How to "zero-phase-adjust" DFT output?

Question

I understand the complex output of a DFT contains both "amplitude" and "phase" information at discrete frequencies.

Amplitude[n] = sqrt((r[n]*r[n]) + (i[n]*i[n]))
Phase[n] = (atan2(i[n],r[n]))
Frequency[n] = n * (sample_rate / (fft_input_length / 2))

It seems that I should be able to use the frequency, amplitude, and phase information to calculate the amplitude of each output bin as if the input at the corresponding frequency had a zero-phase alignment in the FFT input. But I am drawing a blank.

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Hmm, digging deeper into my problem I discovered that the imaginary potion of the FFT output is always 0.0 regardless of the input. So I am guessing my code is flawed or the algorithm is not what I need.

Answer 1

If you want to rotate all DFT result bins to a phase of zero with reference to the start (sample 0): set r[n] = amplitude[n], i[n] = 0; make sure r[n] is symmetric over the full DFT length if you want strictly real data; and compute the IDFT if needed.