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In trying to mimic an amplifier, one fact must be forefront in our brains: distortion is almost always nonlinear! Therefore, instead of looking directly to convolution and linear transforms, we have to think a little bitfirst. The first place we can look at is the Taylor series.
In calculus, we learned about the Taylor Expansion and the Taylor Series , also known as the McLaurin Series . In essence, the expansion follows .
Another idea used in analyzing distortion is the DFT. Before and after using the Taylor Series to "play around" with thesignal, the DFT can be used to analyze the new (or old) sound, seeing which harmonics are the most important. MATLAB has awonderful FFT function that allows for simple and fast DFT calculation.
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