Guitar and Audio technology blog

Wednesday, 3 November 2010

Max/MSP chebyshev polynomials

As an initial experiment using Chebyshev polynomials a basic max/msp patch has been created using the first 4 polynomials to create the first 4 harmonics of a sine wave.  An output wave has been recorded and analysed showing the effects of the polynomials on the signal.  The patch needs to be adapted to allow for individual amplitude control of each harmonic.
Max/MSP patch

Using Audacity to analyse the audio the frequency peaks can clearly be seen at integer multiples of the fundamental as expected.  Also noted the 'hollow' sound when only odd harmonics added.  Further polynomials are to be added to create a larger effect.

Frequency plot of max output

This was designed as an initial experiment and shall be further adapted to allow for better amplitude control.  The waveform was also analysed to show the effects of the harmonics on the input signal, as expected the wave changed and grew more square like with each additional odd harmonic added.  The next stage is to analyse the harmonic output of the amplifier at various different settings and frequencies.  A suspect limitation may be the frequency range that can be modelled accurately due to time constraints.  Meaning a certain range of input frequencies will be defined in the modeller, at least for the current time anyway.

Anthony Evans

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