problems calculating frequency response out of sine sweeps

Question

I'm currently trying to calculate the frequency response of the iphone's speaker/microphone roundtrip. I play a sine sweep on the speaker, record it via the microphone and try to get the frequency response out of that. final goal is to be able to multiply the FR to any given sound to make it sound like the iphones speaker/mic.

My Code so far:

//apply window function
vDSP_vmul(sineSweepMic,1,hammingWindow,1,sineSweepMic,1,n);
vDSP_vmul(sineSweepFile,1,hammingWindow,1,sineSweepFile,1,n);

//put both signals in complex arrays
vDSP_ctoz((DSPComplex *)sineSweepMic, 2, &fftSineSweepMic, 1, nOver2);
vDSP_ctoz((DSPComplex *)sineSweepFile, 2, &fftSineSweepFile, 1, nOver2);

//fft of both file and mic sweeps
vDSP_fft_zrip(fftSetup, &fftSineSweepFile, 1, log2n, FFT_FORWARD);
vDSP_fft_zrip(fftSetup, &fftSineSweepMic, 1, log2n, FFT_FORWARD);

//back to interleaved
vDSP_ztoc(&fftSineSweepFile, 1, (COMPLEX *)sineSweepFile, 2, nOver2);
vDSP_ztoc(&fftSineSweepMic, 1, (COMPLEX *)sineSweepMic, 2, nOver2);

//divide mic-sweep by file-sweep to create frequency response
vDSP_vdiv(sineSweepFile, 1, sineSweepMic, 1, frequencyResponse, 1, n);

this works so far and when i multiply the FR with the initial file-sweep it sounds like the mic-sweep.

My Problem: this only works for the exact file (sweep) the FR is generated from. As soon as i use the FR to modify other sounds, music for example only noise comes out.

i use the FR like this (both in frequency domain, interleaved, not complex, even same length):

    vDSP_vmul(soundToModify, 1, frequencyResponse, 1, soundToModify, 1, n);

My sine-sweep from file played on speaker:

My recorded sine-sweep (attenuated low frequencies visible):

My file sine-sweep multiplied in frequency domain with the FR generated as above in code:

My Goal: in my understanding the frequency response is the information about each frequency, how much it is attenuated or amplified by the system (in my example it is not able to reproduce low frequencies). To get this kind of information i generate a sound containing every desired frequency (sine-sweep) play it and analyze how every frequency is modified by dividing recorded-sweep/file-sweep (division in code).

By multiplying this FR in frequency domain to any sound should modify the frequency amplitudes to mimic a playback on my system, right?

thanks!

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UPDATE: in the end the fault was the missing complex arithmetic and both, the sine-sweep as well as the pink noise worked pretty well as a impulse to recover th impulse response.

to get working code just complex-divide the recorded sweep fft data by the initial sweep fft data.

Answer 1

If you want to recreate the sound of the iPhone speaker/mic, ideally you need to find the impulse response of the system.

What you are doing wrong: finding the FFT of a sine sweep is meaningless since the input frequency is something that changes (linearly or exponentially or other) to begin with, before the system imposes its own frequency response on top of that. As Paul R suggested above, finding FFTs of white noise makes more sense since averaging over many statistically-flat input frequencies will give you the actual frequency response of the system.

However, if your goal is to recreate the sound of the system, you also need to take care of phase, which is not being done in either of the above methods. The 'ideal' way to do it would be to capture the response of the iPhone speaker/mic system to an 'impulse' in a perfectly quiet and dry (no reflections) environment. There are 3 ways to do so: 1. Use a balloon pop sound, or a synthetically created impulse sound to do so. 2. Use Golay Codes, which is a simpler way of averaging many impulse response measurements 3. Use sine sweeps but then use correlation to find the impulse response.

Reference: https://ccrma.stanford.edu/realsimple/imp_meas/imp_meas.pdf

Once you obtain the impulse response measurement, either convolve this with the signal you are trying to 'color', or take the FFT of both signals, multiply in the frequency domain, and then take inverse FFT to get the colored signal.

Explanation: I'll try and explain it to the best of my knowledge: - When you take the FR of an impulse response, you take the magnitude of its FFT, throwing away the phase data. Therefore, there are many filters(systems) with the same magnitude FR that will give you radically different outputs. Case in point will be Allpass Filters - they all have a flat FR but if you put an impulse through them, you can get back a sine sweep, depending on the filter parameters. Clearly, this should point to the fact that though you can always go FROM an IR to a FR, going back in the opposite direction means you are making an arbitrary choice. Hence, you cannot throw away the phase, even for rough estimates. The fact that we cannot hear phase means that we can look at the FR for information about the system but does not allow us to disregard phase in modeling the system. I hope that makes sense? To use a sine sweep, do the following - if s(t) = sin(A(t)) and A(t) = integral[0 to t] (w(t)dt), correlate the signal e(t) = corr(v(t),sin(A(t)) where v(t) = 2 * abs(dw/dt) will produce an impulse. Therefore, if you replace the sine sweep in that correlation with the measured signal, you should obtain its impulse response. Hope that helps! Sorry for it being so math-y.