Frequency Response of FIR Filters

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Cascaded LTI SystemsCascaded LTI Systems• Cascaded LTI system were discussed in Chapter 5 from thetime-domain standpoint• In the frequency-domain there is an alternative view of theinput/output relationships• To begin with consider againxn e jˆ n – n • With LTI #1 followed by LTI #2, the output at frequencyy 1n===H 2e jˆH 2e jˆH 1e jˆH 1e jê jˆ ne jˆ n(6.25)îs(6.26)ECE 2610 Signals and Systems 6–22
Cascaded LTI Systems• With LTI #2 followed by LTI #1, the output at frequencyy 2n==H 1e jˆH 1e jˆH 2e jˆH 2e jê jˆ ne jˆ nis(6.27)• Since H 1e jˆH 2e jˆ = H 2e jˆH 1e jˆ, it follows thaty 1n= y 2n, and we have established that the frequencyresponse for a cascaded system is simply the product of thefrequency responsesˆH cascadee jˆ = He jˆ = H 1e jˆH 2e jˆ(6.28)• We have also shown that a convolution in the time-domain isequivalent to a multiplication in the frequency-domainhn Example: Two System Cascade• ConsiderTime Domain Frequency Domain= h 1n*h 2n H 1e jˆH 2e jˆ = He jˆH 1e jˆ = 1 + e jˆH 2e jˆ–= 1+ 2e jˆ+• The cascade frequency response isHe jˆ–e j2ˆ 1 + e jˆ–= 1+ 2e jˆ+–1 3e jˆ –= + + 3e j2ˆ+–e j2ˆ–e j3ˆ(6.29)ECE 2610 Signals and Systems 6–23
Page 1 and 2: Frequency Responseof FIR FiltersCha
Page 3 and 4: Sinusoidal Response of FIR Systems
Page 5: Sinusoidal Response of FIR Systems>
Page 8 and 9: Superposition and the Frequency Res
Page 10 and 11: Steady-State and Transient Response
Page 12 and 13: Steady-State and Transient Response
Page 14 and 15: Properties of the Frequency Respons
Page 16 and 17: Properties of the Frequency Respons
Page 18 and 19: Graphical Representation of the Fre
Page 20 and 21: Graphical Representation of the Fre
Page 24 and 25: Moving Average Filtering• Given t
Page 26 and 27: Moving Average FilteringPlotting th
Page 28 and 29: Filtering Sampled Continuous-Time S
Page 30 and 31: Filtering Sampled Continuous-Time S
Page 32: Filtering Sampled Continuous-Time S

Frequency Response of FIR Filters

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