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 =