Chapter Four: Synthesis
2. Waveforms  page 2
A different way to look at waveforms is to view a graph of their spectra (pl. of spectrum). Below are graphs of the partials and their relative strength for the same waveforms on the previous page. Illustrations like these are known as spectrographs.
Waveform 
Spectrograph 
sine 

triangle 

sawtooth 

narrow pulse (missing every 5th partial) 
If you summed sine waves at the exact relative frequencies and amplitudes shown above for the nonsine forms, you would recreate these waveforms listed through additive synthesis (see Chapter One). This is sometimes called Fourier synthesis, after Jean Baptiste Fourier (17681830), who postulated that complex waveforms could be broken down to their constituent sine waves. To analyze more complex waveforms, FFT's or Fast Fourier Transforms are used. While the math involved in such analyses may be daunting to some, many current audio programs provide instant graphic analysis.
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