Consider the following zero-pole plots for digital filters. In each case, determine if the filter is...
4. Consider the filter a. (5 pts) Determine b so that |H(0) 1. b. (5 pts) Determine the frequency at which H(ja)l c. (5 pts) Is this filter lowpass, bandpass, or highpass? 2
3. (a) For each of the RC passive filters shown in Fig. 3, sketch the magnitude in dB and phase as a function of frequency (in Hz), with the frequency on a log scale. Indicate the poles and zeros. For the magnitude plots, indicate the slope (in dB/decade) for each region; for regions that exhibit flat magnitude, indicate the value. Likewise, for regions that exhibit flat phase, indicate the value. (b) Indicate the type of each filter (e.g., lowpass, highpass,...
2. Perform a lowpass prototype transform, find, given the following digital filter frequency values. a. Low pass filter with a cutoff of 750 Hz b. High pass filter with a cutoff of 12.57 rad/s c. Bandpass filter with a lower cutoff of 400 Hz and a higher cutoff 725 Hz d. Bandstop filter with a center frequency of 135.3 rad/s and a bandwidth of 84.74 rad/s
Question 1: a) For any linear phase filter, prove that if zo is a zero, then so must zobe. Hint: Using the properties of the z-transform, write h[n] = Eh[N - n) in the z-domain, and substitute 2 = 20. b) For any Type III or Type IV filter, prove that z = 1 is a zero. c) For any Type II filter, prove that z = -1 is a zero. d) In light of the above, find the zeros...
MATLAB
Filter Design using the Parks-McClellan Algorithm Using the Parks-McClellan (PMC) algorithm, design filters with the following specifications: A. Filterlspecifications: Type: lowpass filter Cutoff frequencies: o 0.1t and o0.3 Tolerances: PB 1 dB; SB 40 dB B. Filter 2 specifications: Type: highpass filter Cutoff frequencies: o 0.9 and o0.77 Tolerances: PB 1 dB; SB 40 dB stl Respond to the following questions, a. What is the order of the filter in each case? b. Design the FIR filter using the...
Show all your work for each problem. 1. Given the following DSP system with a sampling rate 8000 Hz, y(0.5x(n)-0.5x(n -1) where y(n) is the output and x(n) is the input a) Find its transfer function, b) Make a pole-zero plot and determine the stability. c) Obtain He) and then He) d) Compute the filter gain at the frequency of 0 Hz, 1000 Hz, 2000 Hz, 3000Hz, 4000 Hz, respectively e Make a magnitude frequency response plot. f) Determine the...
P11.10 Label each of the following pole/zero plots in the z-plane as being that of a LP, HP, BP, BE or AP filter:
2. Consider a second IIR filter a. Determine the system function H(z), pole-zero location (patterns), and plot the pole-zero pattern. b. Determine the analytical expression for frequency response, magnitude, and phase response. c. Choose b so that the maximum magnitude response is equal to 1. d. Plot the pole-zero pattern and the magnitude of the frequency response as a function of normal frequency.
2. Consider a second IIR filter a. Determine the system function H(z), pole-zero location (patterns), and plot...
Topic: Realisation of Digital Filters
A filter has the following realisation: where the
values of the multipliers are a1=-0.57, a2=-0.56, b1=0.55 and
b2=0.69.
Answer the following, giving answers to four decimal
places.
PART 1
For the following transfer functions:
H1(z) = (z+γ1)/ (z+γ2)
and
H2(z) = (z+γ3)/ (z+γ4)
determine the values of the coefficients:
γ1=_____
γ2=_____
γ3=_____
y4=_____
H(=) H(E) H-(-) | [7] الريال T 7) پز xb
Question 3 (30 marks) Consider the digital filter structure shown in the below figure: x[n yIn] 3 (a) Transform the given block diagram to the transposed direct form II one. 2 (b) Determine the difference-equation representation of the system 4 (c) Find the transfer function for this causal filter and state the pole-zero pattern (d) Determine the impulse response of the system 2 (e) For what values of k is the system stable? (f) Determine yln if k 1 and...