DSP FIRST 2e 6. Frequency Response of FIR Filters – Problems with selected Solutions 108


6–1  Output from FIR system given input spectrum 

  • 6–1
 averaging filter   frequency response 
 

6–2  Sinusoidal response of nonlinear system  Solution  

  • 6–2
 linearity   time-invariance   causality 
 

6–3  Matching frequency responses to FIR systems  Solution  

  • 6–3
 impulse response   difference equation   filter coefficients 
 

6–4  Sinusoidal response from FIR frequency response  Solution  

  • 6–4
 sinusoid-in   sinusoid-out 
 

6–5  Matching frequency responses to FIR systems 

  • 6–5
 impulse response   difference equation   filter coefficients 
 

6–6  Sinusoidal response from FIR frequency response 

  • 6–6
 sinusoid-in   sinusoid-out 
 

6–7  Matching frequency responses to FIR systems 

  • 6–7
 impulse response   difference equation   filter coefficients 
 

6–8  Sinusoidal response from FIR frequency response 

  • 6–8
 sinusoid-in   sinusoid-out 
 

6–9  Frequency Response of an FIR Filter  Solution  

  • 6–9
 FIR filter   frequency response 
 

6–10  Cascade of FIR Filters  Solution  

  • 6–10
 FIR   cascade   impulse response 
 

6–11  Determine the Impulse Response and Frequency Response of an FIR Filter  Solution  

  • 6–11
 FIR   impulse response   frequency response 
 

6–12  Frequency Response of an FIR Filter  Solution  

  • 6–12
 FIR filter   frequency response 
 

6–13  Cascade of FIR Filters  Solution  

  • 6–13
 FIR   cascade   impulse response 
 

6–14  Determine the Impulse Response and Frequency Response of an FIR Filter  Solution  

  • 6–14
 FIR   impulse response   frequency response 
 

6–15  Frequency Response of an FIR Filter  Solution  

  • 6–15
 FIR filter   frequency response 
 

6–16  Cascade of FIR Filters  Solution  

  • 6–16
 FIR   cascade   impulse response 
 

6–17  Determine the Impulse Response and Frequency Response of an FIR Filter  Solution  

  • 6–17
 FIR   impulse response   frequency response 
 

6–18  Frequency Response from FIR Difference Equation ♦ Magnitude & Phase  Solution  

  • 6–18
 difference   frequency   LTI 
 

6–19  Frequency Response from FIR Difference Equation ♦ Magnitude & Phase ♦ \(h[n]\)  Solution  

  • 6–19
 difference   frequency   impulse   LTI 
 

6–20  Linearity & Time-Invariance Properties  Solution  

  • 6–20
 frequency   input   LTI   output 
 

6–21  Frequency Response from FIR Difference Equation ♦ Magnitude & Phase ♦ \(h[n]\)  Solution  

  • 6–21
 difference   frequency   impulse   LTI 
 

6–22  Dirichlet (aliased sinc) Function Plot vs. Frequency  Solution  

  • 6–22
 dirichlet   frequency   maximum   sinc 
 

6–23  Output Signal & Frequency Response for FIR Filter Defined by MATLAB Code  Solution  

  • 6–23
 filter   frequency   MATLAB   time 
 

6–24  Design FIR Low-Pass Averager to Null Sinusoidal Inputs Sampled by C/D  Solution  

  • 6–24
 averager   converter   nulling   output 
 

6–25  Frequency Response from FIR Difference Equation 

  • 6–25
 LTI   magnitude   phase   freqz   MATLAB   nulling 
 

6–26  Output of FIR Difference Equation 

  • 6–26
 impulse response   magnitude   phase   sinusoid-in   sinusoid-out 
 

6–27  Dirichlet (aliased sinc) Function Plot vs. Frequency 

  • 6–27
 dirichlet   maximum   period   sinc   zero crossings 
 

6–28  Output of FIR Filter Given Input Spectrum Frequency Response 

  • 6–28
 spectrum   sinusoid-in   sinusoid-out 
 

6–29  Find Output of LTI Filter Given Frequency Response 

  • 6–29
 FIR   difference equation   impulse response   sinusoid-in   sinusoid-out   filter coefficients 
 

