# fft¶

## Purpose¶

Computes a 1- or 2-D Fast Fourier transform.

## Format¶

y = fft(x)
Parameters

x (NxK matrix) – The values used to compute the Fast Fourier transform.

Returns

y (LxM matrix) – where L and M are the smallest powers of 2 greater than or equal to N and K, respectively.

## Examples¶

This is example uses the FFT to find the frequency component of a signal buried in a noise. The first section sets up the parameters for the signal of sampling frequency 1 kHz and a signal duration of 1.5 secs

// Sampling frequency
Fs = 1000;

// Sampling period
big_T = 1/Fs;

// Length of signal
L = 1500;

// Time vector
t = seqa(0, big_T, L);


Now form the signal given by

$0.7*sin(2\pi50t) + sin(2\pi120t)$
// Compute signal
s = 0.7*sin(2*pi*50*t) + sin(2*pi*120*t);


Corrupt the signal with zero-mean white noise:

// Add white noise
x = s + 2*rndn(L,1);


Finally, compute the Fourier transform:

// Compute Fourier transform
y = fft(x);


## Remarks¶

This computes the FFT of x, scaled by $$1/N$$.

This uses a Temperton Fast Fourier algorithm.

If N or K is not a power of 2, x will be padded out with zeros before computing the transform.