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