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Worayot Lertniphonphun<br />

Georgia Institute of Technology<br />

James H. McClellan<br />

Georgia Institute of Technology<br />

26.1 Introduction<br />

© 2001 by CRC Press LLC<br />

26<br />

Digital Filter Design<br />

26.1 Introduction<br />

26.2 Digital Filters<br />

Implementation • Frequency Response • FFT<br />

Implementation • Adaptive and Time-Varying Filters<br />

26.3 Digital Filter Design Problem<br />

Design Specification • Error Measurement • Filter<br />

Characteristics • Filter Design as a Norm Problem<br />

26.4 Conventional Design Methods<br />

IIR Filters from Analog Filters • Windowing • Weighted<br />

Least-Squares • Remez Exchange • Linear Programming<br />

26.5 Recent Design Methods<br />

Complex Remez Algorithm • Constrained Least-<br />

Squares • Generalized Remez Algorithm • Combined<br />

Norm • Generalized Remez Algorithm<br />

26.6 Summary<br />

General Comment • Computer Tools<br />

For computer and information technology (IT) applications, signal processing is an important tool.<br />

Nowadays, it is much more efficient and accurate to work with sampled (or digitized) signals rather than<br />

with analog (or electrical) signals. Once a signal has been sampled, it can be treated as a sequence of<br />

numbers that is a function of a discrete-time variable. When the sampling rate is greater than the Nyquist<br />

rate, the digital signal will completely represent the analog signal, because the analog signal can be<br />

reconstructed from the digital signal. Digital signal processing (DSP) implements various kinds of<br />

mathematical operations, so that physical electrical devices are replaced by computer software or hardware.<br />

Unlike analog systems, DSP can handle very sophisticated jobs with as much accuracy as needed.<br />

The theory of DSP can be found in three excellent references [1–3].<br />

One very basic DSP operation is digital filtering. It is common to use many filters inside a larger DSP<br />

application. Digital filters have widely been used in the following applications:<br />

• Audio: spectral shaping<br />

• Speech: filter banks<br />

• Image: de-blurring, edge-enhancement/detection<br />

• Communications: bandpass filters<br />

• Radar: matched filters

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