A comparison of cascade and wave fixed-point digital-filter structures

Three classes of digital-filter structures, namely two classes of cascade structures and one class of wave structures, are compared with regards to the number of arithmetic operations, the inherent speed capability, the output noise due to product quantization, and the sensitivity to multiplier-coefficient quantization. Four types of filters are considered, namely a Butterworth low-pass filter, a Chebyshev high-pass filter, an elliptic bandstop filter, and an elliptic band-pass filter. The arithmetic is assumed to be of the fixed-point type, numbers are assumed to be in two´s complement representation, and number quantization is assumed to be by rounding.