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Let's Write a Reverb (2021)
No magic numbers, no tricky tuning: a clean and flexible approach to designing a smooth high-quality reverb, using a variation on the classic feedback-delay network (FDN) structure.
— Mark Twain and Albert Einstein, simultaneouslyThe energy of the signal is preserved, but it may occur in a different channel or time in the outputFor single-channel allpasses, this is equivalent to the standard "flat frequency-response", but this definition generalises nicely into multi-dimensional/multi-channel situations. Shuffling and polarity-flipping can technically be considered part of the Hadamard matrix, but I've listed it separately to make it clear that the shuffling/inversion should be different for each step.The delay takes an input (containing some number of echoes) and un-aligns the channels. I didn't like this, and when one day someone asked me to write "a reverb" (no specifics), I sketched out a design which included no IIR allpasses, and was robust enough that I could throw a random-number generator at all the delay times and it would still sound good.
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