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Fourier transforms

<fft> - Discrete Fourier transform.

FFT Discrete Fourier transform.

FFT(X) is the discrete Fourier transform (DFT) of vector X. For

matrices, the FFT operation is applied to each column. For N-D

arrays, the FFT operation operates on the first non-singleton

dimension.

FFT(X,N) is the N-point FFT, padded with zeros if X has less

than N points and truncated if it has more.

FFT(X,[],DIM) or FFT(X,N,DIM) applies the FFT operation across the

dimension DIM.

For length N input vector x, the DFT is a length N vector X,

with elements

N

X(k) = sum x(n)*exp(-j*2*pi*(k-1)*(n-1)/N), 1 <= k <= N.

n=1

The inverse DFT (computed by IFFT) is given by

N

x(n) = (1/N) sum X(k)*exp( j*2*pi*(k-1)*(n-1)/N), 1 <= n <= N.

k=1

See also fft2, fftn, fftshift, fftw, ifft, ifft2, ifftn.

Overloaded methods:

uint8/fft

uint16/fft

gf/fft

codistributed/fft

qfft/fft

iddata/fft

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<fft2> - Two-dimensional discrete Fourier transform.

FFT2 Two-dimensional discrete Fourier Transform.

FFT2(X) returns the two-dimensional Fourier transform of matrix X.

If X is a vector, the result will have the same orientation.

FFT2(X,MROWS,NCOLS) pads matrix X with zeros to size MROWS-by-NCOLS

before transforming.

Class support for input X:

float: double, single

See also fft, fftn, fftshift, fftw, ifft, ifft2, ifftn.

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<fftn> - N-dimensional discrete Fourier Transform.

FFTN N-dimensional discrete Fourier Transform.

FFTN(X) returns the N-dimensional discrete Fourier transform

of the N-D array X. If X is a vector, the output will have

the same orientation.

FFTN(X,SIZ) pads X so that its size vector is SIZ before

performing the transform. If any element of SIZ is smaller

than the corresponding dimension of X, then X will be cropped

in that dimension.

See also fft, fft2, fftshift, fftw, ifft, ifft2, ifftn.

Overloaded methods:

uint8/fftn

uint16/fftn

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<ifft> - Inverse discrete Fourier transform.

IFFT Inverse discrete Fourier transform.

IFFT(X) is the inverse discrete Fourier transform of X.

IFFT(X,N) is the N-point inverse transform.

IFFT(X,[],DIM) or IFFT(X,N,DIM) is the inverse discrete Fourier

transform of X across the dimension DIM.

IFFT(..., 'symmetric') causes IFFT to treat X as conjugate symmetric

along the active dimension. This option is useful when X is not exactly

conjugate symmetric merely because of round-off error. See the

reference page for the specific mathematical definition of this

symmetry.

IFFT(..., 'nonsymmetric') causes IFFT to make no assumptions about the

symmetry of X.

See also fft, fft2, fftn, fftshift, fftw, ifft2, ifftn.

Overloaded methods:

uint8/ifft

uint16/ifft

gf/ifft

qfft/ifft

iddata/ifft

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<ifft2> - Two-dimensional inverse discrete Fourier transform.

IFFT2 Two-dimensional inverse discrete Fourier transform.

IFFT2(F) returns the two-dimensional inverse Fourier transform of matrix

F. If F is a vector, the result will have the same orientation.

IFFT2(F,MROWS,NCOLS) pads matrix F with zeros to size MROWS-by-NCOLS

before transforming.

IFFT2(..., 'symmetric') causes IFFT2 to treat F as conjugate symmetric

in two dimensions so that the output is purely real. This option is

useful when F is not exactly conjugate symmetric merely because of

round-off error. See the reference page for the specific mathematical

definition of this symmetry.

IFFT2(..., 'nonsymmetric') causes IFFT2 to make no assumptions about the

symmetry of F.

Class support for input F:

float: double, single

See also fft, fft2, fftn, fftshift, fftw, ifft, ifftn.

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<ifftn> - N-dimensional inverse discrete Fourier Transform.

IFFTN N-dimensional inverse discrete Fourier transform.

IFFTN(F) returns the N-dimensional inverse discrete Fourier transform of

the N-D array F. If F is a vector, the result will have the same

orientation.

IFFTN(F,SIZ) pads F so that its size vector is SIZ before performing the

transform. If any element of SIZ is smaller than the corresponding

dimension of F, then F will be cropped in that dimension.

