# [music-dsp] Applications of Walsh functions

Joshua Scholar joshscholar at yahoo.com
Fri Feb 25 16:10:21 EST 2005

```----- Original Message -----
From: "Vitaliy Lavruhin" <vsl9 at yandex.ru>
To: "music-dsp" <music-dsp at ceait.calarts.edu>
Sent: Friday, February 25, 2005 7:02 AM
Subject: Re: [music-dsp] Applications of Walsh functions
> Now, interesting part...
> Multiplication of two Walsh spectrums (in "frequency" domain) corresponds
to
> dyadic convolution in "time" domain. That is, where in usual (circular)
> convolution we have substraction, in dyadic convolution we have bitwise
XOR
> (bitwise (a+b) mod 2 <=> bitwise (a-b) mod 2). So filtering in Walsh sense
> implemented via dyadic convolution.
> Dyadic shift of samples in "time" domain corresponds to multiplication of
> original spectrum of signal and Walsh function with number corresponding
to
> amount of shift in "frequency" domain.
>

It's not clear to me from this what dyadic convolution is.

Circular convolution isn't "subtraction" it's the sum of products.
Ie Convolve(f,h)[k] = Sum(i = 0 -> N-1, f[i-k mod N]*h[i])

After reading your description I still have no idea what dyadic convolution
is.  Can you post a simple algorithm like the above?

```

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