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I was doing some research into dithering in audio, and I was always wondering what Audacity's "Shaped" dither was. Well, turns out it's noise shaping, with an FIR filter whose coefficients are:

2.033, -2.165, 1.959, -1.590, 0.6149

The frequency response can be found in Figure 6B of this paper.

But this filter is designed for 44.1 kHz.

How would I determine the coefficients that can replicate this frequency response, but at other sample rates, like 48 kHz?

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  • $\begingroup$ your link is unreachable for me – Not Found. $\endgroup$ Jun 4, 2022 at 17:44
  • $\begingroup$ @MarcusMüller S.P. Lipshitz, J. Vanderkooy and R.A. Wannamaker. Minimally audible noise shaping. J. Audio Eng. Soc. 39, 836-852. (1991) $\endgroup$
    – user41079
    Jun 4, 2022 at 17:56

1 Answer 1

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How would I determine the coefficients that can replicate this frequency response, but at other sample rates, like 48 kHz?

Resample the filter coefficients, just like you'd have to resample a signal. Literally the same methods apply – which also means that your FIR might be longer than just the resampling ratio times the original filter length, because you're (ideally) sinc-interpolating, and hence, getting a potentially infinite impulse response (which you can usually then window with acceptable loss)

Alternatively: find the pole/zero representation, or the continuous-frequency spectrum of your 44.1 kHz filter, and then find the 48 kHz filter that approximates that best.

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