Compare ifft in Matlab with Julia for complex input

Specific Domains Signal and Image Processing
4

Thanks for the challenge of making a MWE. It turns out that some of my thinking was wrong. This is what I should have been doing:

  • Transform to frequency domain
  • Set negative frequency components to zero
  • Multiply positive frequency components by 2 (do not change zero frequency component and take care with the Nyquist frequency component)
  • Transform back to time domain
  • Take real part of the analytic signal

Ergo, you have the original signal.

As an example

using FFTW

# Create signal
dt = 0.2
t = 0:dt:1
y = sin.(2*pi*t)
df = 1/t[end]
yf = fft(y)

# Make signal one sided like rfft
n = length(t)
np = div(n, 2) + 1
yf[np+1:end] = zeros(ComplexF64, n-np)

# Put energy lost from zeroing -ve frequency back in 
if iseven(n)
    yf[2:np-1] = 2*yf[2:np-1]
else
    yf[2:np] = 2*yf[2:np]
end

# Inverse FFT
ynew = ifft(yf)
[y ynew]   # compare y with real part of ynew

MATLAB does the same thing

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