S5-3.2 IIR Filter Design & Realization

Work through these

• Butterworth approximation

  The first of the two classic analog responses, borrowed into a digital course because the design route goes through it. Flat in the passband, and gentle in its transition.

• Chebyshev approximation

  The second, trading ripple for a sharper transition at the same order. Choosing between the two is the first real design decision in this topic.

• Impulse invariant transformation technique

  The first way of mapping an analog design into discrete time, and the one with a flaw. It can alias, which is exactly what the next item avoids.

• Bilinear transform technique and prewarping

  The preferred route, because it cannot alias. The price is frequency warping, and prewarping is the correction; knowing why the step exists is worth more than the formula for it.

• Digital Butterworth and Chebyshev filters

  The two classic responses now realised as digital filters, which is where the topic has been heading. Design one end to end at least once.

• Spectral transformation techniques

  Turning one design into another, so a single lowpass prototype serves highpass and bandpass needs. It saves an enormous amount of repeated work.

• Comparison between FIR and IIR filters

  The choice you actually make in practice, stated as a trade rather than a preference. Phase linearity against filter order is the axis, and the next topic is the other side of it.

• Realization of IIR filters: direct form I and direct form II

  Two structures computing the same response with different amounts of memory. In finite precision that structural choice changes how the filter really behaves, which is the subject of a later topic.

• Lab: design Butterworth and Chebyshev type 1 and 2 LPF, HPF, BPF and BSF in MATLAB

  The bench version of the design work, across all four filter shapes. Doing it in software first is what makes the hardware version in the next item tractable.

• Lab: implement second order IIR filters on the DSK

  The same designs running on a real processor. Second order sections are the standard building block, and this is where you find out why cascading them is preferred to one big filter.