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Multirate Signal Processing for Communications Systems

Course Description

A multirate filter has embedded within its structure a mechanism to implement one or more sample rate changes as part of its signal processing task. One might ask why one would want to change the sample rate. It was once suggested to me that ‘We change sample rate because we didn’t do it right the first time.’ Cute, but not true! We change sample rate to reduce the cost or improve the performance of a signal processing task. One obvious driver for changing sample rate is the Nyquist criterion that directs us to select a sample rate that exceeds the signal’s two sided bandwidth. Thus when we use a filter to reduce the bandwidth of a signal we should also reduce the output sample rate in proportion to the bandwidth reduction. A pleasant surprise is that we can embed the re-sampling operation within the filtering operation to obtain a realization that simultaneously exhibits minimum work load and minimum hardware requirements. Filters containing embedded sample rate changes are linear time varying filters.

These filters offer an amazing list of signal processing options not available to the standard filter structures. The list appears to contain elements of magic. It does!

The traditional structures that accomplish sample rate changes are the polyphase FIR filter, the dyadic half-band filter, and the cascade Integrator and comb filter. Other structures include the polyphase recursive all-pass filter, iterated filters, the Farrow filter, and variants of Taylor series filters. A new architecture, cascade analysis and synthesis filter banks, offers green, minimum energy implementation of filter functions. Filter structures are but the tip of the iceberg. What we need is an understanding how these structures can be modified and applied to various processing tasks. This course addresses both filter structures and filter applications. Material presented in the short course is listed in the following table.

Prerequisites

First course in DSP: Course in Modulation Techniques, FIR Filters, Sampling Theorem and Spectrum Analysis Techniques

Target Audience

Course Outline

Practical Design of Finite Impulse Response Filters

Spectral and time domain characteristics Transition bandwidth, side-lobe levels and spectral envelope
In-band ripple level and paired echoes Remez Algorithm revisited, square-Root Nyquist filter

The Resampling Process

The Nobel Identity I-F sampling Nyquist zone filtering Intentional aliasing and spectral translation

Multirate FIR Filters

Rational ratio and arbitrary ratio interpolators (up and down-resampling)

Polyphase Partitions

Base-band filtering Multi-channel filtering Cascade filters,
cascade Perfect reconstruction analysis-synthesis filter banks

Half Band Filters

Quadrature mirror filters Hilbert transform filters

Cascade Integrator-Comb Filters

Hogenauer filter structures

Recursive Multirate Filters

Polyphase all-pass structures Base-band filtering Multi-channelfiltering Cascade filters

Recursive Half Band Filters

Quadrature mirror filters, Hilbert transform filters

MODEM Applications

Shaping filters with up-sampling Matched filters with up-samplingfor timing recovery
Multi-channel modulation and demodulation, Narrow-band signal and noise generators
Re-sampling for ADC and DAC applications Multirate considerations in equalizer filters

Course Details

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