DSP FIRST 2e – Resources

DSP FIRST 2e 9. z-Transforms – Problems with selected Solutions ⁸⁹

9–1 Impulse and step response for cascaded FIR systems Solution

system function H(z)

9–2 Impulse and step response for cascaded FIR systems

system function H(z)

9–3 Impulse and step response for cascaded FIR systems

system function H(z)

9–4 Difference Equation from \(H(z)\) ♦ Impulse Response \(h[n]\) Solution

difference impulse system

9–5 Cascade of 2 FIR Systems ♦ \(H(z)\) ♦ Zeros ♦ Difference Equation Solution

cascade difference pole zero

9–6 Complex Roots of Polynomial ♦ Plot in \(z\mbox{-}\)Plane Solution

plot polynomial roots

9–7 Output Signal \(y[n]\) from FIR \(H(z)\) and Sinusoidal Input Signal \(x[n]\) Solution

input output system

9–8 Cascade of 2 FIR Systems ♦ \(H(z)\) ♦ Zeros ♦ Difference Equation Solution

cascade difference filter system

9–9 Cascade of 3 FIR Systems: Obtain Overall Difference Equation Solution

cascade difference filter

9–10 Output Signal \(y[n]\) from FIR \(H(z)\) and Sinusoidal Input Signal \(x[n]\) Solution

input output sinusoid system

9–11 \(H(z)\) for FIR Filter ♦ Zeros ♦ Frequency Response ♦ Impulse Response \(h[n]\) Solution

difference filter frequency impulse system zero

9–12 Cascade of 2 FIR Systems ♦ \(H(z)\) ♦ Difference Equation ♦ Impulse Response \(h[n]\) Solution

cascade difference impulse system

9–13 Pole-Zero Plot for \(H(z)\) ♦ Nulling Sinusoidal Inputs ♦ Sketch Frequency Response Solution

difference frequency nulling pole system zero

9–14 System Functions and Frequency Response Solution

H(z) FIR

9–15 Discrete-Time Filtering of a Continuous-Time Signal Solution

LTI FIR pole zero effective frequency response

9–16 FIR Difference Equation from System Function

LTI impulse response H(z)

9–17 \(H(z)\) and output signal for FIR Filter

difference filter FIR zeros frequency response sinusoid-in sinusoid-out

9–18 Compute \(z\mbox{-}\)Transforms of shifted impulses

linearity time delay

9–19 Filtering Sinusoids Using MATLAB

conv H(z) zeros FIR nulling

9–20 Find Ouput of LTI System Function

superposition sinusoid-in sinusoid-out

9–21 \(H(z)\) and Difference Equation for Cascade of 3 FIR Systems

LTI z-Transform difference equation

9–22 Discrete-Time Processing of Continuous-Time Signals

C-to-D converter D-to-C converter H(z)

9–23 Different descriptions of an FIR system Solution

difference equation impulse response frequency response H(z) system function

9–24 3 domains from MATLAB code Solution

frequency response system function H(z) output sound

9–25 \(H(z)\) for cascaded systems Solution

impulse response poles zeros

9–26 \(H(z)\) for cascaded systems Solution

impulse response poles zeros

9–27 Find the System Function \(H(z)\) Given Other System Descriptions Solution

System Function

9–28 Analyze a System Defined by a MATLAB Program

LTI system MATLAB

9–29 Find Outputs of an FIR Filter Defined by a Factored System Function Solution

output factored H(z)

9–30 Deconvolution in cascade of systems Solution

difference equation impulse response

9–31 Frequency response & \(H(z)\) from MATLAB code Solution

sound convolution sinusoidal output

9–32 Three domains: moving among them Solution

difference equation impulse response frequency response system function H(z) Euler's formula

9–33 Impulse response and \(H(z)\) for parallel connection Solution

zeros difference equation system function

9–34 Impulse response and \(H(z)\) for parallel connection Solution

zeros difference equation system function

9–35 Impulse response and \(H(z)\) for parallel connection Solution

zeros difference equation system function

9–36 \(H(z)\) for FIR Filter ♦ Zeros ♦ Frequency Response ♦ Sinusoidal Input Solution

difference filter frequency system

9–37 Difference Equation from \(H(z)\) ♦ Impulse Response \(h[n]\) Solution

difference impulse system

9–38 Difference Equation from \(H(z)\) ♦ Impulse Response \(h[n]\) ♦ Step Response Solution

difference impulse step system

9–39 \(H(z)\) Factored into Cascade of 2 FIR Systems Solution

block cascade filter system

9–40 \(H(z)\) and Difference Equation from Block Diagram for FIR Filter Solution

block difference filter system

9–41 \(H(z)\) and Difference Equation from Block Diagram for FIR Filter Solution

block difference filter system

9–42 Frequency Response from Pole-Zero Plot Solution

pole zero FIR magnitude

9–43 Discrete-Time Filtering of a Continuous-Time Signal Solution

LTI FIR pole zero H(z)

9–44 Cascade of 3 LTI Systems

frequency response difference equation z-Transform

9–45 Ouput of LTI System Function via \(z\mbox{-}\)Transforms

difference equation zeros convolution

9–46 Discrete-Time Processing of Continuous-Time Signals Solution

C-to-D converter D-to-C converter H(z)

