Bandlimited ramp waveform example aiff files

These sound files demonstrate bandlimited synthesis of a ramp wave from its fourier series. Limiting the synthesis to a particular number of harmonics affects the quality of the output. The question is how many are necessary for a satisfactory output?

The table below has example sound files of bandlimited ramps with increasing numbers of harmonics. There are tones over three octaves, starting from roughly 85Hz. Note that for the very large numbers of harmonics, there may be aliasing distortion present, since the harmonics will go above the Nyquist frequency for the 44.1KHz sample rate used for the examples.

Number of Harmonics	Bass sound	+1 Octave	+2 Octave
20
40
60
80
100
150
200
300
400

For my ears, I think the improvement between 100 and 150 harmonics for the bass sound is neglible. The extra harmonics add little or nothing. For the sound an octave higher, I think this point comes sooner, perhaps between 60 and 80 harmonics, but certainly before 100. When you go another octave higher, again the number of harmonics required seems to fall by the same factor. Consequently, I suspect a bandlimited additive synthesis system that deals with 128 harmonics would be sufficient for all but the highest quality applications.

Why does this matter?

If you're trying to design a digital sound synthesis system without aliasing, one way to do it is to use bandlimited waveforms. This reduces high frequency content that we can't hear, but that would cause aliasing distortion. If this approach is taken, there is then a question of how much high frequency content is actually required. I constructed these example files as a way to try and find a practical answer to this question.

If you're interested in the original AIFF files, or can't play them from the table above, you can download them here:

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Bandlimited ramp waveform example aiff files

Why does this matter?

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