Digital IIR Filter Design Methods and Filter Selection Trade-Offs in Hardware Implementation

Digital IIR filters are widely used for signal denoising in signal processing systems. IIR filter implementation requires a lower order with the same design specifications when compared with FIR filters. Among typical IIR categories, Butterworth and Chebyshev filters are two commonly used filters. This paper introduces the fundamental theory of digital IIR filters, reviews two major indirect design approaches including, bilinear transformation and impulse invariance, and explains the different properties of Butterworth, Chebyshev type I and Chebyshev type II filters. Further qualitative comparison of different types of filters is conducted in hardware implementation scenarios. The analysis concludes that Butterworth filters have no ripple in the passband response and superior signal integrity at the cost of higher hardware complexity, whereas Chebyshev filters achieve sharper transition bands with reduced order at the expense of ripples. This work clarifies practical selection principles in scenarios with limited resources and points out that unified quantitative selection metrics for IIR filter hardware deployment remain insufficient for low-cost scenarios.