6–30  Filtering a Signal Given its Frequency Spectrum 

  • 6–30
 sampling   A-D conversion   phasor   nulling 
 

6–31  Linearity & Time-Invariance Properties to Construct Output 

  • 6–31
 input   LTI   output   delta 
 

6–32  Cascade of Two LTI Systems 

  • 6–32
 frequency response   overall difference equation 
 

6–33  Find Impulse and Frequency Response of FIR Filter  Solution  

  • 6–33
 magnitude 
 

6–34  Find Output of FIR Filter for Step and Cosine Inputs  Solution  

  • 6–34
 sinusoid-in   sinusoid-out   Dirichlet 
 

6–35  Find Impulse and Frequency Response of FIR Filter  Solution  

  • 6–35
 magnitude 
 

6–36  Find Output of FIR Filter for Step and Cosine Inputs  Solution  

  • 6–36
 sinusoid-in   sinusoid-out   Dirichlet 
 

6–37  Output from FIR system given input spectrum  Solution  

  • 6–37
 averaging filter   frequency response 
 

6–38  Plot of Dirichlet function  Solution  

  • 6–38
 frequency response   mainlobe width 
 

6–39  Output signal & difference equation from frequency response  Solution  

  • 6–39
 impulse response   cascade   delta   complex exponential 
 

6–40  Sinusoidal response given frequency response  Solution  

  • 6–40
 lowpass   bandpass   highpass   H(z)   sinusoid-in   sinusoid-out 
 

6–41  Sinusoidal response given frequency response  Solution  

  • 6–41
 lowpass   bandpass   highpass   H(z)   sinusoid-in   sinusoid-out 
 

6–42  Cascade Connection of Three FIR Systems  Solution  

  • 6–42
 Cascade   LTI 
 

6–43  Match FIR Frequency Response to other Representations  Solution  

  • 6–43
 FIR   Match 
 

6–44  Determine the Impulse Response and Frequency Response of an FIR Filter  Solution  

  • 6–44
 FIR   Filter   Frequency Response   Impulse Response 
 

6–45  Match FIR Frequency Response to other Representations  Solution  

  • 6–45
 FIR   Match 
 

6–46  Determine the Impulse Response and Frequency Response of an FIR Filter  Solution  

  • 6–46
 FIR   Filter   Frequency Response   Impulse Response 
 

6–47  Match FIR Frequency Response to other Representations  Solution  

  • 6–47
 FIR   Match 
 

6–48  Determine the Impulse Response and Frequency Response of an FIR Filter  Solution  

  • 6–48
 FIR   Filter   Frequency Response   Impulse Response 
 

6–49  Test for Linearity and Time-Invariance ♦ Find the Output Due to Sum of Cosines  Solution  

  • 6–49
 nonlinear system   cosine input 
 

6–50  Cascade Connection of LTI Systems ♦ Frequency Response  Solution  

  • 6–50
 cascade   frequency response 
 

6–51  Determine the Impulse Response and Frequency Response of an FIR Filter  Solution  

  • 6–51
 FIR   filter   impulse response   frequency response 
 

6–52  Frequency Response of Cascade of FIR Filters  Solution  

  • 6–52
 cascade   FIR   frequency response 
 

6–53  Determine the Impulse Response and Frequency Response of an FIR Filter  Solution  

  • 6–53
 FIR   filter   impulse response   frequency response 
 

6–54  Frequency Response of Cascade of FIR Filters  Solution  

  • 6–54
 cascade   FIR   frequency response 
 

6–55  Determine the Impulse Response and Frequency Response of an FIR Filter  Solution  

