Convert the computed amplitude of a complex bin back to its complex form

Question

I am working a dsp algorithm where I take the FFT of a time domain signal, compute the amplitudes of each bin using sqrt(real * real + imaginary * imaginary) and then modify the amplitude. How do I convert the modified amplitude back into the complex domain so that i can run the IFFT and recover the processed time domain signal?

Answer 1

You would most likely want to retain the phase and use this to reconstruct the new bin value. What you're effectively doing is modifying a complex number in polar form, i.e. changing the magnitude but retaining the phase:

mag = sqrt(re^2 + im^2)  ; convert re, im to polar (mag, phi)
phi = atan2(im, re)

mag = mag * scale        ; apply factor `scale` to magnitude

re = mag * cos(phi)      ; convert new mag, phi back to re, im
im = mag * sin(phi)