DSP for MATLAB and LabVIEW: Digital filter design

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Morgan & Claypool Publishers, 2009 - Technology & Engineering - 220 pages
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This book is Volume III of the series DSP for MATLAB™ and LabVIEW™. Volume III covers digital filter design, including the specific topics of FIR design via windowed-ideal-lowpass filter, FIR highpass, bandpass, and bandstop filter design from windowed-ideal lowpass filters, FIR design using the transition-band-optimized Frequency Sampling technique (implemented by Inverse-DFT or Cosine/Sine Summation Formulas), design of equiripple FIRs of all standard types including Hilbert Transformers and Differentiators via the Remez Exchange Algorithm, design of Butterworth, Chebyshev (Types I and II), and Elliptic analog prototype lowpass filters, conversion of analog lowpass prototype filters to highpass, bandpass, and bandstop filters, and conversion of analog filters to digital filters using the Impulse Invariance and Bilinear Transform techniques. Certain filter topologies specific to FIRs are also discussed, as are two simple FIR types, the Comb and Moving Average filters. The entire series consists of four volumes that collectively cover basic digital signal processing in a practical and accessible manner, but which nonetheless include all essential foundation mathematics. As the series title implies, the scripts (of which there are more than 200) described in the text and supplied in code form (available via the internet at www.morganclaypool.com/page/isen) will run on both MATLAB™ and LabVIEW™.The text for all volumes contains many examples, and many useful computational scripts, augmented by demonstration scripts and LabVIEW™ Virtual Instruments (VIs) that can be run to illustrate various signal processing concepts graphically on the user's computer screen. Volume I consists of four chapters that collectively set forth a brief overview of the field of digital signal processing, useful signals and concepts (including convolution, recursion, difference equations, LTI systems, etc), conversion from the continuous to discrete domain and back (i.e., analog-to-digital and digital-to-analog conversion), aliasing, the Nyquist rate, normalized frequency, sample rate conversion and Mu-law compression, and signal processing principles including correlation, the correlation sequence, the Real DFT, correlation by convolution, matched filtering, simple FIR filters, and simple IIR filters. Chapter four of Volume I, in particular, provides an intuitive or "first principle" understanding of how digital filtering and frequency transforms work. Volume II provides detailed coverage of discrete frequency transforms, including a brief overview of common frequency transforms, both discrete and continuous, followed by detailed treatments of the Discrete Time Fourier Transform (DTFT), the z-Transform (including definition and properties, the inverse z-transform, frequency response via z-transform, and alternate filter realization topologies including Direct Form, Direct Form Transposed, Cascade Form, Parallel Form, and Lattice Form), and the Discrete Fourier Transform (DFT) (including Discrete Fourier Series, the DFT-IDFT pair, DFT of common signals, bin width, sampling duration, and sample rate, the FFT, the Goertzel Algorithm, Linear, Periodic, and Circular convolution, DFT Leakage, and computation of the Inverse DFT). Volume IV, the culmination of the series, is an introductory treatment of LMS Adaptive Filtering and applications, and covers cost functions, performance surfaces, coefficient perturbation to estimate the gradient, the LMS algorithm, response of the LMS algorithm to narrow-band signals, and various topologies such as ANC (Active Noise Cancelling) or system modeling, Periodic Signal Removal/Prediction/Adaptive Line Enhancement (ALE), Interference Cancellation, Echo Cancellation (with single- and dual-H topologies), and Inverse Filtering/Deconvolution/Equalization.
 

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Contents

322 CONVERGENCE
125
323 RELATION TO FOURIER TRANSFORM
126
324 RELATION TO zTRANSFORM
127
33 PROTOTYPE ANALOG FILTERS
129
332 SYSTEM FUNCTION AND PROPERTIES
130
333 COMPUTED FREQUENCY RESPONSE
132
334 GENERAL PROCEDURE FOR ANALOGDIGITAL FILTER DESIGN
134
342 DESIGN BY STANDARD PARAMETERS
140

18 DESIGN METHODS
18
182 THREE DESIGN METHODS
19
183 THE COMB AND MOVING AVERAGE FILTERS
20
19 FIR REALIZATION
24
192 CASCADE FORM
26
194 CASCADED LINEAR PHASE FORM
29
110 REFERENCES
31
111 EXERCISES
32
FIR Design Techniques
40
23 SUMMARY OF DESIGN METHODS
41
25 FIR DESIGN VIA WINDOWED IDEAL LOWPASS FILTER
44
251 WINDOWS
45
252 NET FREQUENCY RESPONSE
48
253 WINDOWED LOWPASS FILTERSPASSBAND RIPPLE AND STOP BAND ATTENUATION
52
255 IMPROVING STOPBAND ATTENUATION
56
256 MEETING DESIGN SPECIFICATIONS
59
26 FIR DESIGN VIA FREQUENCY SAMPLING
61
261 USING THE INVERSE DFT
67
262 USING COSINESINE SUMMATION FORMULAS
71
263 IMPROVING STOPBAND ATTENUATION
74
264 FILTERS OTHER THAN LOWPASS
79
265 HILBERT TRANSFORMERS
82
266 DIFFERENTIATORS
92
27 OPTIMIZED FILTER DESIGN
93
272 DESIGN GOAL
94
273 ALTERNATION THEOREM
96
274 A COMMON DESIGN PROBLEM FOR ALL LINEAR PHASE FILTERS
97
275 WEIGHTED ERROR FUNCTION
99
276 REMEZ EXCHANGE ALGORITHM
100
28 REFERENCES
108
Classical IIR Design
124
35 LOWPASS ANALOG CHEBYSHEVTYPEI FILTERS
141
351 DESIGN BY ORDER CUTOFF FREQUENCY AND EPSILON
142
352 DESIGN BY STANDARD PARAMETERS
147
36 LOWPASS ANALOG CHEBYSHEVTYPEII FILTERS
149
362 DESIGN BY STANDARD PARAMETERS
151
37 ANALOG LOWPASS ELLIPTIC FILTERS
153
371 DESIGN BY STANDARD PARAMETERS
154
38 FREQUENCY TRANSFORMATIONS IN THE ANALOG DOMAIN
156
382 LOWPASS TO HIGHPASS
159
383 TRANSFORMATION VIA CONVOLUTION
161
384 LOWPASS TO BANDPASS
164
385 LOWPASS TO BANDSTOP NOTCH
166
39 ANALOG TO DIGITAL FILTER TRANSFORMATION
168
391 IMPULSE INVARIANCE
169
392 THE BILINEAR TRANSFORM
176
310 MATHSCRIPT FILTER DESIGN FUNCTIONS
186
311 PRONYS METHOD
189
312 IIR OPTIMIZATION PROGRAMS
195
Software for Use with this Book
208
A2 DOWNLOADING THE SOFTWARE
209
A5 MULTILINE MCODE EXAMPLES
210
A6 HOW TO SUCCESSFULLY COPYANDPASTE MCODE
211
A7 LEARNING TO USE MCODE
212
VectorMatrix Operations in MCode
214
B22 OUTER PRODUCT
215
B4 MATRIX INVERSE AND PSEUDOINVERSE
216
FIR Frequency Sampling Design Formulas
218
C14 EVEN LENGTH SYMMETRIC TYPE IV
219
Biography
220
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