  • 6–55
 FIR   filter   impulse response   frequency response 
 

6–56  Frequency Response of Cascade of FIR Filters  Solution  

  • 6–56
 cascade   FIR   frequency response 
 

6–57  Sinusoidal response of nonlinear system 

  • 6–57
 Euler's formula   linear   time-invariant   causal 
 

6–58  Frequency response of cascaded systems  Solution  

  • 6–58
 convolution   product 
 

6–59  Impulse response from factored frequency response  Solution  

  • 6–59
 sinusoidal output   nulling   difference equation   superposition 
 

6–60  Frequency response and sinusoidal response  Solution  

  • 6–60
 sinusoid-in   sinusoid-out 
 

6–61  Frequency response and sinusoidal response  Solution  

  • 6–61
 sinusoid-in   sinusoid-out 
 

6–62  Frequency response and sinusoidal response  Solution  

  • 6–62
 sinusoid-in   sinusoid-out 
 

6–63  Output Signal & Frequency Response for FIR Filter Defined by MATLAB Code  Solution  

  • 6–63
 filter   frequency   MATLAB   time 
 

6–64  Output Signal & Frequency Response for FIR Filter Defined by MATLAB Code  Solution  

  • 6–64
 filter   frequency   MATLAB   time 
 

6–65  Frequency Response from FIR Difference Equation ♦ Magnitude & Phase ♦ \(h[n]\)  Solution  

  • 6–65
 difference   frequency   impulse 
 

6–66  Frequency Response from FIR Difference Equation ♦ Sinusoidal Response  Solution  

  • 6–66
 difference   frequency   output 
 

6–67  Frequency Response from FIR Difference Equation ♦ \(h[n]\) ♦ Convolution  Solution  

  • 6–67
 convolution   difference   frequency   impulse 
 

6–68  Output of Averaging Filter Given Input Spectrum 

  • 6–68
 spectrum   MATLAB   ltidemo 
 

6–69  Dirichlet (aliased sinc) Function Plot vs. Frequency 

  • 6–69
 dirichlet   maximum   period   sinc   zero crossings 
 

6–70  Discrete-Time Processing of Continuous-Time Signals 

  • 6–70
 C-to-D converter   D-to-C converter   H(z)   frequency response 
 

6–71  Filtering Sinusoids Using MATLAB 

  • 6–71
 conv   frequency response   zeros   FIR   nulling 
 

6–72  Match Frequency Response to Difference Equation or Impulse Response  Solution  

  • 6–72
 delta 
 

6–73  Sampling Theorem & Frequency Response  Solution  

  • 6–73
 Nyquist Rate   Fourier Series   FIR 
 

6–74  Output and Frequency Response of FIR Filter  Solution  

  • 6–74
 high pass   low pass 
 

6–75  Matching Frequency Responses  Solution  

  • 6–75
 Impulse Response   h[n]   difference equation   delta 
 

6–76  Frequency Response of FIR Filter  Solution  

  • 6–76
 magnitude   output signal   response   delta 
 

6–77  Dirichlet (aliased sinc) Function Plot vs. Frequency  Solution  

  • 6–77
 dirichlet   maximum   period   sinc 
 

6–78  Frequency Response of L-point Running Average FIR Filter  Solution  

  • 6–78
 averager   frequency   running 
 

6–79  Output from FIR Filter for Sinusoidal Input Signal  Solution  

  • 6–79
 averager   filter   output 
 

6–80  Frequency Response from FIR Difference Equation ♦ Magnitude & Phase  Solution  

