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FFFFFFT!
tonestones Posted: 7 Apr 2024, 01:42 PM
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Joined: 11-February 24
I've been fascinated by the faster than a FFT post, and was inspired to look at alternatives to optimize for speed.
I stumbled upon the Hadamard transform, which uses square waves for decomposition of a signal, and therefore requires only additions and subtractions for the calculation of the transform.
Is this something that would be useful for the calculations needed for the reverse scope or do you see limitations?

ref: http://rotormind.com/blog/2019/hadamard-days-night/

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mit Posted: 9 Apr 2024, 11:58 AM
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yeah whatever

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Joined: 4-May 16
Well it's quite a few years since I wrote the ffft page, I've certainly learnt a lot more about DSP since then. The bleps-via-state-machine page was written a lot more recently although it covers slightly different ground.

One thing I've learned while working with microcontrollers is that the limitations are quite different to desktop machines, and especially compared to this imagined computer that exists in the minds of academics. A lot of algorithms are evaluated based on the number of multiply-accumulate operations, which traditionally were the heavy lifting. But modern processors have single-cycle multiply, even for floating point. The real performance cost is in branching, which can break the pipeline and cause the processor to stall. On the Flash synth using the STM32L4, there were five wait states for accessing flash memory, which means an if-condition could take five times longer than a multiply.

The Hadamard transform is super interesting though. In reference to the smallest midi synth someone made the suggestion of using the Haar transform to construct high fidelity audio out of the piezo square waves. Much like beamforming, you could probably get it to work for just one listening position.

In 2016 I wrote a new version of the reverse oscilloscope synthesizer, I really should release it at some point...

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