Help for Homework 2 (due Feb 3)

I've used Nyquist to convert from 16-bit to 8-bit audio by adding white noise (white noise has a uniform random distribution) at the proper amplitude of 1/2 quantization step, and it works, but the noise always sounds rather harsh.

I once compared audio recorded in a room with a noisy ventilation system to audio recorded in a quiet room. I was hoping to show that we should record in the quiet room, but to my surprise the noisy room sounded better.

It seems that the noise in the room provided just the right amount of dither, but this dither sounds better than white noise! I haven't analysed the room noise, but in general it is not as "bright" as white noise, indicating that it does not have as much energy at high frequencies.

So here's the hypothesis: dither with reduced high frequencies will sound better because it is less harsh than white noise dither.

The only way we have discussed to reduce the high frequency content of a signal is by sampling at a lower sample rate. I did not get to all the examples, but the RESAM function in the examples file shows how to downsample a signal (Nyquist will remove all energy above the Nyquist rate) and upsample it back to the default sampling rate.

Using RESAM you should be able to remove some high frequencies from white noise and use it to dither a signal of your choice. (Search the web for .aiff if you need some audio.)

Listen to every step of the process: the original, the white noise, the resampled white noise, the noise added to the original, and finally a quantized version.

I don't know if this will work, but it's a good exercise to boost your intuitions about sampling theory and dither.