Consider a causal, LTI system with a system function H(2) and real impulse response h[n]. Figure...

 

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Consider a causal, LTI system with a system function H(2) and real impulse response h[n]. Figure P6.7.1 plots the system function evaluated on the unit circle, i.e., 20 log10 H(2). The labels ∞ and -∞ indicate that the associated peaks are off-scale for the plot shown, and go to infinity or minus infinity. (a) Carefully sketch a pole-zero plot for H(2) consistent with all the information about H(2) given in the figure. Is there more than one pole-zero diagram consistent with the information in the figure? (b) Could H(2) be a minimum phase system? (c) Could H (2) be a causal, generalized linear phase system? 20 log₁0 H(el)| (dB) 50 40 30 20 10 O -10 -20 -30 -40 -50 0 0.1 0.2 -8 0.3 0.4 0.5 Frequency (co/) 0.6 0.7 Figure P6.7.1: Frequency response magnitude ∞ 0.8 0.9 1 Consider a causal, LTI system with a system function H(2) and real impulse response h[n]. Figure P6.7.1 plots the system function evaluated on the unit circle, i.e., 20 log10 H(2). The labels ∞ and -∞ indicate that the associated peaks are off-scale for the plot shown, and go to infinity or minus infinity. (a) Carefully sketch a pole-zero plot for H(2) consistent with all the information about H(2) given in the figure. Is there more than one pole-zero diagram consistent with the information in the figure? (b) Could H(2) be a minimum phase system? (c) Could H (2) be a causal, generalized linear phase system? 20 log₁0 H(el)| (dB) 50 40 30 20 10 O -10 -20 -30 -40 -50 0 0.1 0.2 -8 0.3 0.4 0.5 Frequency (co/) 0.6 0.7 Figure P6.7.1: Frequency response magnitude ∞ 0.8 0.9 1