I would like to generate brickwall low pass filtered white noise. a cutoff of 1/n is fine for integer n. I suspect that I could mess around with samples that are convolved with the sinc function, but I hope there is a better way? preferably would like to keep the HF noise less than the dither level or if not possible then maby 2x or 4x.


1 Answer 1


Can't be done as stated.

Brick-wall filters have an impulse response that's infinitely long in both time directions, i.e. it is also infinitely non-causal. That can't be implemented.

Other than that the question comes down to a standard low-pass filter design process. You need to specify your requirements in terms of cutoff frequency, passband ripple, transition band width, stop band attenuation, phase distortion, causality, transient preservation, time domain ringing, memory and CPU cost, etc. The "best" filter will be determined by doing the best trade-off between these requirements for your specific application.

This being said, since you want to create noise, you probably don't care much about time domain artifacts and phase distortions, so chances are an IIR filter may work well here, specifically when $n$ gets large and the cutoff very low.

  • $\begingroup$ I don't think the OP means a mathematical brick wall. He/she can Kaiser window a long sinc function and it will be pretty bricky. $\endgroup$ Commented Dec 26, 2023 at 13:39
  • $\begingroup$ Sure, but again that's a standard low pass filter design: Optimize for your specific requirements and constraints. People frequently use "brick-wall" to mean "perfect in all aspects", which you can't have. $\endgroup$
    – Hilmar
    Commented Dec 26, 2023 at 13:48
  • $\begingroup$ I use "brickwall LPF" whenever I mean a sinc impulse response. If it's a windowed sinc that's good n long, it's still a pretty solid brick wall. $\endgroup$ Commented Dec 26, 2023 at 16:55
  • $\begingroup$ I didn't ask for a perfect brickwall, I simply asked to keep HF noise down close to quantization levels so that we can best approximate a brickwall? $\endgroup$ Commented Dec 26, 2023 at 19:55
  • $\begingroup$ for example, with the IIR based approach, if you randomly selected a chunk of n samples where n is the ratio of the nyquist to cutoff frequency, you'd see a bias to not prefer the very top band? supposing that doesn't matter, how do I construct said IIR, so that the FFT of an impulse would have the bands above the cutoff to have a magnitude near enough to the quantization levels? $\endgroup$ Commented Dec 26, 2023 at 20:02

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