Frequency Domain Filtering

On r/puredata Acreil posted this video of generative music made with a pure data patch. It shows a scrolling stereo spectrogram of the music, with wavy lines that represent slices of filtered noise where the filter is always changing. Frequency domain filtering works by applying the Fourier transform to the input signal, resulting in a frequency spectrum which you cut or boost in places, then transform again back into the processed signal. Acreil did a post about this with another video that explains how it works and a link to download the pure data patch. He explains that “frequency domain filtering is nice because what would be a convolution in the time domain becomes a multiplication in the frequency domain.” This kind of processing can make the kind of shapes in a spectrogram that you don’t normally see, because it can make the kind of sounds that you don’t normally hear. The only other thing I know of that looks and sounds similar is the end of the track ‘∆Mᵢ⁻¹=−α ∑ Dᵢ[η][ ∑ Fjᵢ[η−1]+Fextᵢ [η⁻¹]]’ (also known as ‘equation’) from the Windowlicker EP by Aphex Twin. This is the track with the face encoded at the end. The bit that looks like frequency domain filtering is the patch of squiggly lines on the left.

Here’s a close-up on that bit. The face has a different texture – lower resolution, made of lines, whereas these squiggles are smoother, which suggests different techniques were used to make them. But both processes, frequency domain filtering and synthesis from images, involve the Fourier transform. So does the spectrogram. This video of a visual introduction to the Fourier transform by 3Blue1Brown helped me understand what it does.

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