Compute the poles and zeros of each of the filters given in problem 4. Which filters...
Compute the poles and zeros of each of the filters given in problem 4. Which filters are stable?
4a) H(z) = 1/1 + z-3
4b) H(z) = (1+3z-1+2z-2)/(1-z-1)
*I understand that a system is stable if all poles are strictly inside the unit circle, and unstable if any are outside the unit circle. If a pole is ON the unit circle or the boundary of the unit circle like 1 or -1, would that make it stable or unstable?
*I also realized that I could factor some transfer-function equations like the one for 2b. If so, how do I determine if it's stable or unstable if there are no poles?
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Compute the poles and zeros of each of the filters given in
problem 4. Which filters...
please answer them indetail. thanks 4. Let x(n) be a causal sequence. a) b) what conclusion...
please answer them indetail. thanks
4. Let x(n) be a causal sequence. a) b) what conclusion can you draw about the value of its z-transform x(z) at z 00, Use the result in part (a) to check which of the following transforms cannot be associated with a causal sequence (z-1* (z (1-^2-1)- i, x(z) = 321) iii, x(z) = A causal pole-zero system is BIBO stable if its poles are inside the unit circle. Consider now a pole- zero system...
Can Someone please hep me solve this is problem Please. It is really important and it...
Can Someone please hep me solve this is problem Please. It is really important and it has 2 parts. both need to be solved. Thank you in advance A) A DT signal x[n] has the following z-transform X(z)= z+1/2z^2+10z+4 Determine the inverse z-transform, i.e. x[n] for all n Sketch the poles and zeros of X(z), including the unit circle. Determine whether the system is stable or unstable, why? B)Determine the z-transform of x[n-2], using the properties table, write it as...
Question 2: Poles and zeros, and how they affect the transient response modes This question tests...
Question 2: Poles and zeros, and how they affect the transient response modes This question tests your understanding of the effects of nearby poles and ze- ros to the response mode of a specified pole (or conjugate pair). You should also understand what a pole-zero-gain plot is and how it is specified by, and specifies a transfer function A unit impulse function is applied to the system described by the transfer function G(8) = K (8+) (s + 1)(8 +2)...
2. Second-order Butterworth CT and DT filters. (a) [5 pts] Given that He (s)- (s+e4(steJr/4 and t...
2. Second-order Butterworth CT and DT filters. (a) [5 pts] Given that He (s)- (s+e4(steJr/4 and that the corresponding fiter is causal, verify that He(0) 1. that Hc (jw) decreases monotonically with increasing positive values of u. that I He (j) | 2-1/2 (i.e., that wc-1 is the half-power frequency), and that (b) [3 pts] Give an expression for Hd(z), the bilinear transform applied to Hc(s) in part a. Choose T - 2 in the bilinear-transform formula, ie., (1- z1/(1z1)-(z...
alpha = 5.0 beta = 7.1 zeta = 6.9 PROBLEM 1 (20 points). Given the filter with transfer function +28-1+-2 11(2) = 1-(α/10)2-4 (a2/100):-2 Use MATLAB to Find the zeros and poles of H() Plot the pole...
alpha = 5.0
beta = 7.1
zeta = 6.9
PROBLEM 1 (20 points). Given the filter with transfer function +28-1+-2 11(2) = 1-(α/10)2-4 (a2/100):-2 Use MATLAB to Find the zeros and poles of H() Plot the poles and zeros on the -plane. The pot should include the uit circle. Plot the magnitude response (in dB) Plot the phase response. Deliverables: Your MATLAB code used to solve Problem 1 and all the generated plots.
PROBLEM 1 (20 points). Given the filter...
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. T...
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. Topics: Filter Design, Effective Time Constant Design a causal 2nd order, normalized, stable Peak Filter centered at fo 1000Hz. Use only two conjugate poles and two zeros at the origin. The system is to be sampled at Fs- 8000Hz. The duration of the transient should be as close as possible to teft 7.5 ms. The transient is assumed to end when the largest pole elevated...
IF THE POLES OF THE LOCATED AT. b) H(근) のUSE-MATLAS TO PLOT IHI»)! oAT KIN OF A FILTER IS IT? ...
stuck on this question, please show all your work step
by step, thank you.
IF THE POLES OF THE LOCATED AT. b) H(근) のUSE-MATLAS TO PLOT IHI»)! oAT KIN OF A FILTER IS IT? 171 53 lilustrative Examples 5.3 ILLUSTRATIVE EXAMPLES Example 5.3-1: The following difference equation is known as the first- order trapezoidal integration rule in numerical analysis: n) - ) n-O (531) Find: The transfer function. The impulse response. The output if the input is the unit step...
please answer them indetail. thanks
4. Let x(n) be a causal sequence. a) b) what conclusion can you draw about the value of its z-transform x(z) at z 00, Use the result in part (a) to check which of the following transforms cannot be associated with a causal sequence (z-1* (z (1-^2-1)- i, x(z) = 321) iii, x(z) = A causal pole-zero system is BIBO stable if its poles are inside the unit circle. Consider now a pole- zero system...
Question 2: Poles and zeros, and how they affect the transient response modes This question tests your understanding of the effects of nearby poles and ze- ros to the response mode of a specified pole (or conjugate pair). You should also understand what a pole-zero-gain plot is and how it is specified by, and specifies a transfer function A unit impulse function is applied to the system described by the transfer function G(8) = K (8+) (s + 1)(8 +2)...
2. Second-order Butterworth CT and DT filters. (a) [5 pts] Given that He (s)- (s+e4(steJr/4 and that the corresponding fiter is causal, verify that He(0) 1. that Hc (jw) decreases monotonically with increasing positive values of u. that I He (j) | 2-1/2 (i.e., that wc-1 is the half-power frequency), and that (b) [3 pts] Give an expression for Hd(z), the bilinear transform applied to Hc(s) in part a. Choose T - 2 in the bilinear-transform formula, ie., (1- z1/(1z1)-(z...
alpha = 5.0
beta = 7.1
zeta = 6.9
PROBLEM 1 (20 points). Given the filter with transfer function +28-1+-2 11(2) = 1-(α/10)2-4 (a2/100):-2 Use MATLAB to Find the zeros and poles of H() Plot the poles and zeros on the -plane. The pot should include the uit circle. Plot the magnitude response (in dB) Plot the phase response. Deliverables: Your MATLAB code used to solve Problem 1 and all the generated plots.
PROBLEM 1 (20 points). Given the filter...
Problem #1. Topics: Z Transform Find the Z transform of: x[n]=-(0.9 )n-2u-n+5] X(Z) Problem #2. Topics: Filter Design, Effective Time Constant Design a causal 2nd order, normalized, stable Peak Filter centered at fo 1000Hz. Use only two conjugate poles and two zeros at the origin. The system is to be sampled at Fs- 8000Hz. The duration of the transient should be as close as possible to teft 7.5 ms. The transient is assumed to end when the largest pole elevated...
stuck on this question, please show all your work step
by step, thank you.
IF THE POLES OF THE LOCATED AT. b) H(근) のUSE-MATLAS TO PLOT IHI»)! oAT KIN OF A FILTER IS IT? 171 53 lilustrative Examples 5.3 ILLUSTRATIVE EXAMPLES Example 5.3-1: The following difference equation is known as the first- order trapezoidal integration rule in numerical analysis: n) - ) n-O (531) Find: The transfer function. The impulse response. The output if the input is the unit step...
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