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FFT - compute fast Fourier transform

iFFT - compute inverse fast Fourier transform

Calling Sequence

FFT(m, x, y)

evalhf(FFT(m, var(x), var(y)))

iFFT(m, x, y)

evalhf(iFFT(m, var(x), var(y)))

Parameters

m

-

non-negative integer

x, y

-

arrays of floats indexed from 1 to 2^m

Description

• 

Important: The FFT and iFFT functions have been deprecated.  For FFT, use the superseding functions DiscreteTransforms[FourierTransform] and SignalProcessing[FFT] instead.  For iFFT, use the superseding functions DiscreteTransforms[InverseFourierTransform] and SignalProcessing[InverseFFT] instead. These new functions can compute the fast Fourier transform for sequences of arbitrary length (not restricted to a power of 2).

• 

The FFT(m,x,y) and iFFT(m,x,y) commands compute in place the fast Fourier transform and the inverse fast Fourier transform of a complex sequence of length 2m.

• 

The first argument m should be a non-negative integer and the second and third arguments x and y should be arrays of floats indexed from 1 to 2m .  The array x contains the real part of the complex sequence on input and contains the real part of the fast Fourier transform on output.  The array y contains the imaginary part of the complex sequence on input and contains the imaginary part of the fast Fourier transform on output. Both procedures return 2^m, the number of points in the complex sequence.

• 

These procedures may be invoked with evalhf, which uses the hardware floating-point number system.

Examples

Important: The FFT and iFFT functions have been deprecated.  For FFT, use the superseding functions DiscreteTransforms[FourierTransform] and SignalProcessing[FFT] instead.  For iFFT, use the superseding functions DiscreteTransforms[InverseFourierTransform] and SignalProcessing[InverseFFT] instead.

x:=array7.,5.,6.,9.:

y:=array0,0,0,0:

FFT2,x,y

4

(1)

printx

27.1.1.1.

(2)

printy

04.0.4.

(3)

iFFT2,x,y

4

(4)

printx

7.0000000005.0000000006.0000000009.000000000

(5)

printy

0.0.0.0.

(6)

See Also

DiscreteTransforms, DiscreteTransforms[FourierTransform], int, inttrans[laplace], inttrans[mellin], Matlab[fft], SignalProcessing[FFT]

References

  

Oppenheim, Allan, V., and Schafer, Ronald W. Digital Signal Processing. New Jersey: Prentice-Hall, 1975.  See Fig. 6.5, p. 332.


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