Going one step further, we can use the bandpass FIR filter design technique to design a highpass FIR filter. To obtain the coefficients for a highpass filter, we need only modify the shifting sequence sshift(k) to make it represent a sampled sinusoid whose frequency is fs/2. This process is shown in Figure 5-29. Our final 31-tap highpass FIR filter's hhp(k) coefficients are


Figure 5-29. Highpass filter with frequency response centered at fs/2: (a) generating 31-tap filter coefficients hhp(k); (b) frequency magnitude response |Hhp(m)|.

whose |Hhp(m)| frequency response is the solid curve in Figure 5-29(b). Because sshift(k) in Figure 5-29(a) has alternating plus and minus ones, we can see that hhp(k) is merely hlp(k) with the sign changed for every other coefficient. Unlike |Hbp(m)| in Figure 5-28(b), the |Hhp(m)| response in Figure 5-29(b) has the same amplitude as the original |Hlp(m)|.

Again, notice that the hlp(k) low-pass coefficients in Figure 5-29(a) have not been modified by any window function. In practice, we'd use a windowed hlp(k) to reduce the passband ripple before implementing Eq. (5-21).

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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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