# [pd-ot] electric circuits in software

Miguel Ramos pd at anjos.strangled.net
Thu Apr 27 15:27:29 CEST 2006

```Qui, 2006-04-27 às 11:39 +0800, Chris McCormick escreveu:
> Heheh. One thing I've always wondered about (and I could be about to
> highlight my total lack of signal progressing understanding) is the
> representation of two waveforms at Nyquist; if you have a squarewave
> and a sawtooth wave, both sampled at 44100 and playing at a frequency
> of 22050, these waves will both be represented by two samples each,
> correct? So when they are sent back into the analogue domain, won't these
> two waveforms look identical? Wouldn't they look like exactly the same
> sound? On analogue gear, wouldn't it be the case that the exact shape
> of the waveforms would be more accurately represented (e.g. a sawtooth
> and a squarewave at 22050 would look like such)?
>
> Best,
>
> Chris.

Your right that both waves will be identical. When converted to analog,
both will be converted more or less to a sine wave at 22050, since the
DAC has a lowpass filter set to this frequency to avoid aliasing to
higher frequencies.

With analog hardware, when passing through a system that will have less
response to higher frequencies, the same will happen, both will be more
or less sinewaves. Actually, if you put a lowpass filter at 22k, the
result will be the same.

Basically, the squarewave and sawtooth you mentioned, with a fundamental
of 22050, will only differ in their partials, and these will have a
frequency which is >= 44100.

So, there's no way to turn it around... You can faithfully represent
digitally anything with frequency <= 22050.

Never forget that if you put an analog square wave on one end of a long
cable, on the other end what you will receive won't be a square wave,
but a rounded version of it.
Moreover, a squarewave is a digital concept mainly. There's really no
way to do it in analog.

--
Miguel Ramos

```