Randomize phase shift in Fourier Transform

[astrogirl123]

I have some questions regarding shifting the phase of a Fourier transformed spectrum :

I have a spectrum with flux on the Y-axis and wavelength on the X-axis. What I want to do is take the Fourier transform of this spectrum. Then add a random phase between 0 and 2pi to the phase only. Then take the inverse Fourier Transform of this. The piece of code I wrote in IDL for a simple example is below. I was hoping to scramble up the spectrum by doing this. But I am not sure if I have achieved that goal. I have two questions

1. The final spectrum ( for some random phases) are vertically offset from the original spectrum. If the DC component is zero in the original spectrum, then this problem doesn't exist! Why is that so?

2. The amplitude of the final signal varies a lot from the original spectrum. I wasnt expecting that either. why is that?

3. All I want is that the components of the original spectrum be jumbled up in the X-direction (ie the wavelength direction). How can it be done?

MY CODE :

n = 256
x = FINDGEN(n)
y = COS(x*!PI/6)*EXP(-((x - n/2)/30)^2/2)+1.00

tek_color

yfft = fft(y)

magnitude = abs(yfft)
angle = ph(yfft)

for count=0, 300 do begin

rand = randomu(seed, 1)*2*!pi
randph = replicate(rand, 256)

fft_signal = magnitude*exp(complex(0,1)*(angle+randph))
ifft_signal = (fft(fft_signal, /inverse))

wait, 0.2

plot, x, y
oplot, x, (ifft_signal), color=2

endfor

end

 

[lippyka]

1. When you add a random phase to the Fourier transformed spectrum, you are changing the relative phases of different frequency components. This can cause the resulting signal to have a DC component that is different from the original signal, resulting in the vertical offset. To avoid this issue, you can normalize the magnitude of the Fourier transformed spectrum before adding the random phase and then renormalizing it afterwards. 2. The amplitude of the final signal can vary significantly compared to the original signal because the random phase shift can cause the various frequency components of the signal to interfere with each other in unpredictable ways. 3. To jumble up the components of the original spectrum in the X-direction, you can use a phase randomization approach similar to the one described above but instead of randomly shifting all the phases by the same amount, you can randomly shift the phases of each frequency component independently.