![Page 1: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/1.jpg)
Sampling of Continuous-Time SignalsReference chapter 4 in Oppenheim and Schafer.
![Page 2: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/2.jpg)
T = sampling period fs = sampling frequency
Periodic Sampling of Continuous Signals
when expressing frequencies in radians per second.
![Page 3: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/3.jpg)
Mathematical Model for Periodic Sampling
Impulse train modulator followed by conversion of impulse train to sequence.
![Page 4: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/4.jpg)
Mathematical Model for Periodic Sampling
![Page 5: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/5.jpg)
Mathematical Model for Periodic Sampling
![Page 6: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/6.jpg)
Frequency-Domain Representation of Sampling
![Page 7: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/7.jpg)
Figure 4.3 Frequency-domain representation of sampling in the time domain. (a) Spectrum of the original signal. (b) Fourier transform of the sampling function. (c) Fourier transform of the sampled signal with Ωs > 2ΩN. (d) Fourier transform of the sampled signal with Ωs < 2ΩN.
aliasing (distortion)
![Page 8: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/8.jpg)
Recovery of Signal
![Page 9: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/9.jpg)
Figure 4.4 Exact recovery of a continuous-time signal from its samples using an ideal lowpass filter.
![Page 10: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/10.jpg)
Aliasing Example with Cosine
no aliasing reconstruction:
with aliasing reconstruction:
(taken on identity, alias, of lower frequency signal)
![Page 11: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/11.jpg)
Sampling Theorem
![Page 12: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/12.jpg)
General Case for Discrete-time Fourier Transform (DTFT)
![Page 13: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/13.jpg)
General Case for Discrete-time Fourier Transform (DTFT)
![Page 14: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/14.jpg)
Examples of ambiguity due to sampling.
![Page 15: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/15.jpg)
Figure 4.6 (a) Continuous-time and (b) discrete-time Fourier transforms for sampled cosine signal with frequency Ω0 = 4000π and sampling period T = 1/6000.
![Page 16: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/16.jpg)
Examples of ambiguity due to sampling.First case with no aliasing.
Second case with aliasing.
![Page 17: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/17.jpg)
Reconstruction of a band limited signal from its samples.
![Page 18: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/18.jpg)
Figure 4.7 (a) Block diagram of an ideal bandlimited signal reconstruction system. (b) Frequency response of anideal reconstruction filter. (c) Impulse response of an ideal reconstruction filter.
![Page 19: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/19.jpg)
Figure 4.8 Ideal bandlimited interpolation.
![Page 20: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/20.jpg)
Figure 4.9 (a) Ideal bandlimited signal reconstruction. (b) Equivalent representation as an ideal D/C converter.
![Page 21: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/21.jpg)
Discrete-Time Processing of Continuous-Time Signals
![Page 22: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/22.jpg)
Discrete-Time Processing of Continuous-Time Signals
![Page 23: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/23.jpg)
Discrete-Time LTI Processing of Continuous-Time Signals
![Page 24: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/24.jpg)
Discrete-Time LTI Processing of Continuous-Time Signals
![Page 25: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/25.jpg)
![Page 26: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/26.jpg)
Figure 4.11 (a) Frequency response of discrete-time system in Figure 4.10. (b) Corresponding effective continuous-time frequency response for bandlimited inputs.
![Page 27: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/27.jpg)
Figure 4.12 (a) Fourier transform of a bandlimited input signal. (b) Fourier transform of sampled input plotted as a function of continuous-time frequency Ω. (c) Fourier transform X (ejω) of sequence of samples and frequency response H(ejω) of discrete-time system plotted versus ω. (d) Fourier transform of output of discrete-time system. (e) Fourier transform of output of discrete-time system and frequency response of ideal reconstruction filter plotted versus Ω. (f) Fourier transform of output.
![Page 28: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/28.jpg)
![Page 29: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/29.jpg)
![Page 30: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/30.jpg)
Figure 4.13 (a) Frequency response of a continuous-time ideal bandlimited differentiator Hc (jΩ) = jΩ, |Ω| < π/T.(b) Frequency response of a discrete-time filter to implement a continuous-time bandlimited differentiator.
![Page 31: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/31.jpg)
![Page 32: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/32.jpg)
Figure 4.14 (a) Continuous-time LTI system. (b) Equivalent system for bandlimited inputs.
![Page 33: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/33.jpg)
![Page 34: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/34.jpg)
Continuous-Time Processing of Discrete-Time Signals
![Page 35: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/35.jpg)
![Page 36: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/36.jpg)
![Page 37: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/37.jpg)
![Page 38: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/38.jpg)
Figure 4.16 (a) Continuous-time processing of the discrete-time sequence (b) can produce a new sequence with a “half-sample” delay.
![Page 39: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/39.jpg)
Figure 4.17 The moving-average system represented as a cascade of two systems.
Moving-Average Example
![Page 40: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/40.jpg)
M = 5
![Page 41: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/41.jpg)
In this case works out to delay of 5/2 or 2.5 samples.
![Page 42: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/42.jpg)
Figure 4.18 Illustration of moving-average filtering. (a) Input signal x[n] = cos(0.25πn). (b) Corresponding output of six-point moving-average filter.
![Page 43: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/43.jpg)
Changing the Sampling Rate with Discrete-Time Processing
“resampling”
![Page 44: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/44.jpg)
“downsampling”“(sampling rate) compressor”
![Page 45: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/45.jpg)
![Page 46: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/46.jpg)
![Page 47: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/47.jpg)
Figure 4.20 Frequency-domain illustration of downsampling.
![Page 48: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/48.jpg)
Figure 4.21 (a)–(c) Downsampling with aliasing. (d)–(f) Downsampling with prefiltering to avoid aliasing.
![Page 49: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/49.jpg)
![Page 50: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/50.jpg)
![Page 51: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/51.jpg)
![Page 52: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/52.jpg)
“interpolator”
![Page 53: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/53.jpg)
![Page 54: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/54.jpg)
![Page 55: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/55.jpg)
Figure 4.24 Frequency-domain illustration of interpolation.
![Page 56: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/56.jpg)
Figure 4.25 Impulse response for linear interpolation.
![Page 57: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/57.jpg)
Figure 4.26 (a) Illustration of linear interpolation by filtering. (b) Frequency response of linear interpolator compared with ideal lowpass interpolation filter.
![Page 58: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/58.jpg)
Figure 4.27 Illustration of interpolation involving 2K = 4 samples when L = 5.
![Page 59: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/59.jpg)
Figure 4.28 Impulse responses and frequency responses for linear and cubic interpolation.
![Page 60: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/60.jpg)
Figure 4.29 (a) System for changing the sampling rate by a noninteger factor. (b) Simplified system in which the decimation and interpolation filters are combined.
![Page 61: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/61.jpg)
Figure 4.30 Illustration of changing the sampling rate by a noninteger factor.
![Page 62: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/62.jpg)
![Page 63: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/63.jpg)
![Page 64: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/64.jpg)
![Page 65: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/65.jpg)
![Page 66: Sampling of Continuous-Time Signals - Clemson …ekp/courses/ece8440/assets/844_Ch4... · Periodic Sampling of Continuous Signals ... Figure 4.16 (a) Continuous-time processing of](https://reader031.vdocuments.us/reader031/viewer/2022022014/5b38d60a7f8b9a310e8dc344/html5/thumbnails/66.jpg)