9–47 Cascade FIR Systems Solution

Impulse Response H(z) delta

9–48 Discrete-Time Filtering of Continuous-Time Signals Solution

Cosine input Spectrum H(z)

9–49 Zeros of Cascaded FIR Systems Solution

difference equation system function H(z) nulling z-plane equivalent system

9–50 Frequency Response from \(H(z)\) ♦ Nulling ♦ Sinusoidal Input Solution

frequency nulling sinusoid system

9–51 Output Signal \(y[n]\) from FIR \(H(z)\) and Complex Exponential Input \(x[n]\) Solution

exponential filter phasor system

9–52 Difference Equation from \(H(z)\) ♦ Frequency Response Solution

difference frequency system

9–53 Complex Roots of Polynomial ♦ Plot in \(z\mbox{-}\)Plane Solution

plot polynomial roots

9–54 Output Signal \(y[n]\) from FIR \(H(z)\) and Periodic Input Signal \(x[n]\) Solution

filter output period system

9–55 \(H(z)\) for FIR Filter ♦ Zeros ♦ Complex Exponential Inputs Solution

exponential filter roots system

9–56 Cascade of 3 FIR Systems: Obtain Overall Difference Equation Solution

cascade difference filter

9–57 Output Signal \(y[n]\) from FIR \(H(z)\) and Complex Exponential Input \(x[n]\) Solution

exponential filter phasor system

9–58 Frequency Response and \(H(z)\) from Difference Equation

poles zeros system function

9–59 Output via \(z\mbox{-}\)transform method

impulse response H(z)

9–60 Output Signal \(y[n]\) from FIR \(H(z)\) and Various Inputs

superposition impulse response sinusoidal reponse

9–61 Cascade of 2 FIR Systems ♦ \(H(z)\) ♦ Impulse Response \(h[n]\) Solution

cascade impulse system

9–62 Output Signal \(y[n]\) from FIR \(H(z)\) and Various Inputs Solution

superposition impulse response sinusoidal reponse

9–63 Difference Equation from \(H(z)\) ♦ Zeros & Poles Solution

Running sum z-plane

9–64 \(H(z)\) for FIR Filter ♦ Zeros ♦ Frequency Response Solution

difference filter frequency system

9–65 Difference Equation from \(H(z)\) ♦ Zeros & Poles ♦ Impulse Response \(h[n]\) Solution

difference impulse system

9–66 Cascade of 2 FIR Systems ♦ \(H(z)\) ♦ Difference Equation ♦ Impulse Response \(h[n]\) Solution

cascade difference impulse system

9–67 Pole-Zero Plot for \(H(z)\) ♦ Nulling Sinusoidal Inputs ♦ Length of FIR Filter Solution

difference exponential filter nulling system

9–68 Design FIR \(H(z)\) to Null Sinusoidal Inputs Sampled by C/D Solution

converter nulling sampling system

9–69 Difference Equation from \(H(z)\) ♦ Frequency Response ♦ Impulse Response \(h[n]\) Solution

difference frequency impulse system

9–70 Complex Roots of Polynomial ♦ Plot in \(z\mbox{-}\)Plane Solution

plot polynomial roots

9–71 Difference Equation from \(H(z)\) ♦ Frequency Response ♦ Sinusoidal Input Solution

difference frequency system

9–72 Difference Equation from \(H(z)\) ♦ Zeros & Poles Solution

difference period pole system zero

9–73 Difference Equation from \(H(z)\) ♦ Zeros ♦ Complex Exponential Inputs Solution

difference exponential system zero

9–74 Difference Equation from \(H(z)\) ♦ Impulse Response \(h[n]\) Solution

difference impulse system

9–75 Difference Equation from \(H(z)\) ♦ Impulse Response \(h[n]\) ♦ Step Response Solution

difference impulse step system

9–76 Digital Filtering of Continuous-Time Signals

LTI system C/D converter D/C converter H(z)

9–77 Sum of Signals through \(H(z)\)

superposition impulse response sinusoidal reponse

9–78 Difference Equation and \(H(z)\) for Cascaded Systems

poles zeros

9–79 Difference Equation for Cascade of 3 Systems

equivalent system

9–80 Difference Equation from \(H(z)\) ♦ Impulse Response \(h[n]\) Solution

difference Dirac impulse system

9–81 Discrete-Time Filtering of a Continuous-Time Signal Solution

LTI FIR pole zero

9–82 Discrete-Time Filtering of a Continuous-Time Signal Solution

LTI FIR pole zero

9–83 Response of LTI System Function Solution

impulse response H(z) superposition sinusoid-in sinusoid-out

9–84 Discrete-Time Processing of Continuous-Time Signals Solution

C-to-D converter D-to-C converter H(z)

9.7–85 Complex Roots of Polynomial ♦ Plot in \(z\mbox{-}\)Plane Solution

complex plot polynomial roots

9.12–86 Cascade of Systems Solution

cascade difference frequency system

9.14–87 Response of Cascade Solution

cascade input LTI output

9.15–88 Filter plus A/D and D/A Solution

converter filter sampling system

9.16–89 Cascade of 2 FIR Systems ♦ \(H(z)\) ♦ Impulse Response \(h[n]\) Solution

cascade difference impulse system