Figure 8.1 (p. 615) Time-domain condition for distortionless transmission of a signal through a linear time-invariant system. Signals and Systems, 2/E.

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Presentation transcript:

Figure 8.1 (p. 615) Time-domain condition for distortionless transmission of a signal through a linear time-invariant system. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.2 (p. 615) Frequency response for distortionless transmission through a linear time-invariant system. (a) Magnitude response. (b) Phase response. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8. 3 (p. 617) Frequency response of ideal low-pas filter Figure 8.3 (p. 617) Frequency response of ideal low-pas filter. (a) Magnitude response. (b) Phase response. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.4 (p. 618) Time-shifted form of the sinc function, representing the impulse response of an ideal (but noncausal) low-pass filter for c = 1 and t0 = 8. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.5 (p. 620) Sine integral. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.6 (p. 620) Pulse response of an ideal low-pass filter for input pulse of duration T0 = 1 s and varying filter cutoff frequency c: (a) c = 4 rad/s; (b) c = 2 rad/s; and (c) c = 0.4 rad/s. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.7 (p. 622) The Gibbs phenomenon, exemplified by the pulse response of an ideal low-pass filter. The overshoot remains essentially the same despite a significant increase in the cutoff frequency c: (a) cT0 = 10 rad and (b) cT0 = 40 rad. The pulse duration T0 is maintained constant at 1 s. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.8 (p. 624) Tolerance diagram of a practical low-pass filter: the passband, transition band, and stopband are shown for positive frequencies. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8. 9 (p. 625) Two different forms of function F2(): (a) K = 3 Figure 8.9 (p. 625) Two different forms of function F2(): (a) K = 3. (b) K = 4. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.10 (p. 627) Magnitude response of Butterworth filter for varying orders. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.11 (p. 628) Distribution of poles of H(s)H(–s) in the s-plane for two different filter orders: (a) K = 3 and (b) K = 4, for which the total number of poles is 6 and 8, respectively. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.12 (p. 629) Magnitude response of Chebyshev filter for order (a) K = 3 and (b) K = 4 and passband ripple = 0.5 dB. The frequencies b and a in case (a) and the frequencies a1 and b, and a2 in case (b) are defined in accordance with the optimality criteria for equiripple amplitude response. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.13 (p. 630) Magnitude response of inverse Chebyshev filter for order (a) K = 3 and (b) K = 4 and stopband ripple = 30 dB. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.14 (p. 633) Low-pass Butterworth filters driven from ideal current source: (a) order K = 1 and (b) order K = 3. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.15 (p. 634) System for filtering a continuous-time signal, built around a digital filter. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.16 (p. 636) Magnitude response of rectangular window for a FIR filter of order K = 12, depicted on 0    . Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.17 (p. 637) Impulse response of Hamming window for FIR filter of order M = 12. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.18 (p. 638) Comparison of magnitude responses of rectangular and Hamming windows for a filter of order M = 12, plotted in decibels. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.19 (p. 639) Comparison of magnitude responses (plotted on a dB scale) of two low-pass FIR digital filters of order M = 12 each, one filter using the rectangular window and the other using the Hamming window. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.20 (p. 640) Structure for implementing an FIR digital filter. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.21 (p. 641) Magnitude response of FIR digital filter as differentiator, designed using (a) a rectangular window and (b) a Hamming window. In both cases, the filter order M is 12. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.22 (p. 643) (a) Waveform of raw speech signal, containing an abundance of high-frequency noise. (b) Waveform of speech signal after passing it through a low-pass FIR digital filter of order M = 98 and cutoff frequency fc = 3.1 X 103 rad/s. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.23 (p. 644) (a) Magnitude spectrum of unfiltered speech signal. (b) Magnitude spectrum of unfiltered speech signal. Note the sharp cutoff of the spectrum around 3100 Hz. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.24 (p. 646) Illustration of the properties of the bilinear transform. The left half of the s-plane (shown on the left) is mapped onto the interior of the unit circle in the z-plane (shown on the right). Likewise, the right half of the s-plane is mapped onto the exterior of the unit circle in the z-plane. The two corresponding regions are shown shaded. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.25 (p. 647) Graphical plot of the relation between the frequency  pertaining to the discrete-time domain and the frequency  pertaining to the continuous-time domain:  = 2 tan-1 (). Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.26 (p. 648) Impulse response of digital IIR low-pass filter with Butterworth response of order 3 and 3-dB cutoff frequency c = 0.2. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.27 (p. 648) Cascade implementation of IIR low-pass digital filter, made up of a first-order section followed by a second-order section. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.28 (p. 649) (a) Magnitude response of the IIR low-pass digital filter characterized by the impulse response shown in Fig. 8.26, plotted in decibels. (b) Phase response of the filter. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.29 (p. 650) Cascade connection of a dispersive (LTI) channel and an equalizer for distortionless transmission. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.

Figure 8.30 (p. 653) Magnitude response of Butterworth channel of order 1: dashed and dotted (— •— •) curve. Magnitude response of FIR equalizer of order M = 12: dashed (— —) curve. Magnitude response of equalized channel: continuous curve. The flat region of the overall (equalized) magnitude response is extended up to about  = 2.5. Signals and Systems, 2/E by Simon Haykin and Barry Van Veen Copyright © 2003 John Wiley & Sons. Inc. All rights reserved.