By Artur Krukowski
This ebook provides the research of precise kind of IIR polyphase filter out constructions mixed with frequency transformation options, and their program for customized fixed-point implementation. that includes a wealth of layout and research thoughts, it comprises enough introductory fabric to allow non-experts to appreciate the subjects.
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Additional info for DSP System Design: Complexity Reduced IIR Filter Implementation for Practical Applications
The method is based on the cascaded structure of halfband filters transformed with frequency transformation, as shown below. 2 Cascading polyphase halfband LPF transformed by The idea of cascaded polyphase lowpass filters achieving spike-free stopband, having a baseband equal the integer-fraction of Nyquist frequency is based on the idea of converting a prototype lowpass filter into a multiband filter using a frequency transformation. It replaces each delayer of the original filter transfer function with where k is an integer equal to number of required filter replicas around the unit circle as in Figure 1-18.
1 Nyquist-rate converter versus oversampling ones The function of an A/D converter is to convert a continuous-time, analog input signal x(t) into a sequence of digital codes y(k). Generally, A/D converters can be divided into two groups according to the sampling rate: the so called Nyquist rate ones and the oversampled ones (oversampling and oversampling ones) . Block diagrams of the Nyquist converter and both types of the oversampled ones are given in Figure 1-30. The conventional Nyquist rate converters, called Nyquist Rate Pulse Code Modulation (PCM) one, sample the analog signal at its Nyquist frequency, or a little above.
The conclusion is that the more paths that are used, the less performance the filter can achieve for the same number of coefficients, both in terms of the achievable stopband attenuation for the given transition bands and considering also high spikes in the stopband magnitude response which for almost all applications have to be got rid of. 3 Compensating for peaks in the stopband The problem of decreasing the spikes in the stopband of multi-path polyphase lowpass filter magnitude response is not a trivial task.