  • 6–80
 blurring   difference   filter   frequency 
 

6–81  Filter Characteristics Derived from MATLAB Plot of Output Signal  Solution  

  • 6–81
 filter   DC gain   MATLAB   zero 
 

6–82  Cascade of 2 FIR Filters ♦ Multiplying Frequency Responses  Solution  

  • 6–82
 averager   cascade   delay   frequency 
 

6–83  Dirichlet (aliased sinc) Function Plot vs. Frequency  Solution  

  • 6–83
 dirichlet   maximum   period   sinc 
 

6–84  Linearity & Time-Invariance Properties  Solution  

  • 6–84
 frequency   LTI   output 
 

6–85  Frequency Response from FIR Difference Equation ♦ Magnitude & Phase  Solution  

  • 6–85
 difference   filter   frequency 
 

6–86  Output Signal when given Input Spectrum and FIR Frequency Response  Solution  

  • 6–86
 filter   frequency   spectrum 
 

6–87  Frequency Response for Digital Filter defined by MATLAB 

  • 6–87
 output signal   time response   magnitude 
 

6–88  Digital Spectrum through Frequency Response 

  • 6–88
 Dirichlet 
 

6–89  Frequency Response from FIR Difference Equation ♦ \(h[n]\) ♦ Sinusoidal Response  Solution  

  • 6–89
 difference   exponential   frequency   impulse 
 

6–90  Frequency Response from FIR Difference Equation ♦ Magnitude & Phase ♦ \(h[n]\)  Solution  

  • 6–90
 difference   frequency   impulse 
 

6–91  Frequency Response from FIR Difference Equation ♦ Sinusoidal Response  Solution  

  • 6–91
 difference   filter   frequency 
 

6–92  Plot Dirichlet Function 

  • 6–92
 aliased sinc function 
 

6–93  FIR Difference Equation from Frequency Response ♦ Complex Exponential Input  Solution  

  • 6–93
 difference   Dirac   exponential   frequency 
 

6–94  Cascade of 2 FIR Filters ♦ Multiplying Frequency Responses  Solution  

  • 6–94
 cascade   exponential   filter   frequency   multiplication   system 
 

6–95  Frequency Response from FIR Difference Equation ♦ Magnitude & Phase  Solution  

  • 6–95
 difference   filter   frequency 
 

6–96  FIR Difference Equation from Frequency Response ♦ Response for Input Spectrum  Solution  

  • 6–96
 difference   exponential   filter   frequency   spectrum 
 

6–97  Output from FIR Filter for Sinusoidal Input Signal  Solution  

  • 6–97
 amplitude   discrete   filter   period 
 

6–98  FIR Filters And Sinusoids Using MATLAB  Solution  

  • 6–98
 frequency response   difference equation   sinusoids 
 

6–99  FIR Filters And Sinusoids Using MATLAB  Solution  

  • 6–99
 frequency response   difference equation   sinusoids 
 

6–100  Output of FIR Difference Equation  Solution  

  • 6–100
 impulse response   magnitude   phase   sinusoid-in   sinusoid-out 
 

6–101  Filtering a Signal Given its Frequency Spectrum  Solution  

  • 6–101
 sampling   A-D conversion   phasor   nulling   complex amplitude 
 

6–102  Cascade of Two LTI Systems  Solution  

  • 6–102
 LTI   frequency response   difference equation 
 

6–103  Discrete-Time Processing of Continuous-Time Signals  Solution  

  • 6–103
 C-to-D converter   D-to-C converter   Dirichlet   frequency response 
 

6–104  Find Impulse and Frequency Response of FIR Filter  Solution  

  • 6–104
 magnitude   filter coefficients 
 

6–105  Sinusoids and Sampling  Solution  

  • 6–105
 Nyquist   frequency   reconstruction   D-to-C   MATLAB   difference equation   sinusoid-in   sinusoid-out 
 

6–106  Find Impulse and Frequency Response of FIR Filter  Solution  

  • 6–106
 magnitude 
 

6.1–107  Dirichlet (aliased sinc) Function Plot vs. Frequency  Solution  

  • 6–107
 dirichlet   maximum   period   sinc 
 

6.9–108  Linearity & Time-Invariance Properties  Solution  

  • 6–108
 input   LTI   output