Page 65 - Basics of MATLAB and Beyond

fft One-dimensional fast Fourier transform
fft2 Two-dimensional fast Fourier transform
fftn N-dimensional fast Fourier transform
fftshift Move zeroth lag to centre of transform
ifft Inverse one-dimensional fast Fourier transform
ifft2 Inverse two-dimensional fast Fourier transform
ifftn inverse N-dimensional fast Fourier transform
abs Absolute value (complex magnitude)
angle Phase angle
cplxpair Sort complex numbers into complex conjugate pairs
nextpow2 Next power of two
unwrap Correct phase angles
The FFT of the column vector

y=[2010211 0]’;
is

>> Y = fft(y)
Y =
7.0000
-0.7071+ 0.7071i
2.0000- 1.0000i
0.7071+ 0.7071i
5.0000
0.7071- 0.7071i
2.0000+ 1.0000i
-0.7071- 0.7071i

The first value of Y is the sum of the elements of y, and is the amplitude
of the “zero-frequency”, or constant, component of the Fourier series.
Terms 2 to 4 are the (complex) amplitudes of the positive frequency
Fourier components. Term 5 is the amplitude of the component at the
Nyquist frequency, which is half the sampling frequency. The last three
terms are the negative frequency components, which, for real signals, are
complex conjugates of the positive frequency components.
The fftshift function rearranges a Fourier transform so that the
negative and positive frequencies lie either side of the zero frequency.
Companion M-Files Feature 4 The function fftfreq gives
you a two-sided frequency vector for use with fft and fftshift.
For example, the frequency vector corresponding to an 8-point
FFT assuming a Nyquist frequency of 0.5 is

>> fftfreq(.5,8)’
ans =

c 2000 by CRC Press LLC