Because Chebyshev filters with an order n above 10 or 12 would be unusual, this table look-up approach can be considered, practically speaking, complete. Here, we will side step the entire computational issue, as legions of engineers have done before us, and simply look up the Chebyshev polynomials, by order, in a switch statement. For an excellent review and comparison of computational techniques for computing Chebyshev polynomials see this paper by Wolfram Koepf. Finding Chebyshev polynomials for a given order represent a computational challenge, and when computed often exhibit various numerical instabilities (often overflow) if not done properly. Simply put, the more ripple allowed in the passband, the steep roll-off the filter achieves.Ĭhebyshev filters derive their name from Chebyshev polynomials. Type 1 Chebyshev filters trade-off steeper roll-off with ripple in the pass band and in the limit of zero ripple, mimic Butterworth filters. We will only discuss the type 1 filters here, as the type 2 filters are rarely used. The Butterworth filter was discussed in a previous blog article.Ĭhebyshev filters come in two flavors defined by either allowing ripple in the pass-band (type 1) or ripple the stop-band (type 2). In this postI will give a short introduction to Chebyshev filters, present a code implementation, and end with a usage example. There are three classes of widely used IIR (recursive) filters in signal processing: Butterworth, Chebyshev, and elliptical.
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