To find and plot the Pole Zero Map
The zeros are at locations where the numerator polynomial is zero. So
So the zeros are at
The poles are at locations where the denominator polynomial is zero. So
First Pole
Another way to find the pole is
So the pole is at
The pole is at the point at an angle at a distance 0.95.
Second Pole
Another way to find the pole is
So the pole is at
The pole is at the point at an angle at a distance 0.95.
Third Pole
Another way to find the pole is
So the pole is at
The pole is at the point at an angle at a distance 0.95.
Fourth Pole
Another way to find the pole is
So the pole is at
The pole is at the point at an angle at a distance 0.95.
So the poles are at
Hence the pole zero plot will be
To find and plot the Magnitude Response
We know that
So
Using
We get
To get the frequency response put
Using MATLAB
clc;
clear all;
close all;
b = [1, 0, -1];
a1 = [1, -1.3435, 0.9025];
a2 = [1, 0, 0.9025];
a = conv(a1, a2);
w = -pi:pi/1000:pi;
H = freqz(b, a, w);
plot(w/pi, abs(H), 'linewidth', 2);
grid;
xlabel('Normalized Frequency, \omega (\times \pi units)');
ylabel('|H(e^{j\omega})|');
title('Magnitude Response');
sys = tf(b,a,1)
figure
pzmap(sys)
After executing we get
please show steps and formulas. Plot the magnitude of the and the pole- zero plot frequency...
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...
For each of the transfer functions given below, draw the pole-zero plot and plot the magnitude separate from the phase as a function of frequency. Show only the asymptotic terms that make up the transfer function and then add them to show the composite plot. You can verify your plots (to some extent) by using MATLAB to generate the plots but only as a check that the work you have done is correct. The work that will count for points...
please show all steps and matlab plot , 5) Design a one-pole, one-zero passive filter to have a low-frequency gain of -32 dB, a high-frequency gain of 0 dB, and a cutoff frequency of 2,000 Hz. Specify the circuit and all component values. Use Matlab to plot the magnitude and phase frequency response for your filter. 5) Design a one-pole, one-zero passive filter to have a low-frequency gain of -32 dB, a high-frequency gain of 0 dB, and a cutoff...
I (K Pole-Zero Plot #1 Pole-Eero Plot 15 L. Pole-Zero Plot IMI 4z1 15 Prde-Zero Plot #5 Pole-Zero Plat #6 Tine Index (n) Problem P-10.20. Match a pole-zero plot (1-6) to each of the impulse response plots (J-N) shown above (Figure P-10.20 from p. 464) Note: Beach Board causes the magnitude Impulse Response Plot number order to be in random order Pole-Zero Plot #1 Pole-Zero Plot #2 Pole-Zero Plot #3 1, hin] Plot (N) hin] Plot (K) h[n] Plot (M)...
Below is the zero and poles plot of a system. What is the magnitude response of this system? Pole/Zero Plot 0.5 0 0.5 0.5 0 Real Part 0.5 H(J) : (exp(2*90i*theta)-2"exp(%itthet exp(2-i.6)-2 exp(i-0)+2 exp(2 i.)-exp(i.0)+0.5 Your last answer was interpreted as follows: CHR The variables found in your answer were: [e] Incorrect answer. Below is the zero and poles plot of a system. What is the magnitude response of this system? Pole/Zero Plot 0.5 0 0.5 0.5 0 Real Part...
no need for pole-zero plot 7. Determine the system function, magnitude response, and phase response of the fol- lowing systems and use the pole-zero pattern to explain the shape of their magnitude response (a) y[n] = 1(x(n]-x(n-1), ln -2
For each of the transfer functions given below, draw the pole-zero plot and using the log- semilog paper provided on Blackboard to plot the magnitude separate from the phase as a function of frequency. Show only the asymptotic terms that make up the transfer function and then add them to show the composite plot. You can verify your plots (to some extent) by using MATLAB to generate the plots but only as a check that the work you have done...
Please show all work Problem 4 Questions about the frequency response of an FIR filter: (a) Determine a formula for the frequency response of an FIR filter defined by the pole-zero plot below: Pole-Zero Plot #1 0.5 -0.5 -1 1 -0.5 0 051 Real part (b) For the FIR filter in part (a), write a simplified version of the frequency response H(e'ω) and use it to prove that the maximum value of the frequency response magnitude will be at ω-tr/2....
The pole-zero plot of a cosine oscillator filter is shown below. The oscillation frequency is one quarter of the sampling frequency (Fs/4). Pole-Zero Plot for the Non-Damped Cosine Oscillator zp R-1 0.8 06 0.4 0.2 zct zc2 2nd order -0.2 -0.4 -0.6 -0.8 -1 zp -1 -0.5 0.5 Real Part O True False Imaginary Part
Question 3 The pole-zero plot of a sinusoidal oscillator filter is shown below. If the system is working at Fs = 8000Hz, the output tone has a frequency of 1000 Hz. Pole-Zero Plot for the Non-Damped Cosine Oscillator Imaginary Part 201 202 2nd order The X zp -1 -0. 50 0. 51 Real Part True False