.NODE

Section G.1. FREQUENCY RESPONSE OF A COMB FILTER

G 1 FREQUENCY RESPONSE OF A COMB FILTER

The frequency response of a comb filter is Hcomb(z) evaluated on the unit circle. We start by substituting ejw for z in Hcomb(z) from Eq. (7-2), because z = ejw defines the unit circle, giving

Factoring out the half-angled exponential e–jwN/2, we have

Equation G-2

Using Euler's identity 2jsin(a) = eja – e–ja, we arrive at

Equation G-3

Replacing j with ejp/2, we have

Equation G-4

Determining the maximum magnitude response of a filter is useful in DSP. Ignoring the phase shift term (complex exponential) in Eq. (G-4), the frequency-domain magnitude response of a comb filter is

Equation G-5

with the maximum magnitude being 2.

URL http://proquest.safaribooksonline.com/0131089897/app07lev1sec1

 
Amazon
 
 
Prev don't be afraid of buying books Next
 
 

Chapter One. Discrete Sequences and Systems

Chapter Two. Periodic Sampling

Chapter Three. The Discrete Fourier Transform

Chapter Four. The Fast Fourier Transform

Chapter Five. Finite Impulse Response Filters

Chapter Six. Infinite Impulse Response Filters

Chapter Seven. Specialized Lowpass FIR Filters

Chapter Eight. Quadrature Signals

Chapter Nine. The Discrete Hilbert Transform

Chapter Ten. Sample Rate Conversion

Chapter Eleven. Signal Averaging

Chapter Twelve. Digital Data Formats and Their Effects

Chapter Thirteen. Digital Signal Processing Tricks

Appendix A. The Arithmetic of Complex Numbers

Appendix B. Closed Form of a Geometric Series

Appendix C. Time Reversal and the DFT

Appendix D. Mean, Variance, and Standard Deviation

Appendix E. Decibels (dB and dBm)

Appendix F. Digital Filter Terminology

Appendix G. Frequency Sampling Filter Derivations

Appendix H. Frequency Sampling Filter Design Tables

show all menu





Understanding Digital Signal Processing
Understanding Digital Signal Processing (2nd Edition)
ISBN: 0131089897
EAN: 2147483647
Year: 2004
Pages: 183
Similar book on Amazon

Flylib.com © 2008-2017.
If you may any questions please contact us: flylib@qtcs.net