A few sound samples and accompanying explanations...

Sampling rate and sample depth

Sampling rate must be at least twice the highest frequency in the signal spectrum (it can be proved, but you are not electrical engineers, and I don't remember the proof any more; but if you really need it, just let me know and I will try to find it :-) Since the audible sounds go up to 20kHz, sampling rate must be at least 40kHz. In fact, CD quality sound uses 44.1kHz sampling rate with 16 bit sample depth for each channel.

Madonna sounds quite good at 44kHz and 16 bits: listen to the WAV file (warning: it's 4.4MB), and take a look at a snapshot of spectral density, as well as a short time diagram.

If you downsample it to 22kHz, while retaining 16 bits per sample, it comes through like this WAV file (about 2.1MB), and you can take a look at a snapshot of spectral density - notice how it goes down just above 10000Hz (sampling frequency is 22kHz, so everything beyond 11kHz or so does NOT exist). However, the subjective quality of the sound is quite OK ... at least that's what my ears tell me, but you're allowed to disagree.

You can also downsample it to 22kHz and 8 bits per sample, here's the WAV file (about 1MB). Things are beginning to get worse ...

When you sample at 8kHz with 8 bits (which corresponds to telephone quality), it sounds like this WAV file (which is only about 370KB in size). Notice both distortion (you cannot hear any 's') and noise. Now, if you look at the spectral density snapshot, you may notice random spikes of approximately equal magnitude all over the audible range, which is characteristic of white noise. It is actually caused by quantization error - we used only 8 bits.

Sounds of similar quality may be obtained by filtering a 'good' signal to, say, 11kHz (spectrum), or even 4kHz (spectrum). In both cases, there is no noise (or very little, compared to the file above) - but we still lose the high frequencies.

MIDI files

As we said in class (and it says so in the lecture notes), MIDI files contain musical score, i.e., musical notes, instruments that play them, and instructions how to play them. The quality of MIDI output depends primarily on the stored wavetable - a database of sounds for each instrument (about 120 of them in MIDI). Here are some samples to help you find out about the difference.

The original of "Thus spoke Zaratustra" from 2001: a Space Odyssey is a MIDI file which takes only about 16 KB; if you want to hear the difference, download the file to your disk, then play it in all audio players you can get (Windows Media Player, QuickTime, or any other you might have). For your convenience, however, I've provided digital audio output from two players, as shown below.

• When played through Windows Media Player (I forgot the version), sounds like this WAV file sampled at 22kHz with 16 bits per sample; its size is 6.1MB, and here is a spectrum snapshot.
• When played through QuickTime (most likely, v. 4), sounds like this WAV file sampled at 22kHz with 16 bits per sample; its size is 6.1MB, and here is a spectrum snapshot - notice the different spectral density.

Finally, there is a 30KB MIDI file of Madonna's "Like A Virgin" ... without any voice, of course.

MP3 perceptual coding scheme

Perceptual coding can achieve good compression while retaining good subjective quality: check the MP3 files at 128kbits/s (CD quality sound at one-tenth size) and even 32kbits/s. (You'll need some MP3-capable player for this).

Similar quality may be obtained with RealAudio compression at 32kbits/s and 96kbits/s. (You'll need RealPlayer for this.)