book

Introduction to Digital Signal Processing

by Robert Meddins

September 2000

Intermediate to advanced

161 pages

4h 27m

English

Newnes

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1.1 CHAPTER PREVIEW1.2 ANALOGUE SIGNAL PROCESSING1.3 AN ALTERNATIVE APPROACH1.4 THE COMPLETE DSP SYSTEM1.5 RECAP1.6 DIGITAL DATA PROCESSING1.7 THE RUNNING AVERAGE FILTER1.8 REPRESENTATION OF PROCESSING SYSTEMS1.9 SELF-ASSESSMENT TEST1.10 FEEDBACK (OR RECURSIVE) FILTERS1.11 SELF-ASSESSMENT TEST1.12 CHAPTER SUMMARY1.13 PROBLEMS
2.1 CHAPTER PREVIEW2.2 SIGNAL TYPES2.3 THE REPRESENTATION OF DISCRETE SIGNALS2.4 SELF-ASSESSMENT TEST2.5 RECAP2.6 THE z-TRANSFORM2.7 z-TRANSFORM TABLES2.8 SELF-ASSESSMENT TEST2.9 THE TRANSFER FUNCTION FOR A DISCRETE SYSTEM2.10 SELF-ASSESSMENT TEST2.11 MATLAB AND SIGNALS AND SYSTEMS2.12 RECAP2.13 DIGITAL SIGNAL PROCESSORS AND THE z-DOMAIN2.14 FIR FILTERS AND THE z-DOMAIN2.15 IIR FILTERS AND THE z-DOMAIN2.16 SELF-ASSESSMENT TEST2.17 RECAP2.18 CHAPTER SUMMARY2.19 PROBLEMS

3.1 CHAPTER PREVIEW3.2 POLES, ZEROS AND THE s-PLANE3.3 POLE–ZERO DIAGRAMS FOR CONTINUOUS SIGNALS3.4 SELF-ASSESSMENT TEST3.5 RECAP3.6 FROM THE s-PLANE TO THE z-PLANE3.7 STABILITY AND THE z-PLANE3.8 DISCRETE SIGNALS AND THE z-PLANE3.9 ZEROS3.10 THE NYQUIST FREQUENCY3.11 SELF-ASSESSMENT TEST3.12 THE RELATIONSHIP BETWEEN THE LAPLACE AND z-TRANSFORM3.13 RECAP3.14 THE FREQUENCY RESPONSE OF CONTINUOUS SYSTEMS3.15 SELF-ASSESSMENT TEST3.16 THE FREQUENCY RESPONSE OF DISCRETE SYSTEMS3.17 UNSTABLE SYSTEMS3.18 SELF-ASSESSMENT TEST3.19 RECAP3.20 CHAPTER SUMMARY3.21 PROBLEMS
4.1 CHAPTER PREVIEW4.2 FILTER BASICS4.3 FIR AND IIR FILTERS4.4 THE DIRECT DESIGN OF IIR FILTERS4.5 SELF-ASSESSMENT TEST4.6 RECAP4.7 THE DESIGN OF IIR FILTERS VIA ANALOGUE FILTERS4.8 THE BILINEAR TRANSFORM4.9 SELF-ASSESSMENT TEST4.10 THE IMPULSE-INVARIANT METHOD4.11 SELF-ASSESSMENT TEST4.12 POLE–ZERO MAPPING4.13 SELF-ASSESSMENT TEST4.14 MATLAB AND s-TO-z TRANSFORMATIONS4.15 CLASSIC ANALOGUE FILTERS4.16 FREQUENCY TRANSFORMATION IN THE s-DOMAIN4.17 FREQUENCY TRANSFORMATION IN THE z-DOMAIN4.18 SELF-ASSESSMENT TEST4.19 RECAP4.20 PRACTICAL REALIZATION OF IIR FILTERS4.21 CHAPTER SUMMARY4.22 PROBLEMS
5.1 CHAPTER PREVIEW5.2 INTRODUCTION5.3 PHASE-LINEARITY AND FIR FILTERS5.4 RUNNING AVERAGE FILTERS5.5 THE FOURIER TRANSFORM AND THE INVERSE FOURIER TRANSFORM5.6 THE DESIGN OF FIR FILTERS USING THE FOURIER TRANSFORM OR ‘WINDOWING’ METHOD5.7 WINDOWING AND THE GIBBS PHENOMENON5.8 HIGHPASS, BANDPASS AND BANDSTOP FILTERS5.9 SELF-ASSESSMENT TEST5.10 RECAP5.11 THE DISCRETE FOURIER TRANSFORM AND ITS INVERSE5.12 THE DESIGN OF FIR FILTERS USING THE ‘FREQUENCY SAMPLING’ METHOD5.13 SELF-ASSESSMENT TEST5.14 RECAP5.15 THE FAST FOURIER TRANSFORM AND ITS INVERSE5.16 MATLAB AND THE FFT5.17 RECAP5.18 A FINAL WORD OF WARNING5.19 CHAPTER SUMMARY5.20 PROBLEMS

Content preview from Introduction to Digital Signal Processing

Appendix B

Frequency transformations in the s- and z-domains

s-DOMAIN TRANSFORMATIONS

To transform from a lowpass filter with cut-off frequency ω:

where Ω_c is the new cut-off frequency for the low and highpass filters, and Ω₁ and Ω_h are the lower and higher cut-off frequencies for the bandstop and bandpass filters.