We can frequency translate a real bandpass signal toward zero Hz, converting it to a lowpass signal, without the need for mixing multipliers using decimation by an integer factor D as shown in Figure 13-75(a). If the bandpass filter provides an output signal of bandwidth B Hz, located as shown in Figure 13-75(b) and Figure 13-75(d) where k is a positive integer, decimation by D will yield lowpass signals whose spectra are shown in Figure 13-75(c) and Figure 13-75(e) depending on whether integer k is odd or even. Please notice the inverted spectra in Figure 13-75(e). To avoid decimated output aliasing errors, we must satisfy the Nyquist criterion and ensure that xBP(n)'s bandwidth B is not greater than fs/2D.

Figure 13-75. Real bandpass signal translation using decimation by D.

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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

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