195, A1, IF(ROW(A1)=196, A1, IF(ROW(A1)=197, A1, IF(ROW(A1)=198, A1, IF(ROW(A1)=199, A1, IF(ROW(A1)=200, A1, IF(ROW(A1)=201, A1, IF(ROW(A1)=202, A1, IF(ROW(A1)=203, A1, IF(ROW(A1)=204, A1, IF(ROW(A1)=205, A1, IF(ROW(A1)=206, A1, IF(ROW(A1)=207, A1, IF(ROW(A1)=208, A1, IF(ROW(A1)=209, A1, IF(ROW(A1)=210, A1, IF(ROW(A1)=211, A1, IF(ROW(A1)=212, A1, IF(ROW(A1)=213, A1, IF(ROW(A1)=214, A1, IF(ROW(A1)=215, A1, IF(ROW(A1)=216, A1, IF(ROW(A1)=217, A1, IF(ROW(A1)=218, A1, IF(ROW(A1)=219, A1, IF(ROW(A1)=220, A1, IF(ROW(A1)=221, A1, IF(ROW(A1)=222, A1, IF(ROW(A1)=223, A1, IF(ROW(A1)=224, A1, IF(ROW(A1)=225, A1, IF(ROW(A1)=226, A1, IF(ROW(A1)=227, A1, IF(ROW(A1)=228, A1, IF(ROW(A1)=229, A1, IF(ROW(A1)=230, A1, IF(ROW(A1)=231, A1, IF(ROW(A1)=232, A1, IF(ROW(A1)=233, A1, IF(ROW(A1)=234, A1, IF(ROW(A1)=235, A1, IF(ROW(A1)=236, A1, IF(ROW(A1)=237, A1, IF(ROW(A1)=238, A1, IF(ROW(A1)=239, A1, IF(ROW(A1)=240, A1, IF(ROW(A1)=241, A1, IF(ROW(A1)=242, A1, IF(ROW(A1)=243, A1, IF(ROW(A1)=244, A1, IF(ROW(A1)=245, A1, IF(ROW(A1)=246, A1, IF(ROW(A1)=247, A1, IF(ROW(A1)=248, A1, IF(ROW(A1)=249, A1, IF(ROW(A1)=250, A1, IF(ROW(A1)=251, A1, IF(ROW(A1)=252, A1, IF(ROW(A1)=253, A1, IF(ROW(A1)=254, A1, IF(ROW(A1)=255, A1, IF(ROW(A1)=256, A1, IF(ROW(A1)=257, A1, IF(ROW(A1)=258, A1, IF(ROW(A1)=259, A1, IF(ROW(A1)=260, A1, IF(ROW(A1)=261, A1, IF(ROW(A1)=262, A1, IF(ROW(A1)=263, A1, IF(ROW(A1)=264, A1, IF(ROW(A1)=265, A1, IF(ROW(A1)=266, A1, IF(ROW(A1)=267, A1, IF(ROW(A1)=268, A1, IF(ROW(A1)=269, A1, IF(ROW(A1)=270, A1, IF(ROW(A1)=271, A1, IF(ROW(A1)=272, A1, IF(ROW(A1)=273, A1, IF(ROW(A1)=274, A1, IF(ROW(A1)=275, A1, IF(ROW(A1)=276, A1, IF(ROW(A1)=277, A1, IF(ROW(A1)=278, A1, IF(ROW(A1)=279, A1, IF(ROW(A1)=280, A1, IF(ROW(A1)=281, A1, IF(ROW(A1)=282, A1, IF(ROW(A1)=283, A1, IF(ROW(A1)=284, A1, IF(ROW(A1)=285, A1, IF(ROW(A1)=286, A1, IF(ROW(A1)=287, A1, IF(ROW(A1)=288, A1, IF(ROW(A1)=289, A1, IF(ROW(A1)=290, A1, IF(ROW(A1)=291, A1, IF(ROW(A1)=292, A1, IF(ROW(A1)=293, A1, IF(ROW(A1)=294, A1, IF(ROW(A1)=295, A1, IF(ROW(A1)=296, A1, IF(ROW(A1)=297, A1, IF(ROW(A1)=298, A1, IF(ROW(A1)=299, A1, IF(ROW(A1)=300, A1, IF(ROW(A1)=301, A1, IF(ROW(A1)=302, A1, IF(ROW(A1)=303, A1, IF(ROW(A1)=304, A1, IF(ROW(A1)=305, A1, IF(ROW(A1)=306, A1, IF(ROW(A1)=307, A1, IF(ROW(A1)=308, A1, IF(ROW(A1)=309, A1, IF(ROW(A1)=310, A1, IF(ROW(A1)=311, A1, IF(ROW(A1)=312, A1, IF(ROW(A1)=313, A1, IF(ROW(A1)=314, A1, IF(ROW(A1)=315, A1, IF(ROW(A1)=316, A1, IF(ROW(A1)=317, A1, IF(ROW(A1)=318, A1, IF(ROW(A1)=319, A1, IF(ROW(A1)=320, A1, IF(ROW(A1)=321, A1, IF(ROW(A1)=322, A1, IF(ROW(A1)=323, A1, IF(ROW(A1)=324, A1, IF(ROW(A1)=325, A1, IF(ROW(A1)=326, A1, IF(ROW(A1)=327, A1, IF(ROW(A1)=328, A1, IF(ROW(A1)=329, A1, IF(ROW(A1