CODEWITHSUNDEEP
fftfftw
Minh Nguyen
Minh Nguyen

Reputation: 31

Why does fftw3 inverse fourier transform's produces output vector of type double?

I want to take inverse fourier transform of a signal. I use this

fftw_plan_dft_c2r_1d

however, the output vector is required to be double. The question is isn't that the IFFT of a signal gives complex number result?

Upvotes: 1

Views: 399

Answers (1)

SleuthEye
SleuthEye

Reputation: 14579

The definition of the Discrete Fourier Transform (DFT) allows for the time-domain input to be a complex valued signal and produces a frequency-domain result which is in general also complex valued. Correspondingly the inverse transform of that complex-valued frequency-domain result would produce the same (or at least within the available implementation's numerical precision) original time-domain signal. The result of the inverse transform could thus be complex.

Just the same, if we restrict time-domain inputs of the forward transform to real-valued signals then we would similarly expect the inverse transform of the corresponding frequency-domain spectrum to give us back the same original real-valued signal.

Note that the forward transform of those real-valued signal produces a frequency domain result that exhibits Hermitian symmetry (and conversely, if a frequency domain signal has Hermitian symmetry it must be the transform of a real valued signal). fftw_plan_dft_c2r_1d then computes the inverse transform (which is real-valued and stored in double) under the assumption that the frequency domain spectrum indeed has Hermitian symmetry.

Upvotes: 2

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