Graphics Programs Reference
In-Depth Information
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=[20102110]';
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 =
