文档介绍：Signal Processing Toolbox
Discrete Fourier Transform
The discrete Fourier transform, or DFT, is the primary tool of digital signal processing.
The foundation of the Signal Processing Toolbox is the fast Fourier transform (FFT), a
method puting the DFT with reduced execution time. Many of the toolbox
functions (including z-domain frequency response, spectrum and cepstrum analysis,
and some filter design and implementation functions) incorporate the FFT.
MATLAB provides the functions fft and ifft pute the discrete Fourier
transform and its inverse, respectively. For the input sequence x and its transformed
version X (the discrete-time Fourier transform at equally spaced frequencies around the
unit circle), the two functions implement the relationships
In these equations, the series subscripts begin with 1 instead of 0 because of the
MATLAB vector indexing scheme, and
Note MATLAB uses a negative j for the fft function. This is an engineering
j.
fft, with a single input argument x, computes the DFT of the input vector or matrix. If x
is a vector, fft x is a rectangular array, fft
computes the DFT of each array column.
For example, create a time vector and signal:
x = sin(2*pi*15*t) + sin(2 *pi*40*
The DFT of the signal, and the magnitude and phase of the transformed sequence, are
then
To plot the magnitude and phase, type the mands:
f = (0:leng