Analog modeling
Christopher Bennett · Focal Press eBooks · 2020
This chapter begins with an in-depth look at the relationship between the z -transform and the s -transform (a comparable transformation for analog signals), as this mapping forms the basis for converting from the analog to the digital domain. The first technique introduced is the impulse invariance transform, which preserves the IR of an analog filter or systems. However, this technique can suffer from aliasing. Next, the bilinear transform is introduced, which preserves the critical frequencies of the frequency response. Artifacts associated with this transformation are discussed, such as frequency warping, as well as techniques to mitigate this, using pre-warping. Programming examples are included for both of these transformations, bringing an RC analog filter to the digital domain. Next, the technique of frequency sampling is discussed, using both minimum phase or linear phase, resulting in an FIR structure. A programming example using frequency sampling is included for bringing an analog second-order filter into the digital domain. Finally, non-linear audio modeling is investigated by revisiting the Exponential Sine Sweep. This technique can be used to also collect non-linear IRs for characterizing and modeling non-linear aspects of audio systems, such as diodes, tubes, and transistors.