IFFTN(..., 'symmetric') causes IFFTN to treat F as multidimensionally

conjugate symmetric so that the output is purely real. This option is

useful when F is not exactly conjugate symmetric merely because of

round-off error. See the reference page for the specific mathematical

definition of this symmetry.

IFFTN(..., 'nonsymmetric') causes IFFTN to make no assumptions about the

symmetry of F.

See also fft, fft2, fftn, fftshift, fftw, ifft, ifft2.

Overloaded methods:

uint8/ifftn

uint16/ifftn

Reference page in Help browser

doc ifftn

<fftshift> - Shift zero-frequency component to center of spectrum.

FFTSHIFT Shift zero-frequency component to center of spectrum.

For vectors, FFTSHIFT(X) swaps the left and right halves of

X. For matrices, FFTSHIFT(X) swaps the first and third

quadrants and the second and fourth quadrants. For N-D

arrays, FFTSHIFT(X) swaps "half-spaces" of X along each

dimension.

FFTSHIFT(X,DIM) applies the FFTSHIFT operation along the

dimension DIM.

FFTSHIFT is useful for visualizing the Fourier transform with

the zero-frequency component in the middle of the spectrum.

Class support for input X:

float: double, single

See also ifftshift, fft, fft2, fftn, circshift.

Reference page in Help browser

doc fftshift

<ifftshift> - Inverse FFTSHIFT.

IFFTSHIFT Inverse FFT shift.

For vectors, IFFTSHIFT(X) swaps the left and right halves of

X. For matrices, IFFTSHIFT(X) swaps the first and third

quadrants and the second and fourth quadrants. For N-D

arrays, IFFTSHIFT(X) swaps "half-spaces" of X along each

dimension.

IFFTSHIFT(X,DIM) applies the IFFTSHIFT operation along the

dimension DIM.

IFFTSHIFT undoes the effects of FFTSHIFT.

Class support for input X:

float: double, single

See also fftshift, fft, fft2, fftn.

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doc ifftshift

<fftw> - Interface to FFTW library run-time algorithm tuning control.

FFTW Interface to FFTW library run-time algorithm tuning control.

The MATLAB functions FFT, IFFT, FFT2, IFFT2, FFTN, and IFFTN functions

use a library called FFTW. The FFTW library has the ability to

experimentally determine the quickest computational method to compute

the FFT of a particular size and dimensionality. The FFTW function

provides an interface to this run-time algorithm tuning.

FFTW('planner', METHOD) sets the FFTW library planner method used for

subsequent calls to FFT, IFFT, FFT2, IFFT2, FFTN, and IFFTN. METHOD can

be one of these strings: 'estimate', 'measure', 'patient', and

'exhaustive', or 'hybrid'. If the planner method is 'estimate', then

the FFTW library chooses algorithms based on a quick heuristic. The

resulting algorithms are sometimes suboptimal. If you specify

'measure', the FFTW library will experiment with many different

algorithms to compute an FFT of a given size. The library caches the

result in an internal "wisdom" database so that it can reused the

next time an FFT of the same size is computed. Methods 'patient' and

'exhaustive' are similar to 'measure' except that they take much

longer. If the planner method is 'hybrid', then MATLAB uses the

'measure' method for FFT dimensions of 8192 or smaller, and it uses

the 'estimate' method for larger dimensions. The default planner

method is 'estimate'.

METHOD = FFTW('planner') returns the current planner method.

STR = FFTW('dwisdom') returns the FFTW library's internal

double-precision wisdom database as a string. The string can be saved

and then later reused in a subsequent MATLAB session using the next

syntax.

STR = FFTW('swisdom') returns the FFTW library's internal

single-precision wisdom database as a string.

FFTW('dwisdom',STR) loads FFTW wisdom, represented as a string, into the

FFTW library's internal double-precision wisdom database.

FFTW('dwisdom','') or FFTW('dwisdom',[]) clears the internal wisdom

database.

FFTW('swisdom',STR) loads FFTW wisdom, represented as a string, into the

FFTW library's internal single-precision wisdom database.

FFTW('swisdom','') or FFTW('swisdom',[]) clears the internal wisdom

database.

For more information about the FFTW library, see http://www.fftw.org.

See also fft, fft2, fftn, ifft, ifft2, ifftn, fftshift.

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