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Im simulating a system in code, the real system uses a 3Mhz sample rate on PDM, trying to simulate the feedback response, in the feedback path there is a system, this system has a impulse response of ~512k coeficients, currently processing the feedback in a time domain basis, meaning, once a sample is received, then a full convolution is done. Trying to benchmark a frequency domain solution to see if it will be quicker, is it possible to do sample by sample?

My implementation in time domain has all H coefficients in memory and there is a buffer filled with the current sample, and all previous samples, the hard part is to calculate the position in which to overlap H with the signal and then H is flipped, and a dot product is done. ie. first input signal is received, this sample is multiplied by the last H coefficient (H(n)), second sample arrived, then first sample is multiplied by the H(n-1) coef, and second sample against H(n), then they are all added.

As you may imagine this process is very slow, when the input samples reach 512k samples, we have a full signal to H convolution, this takes around 3 seconds.

is it possible to have the operations done in frequency domain? probably will need to do FFT at every sample of the full buffer or at least H size right? FFT is pretty optimized so could I shave some milliseconds off?

user2982010
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The standard way of implementing an FIR filter in the frequency domain is the overlap-add (or overlap save). See for example: https://en.wikipedia.org/wiki/Overlap%E2%80%93add_method

In your case this would be indeed substantially faster than the direct time domain convolution. However, it does incurs significant latency. It's not "sample-by-sample" but "frame-by-frame" where the frame length is the length of the impulse response. You can only start processing a frame once you have accumulated a full frame.

In most feedback systems that type of latency is a show stopper, but that depends on your specific application. You can get a lower latency using hybrids of direct convolution and frequency overlap add. For example you could break down the 512 samples into 4 sections of 128: Implement the first one with direct convolution and the other 3 using a "block convolver" which are three sections of overlap-add that share the same FFT stage (for efficiency)

Hilmar
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  • yeah when I first starter approaching this issue I tried doing it time domain in a block fashion (faster overall), but the latency and sudden change on the feedback signal made the system unstable, so now I need to do it sample by sample, so it means that its not possible to do it sample by sample on a freq domain? – user2982010 Aug 29 '23 at 21:33
  • Yes, it's possible. You can cascade a time domain low-latency FIR filter with a higher latency (but more efficient) frame based frequency domain filter (OLA). The FIR does the early samples of the impulse response and the OLA does the rest – Hilmar Aug 30 '23 at 13:19