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Consider a system with a real impulse response. If we know its magnitude response | H(w)...
Consider a LTI system with impulse response h[n] = u[n]*a^n, where |a| < 1. a) Determine...
Consider a LTI system with impulse response h[n] = u[n]*a^n, where |a| < 1. a) Determine the frequency response of the system. b) Find the magnitude response and the phase response, given a = 1/2. No plots. c) Consider a LTI system whose impulse response h1[n] is a time-shifted version of h[n], i.e., h1[n] = h[n − n0]. Compute the frequency response H1(e^(jΩ)), and represent H1(e^(jΩ)) in terms of H(e^(jΩ)).
Consider a discrete-time LTI system with impulse response Sketch the magnitude of the frequency response of...
Consider a discrete-time LTI system with impulse response
Sketch the magnitude of the frequency response
of the system. Provide enough details in your sketch to convey the
pattern.
sin((2n/3)n hln h[n] =
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts)...
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts) Obtain and plot the unit step response of S. (b) (2pts) Is S stable? Is it causal? Explain Two unrelated questions (c) (2pts) Is the ideal low-pass continuous-time filter (frequency response H(w) for H()0 otherwise) causal? Explain (d) (4 pts) Is the discrete-time...
Consider a real LTI system with the following properties. 1 - Its frequency response H(w) is...
Consider a real LTI system with the following properties. 1 - Its frequency response H(w) is real and linear on [0, 1] (and therefore on ( - 11,0] by symmetry) as illustrated below (warning: the true values and signs of Q and b may not be those shown in the graph which is only for illustration). 2. It preserves the input ( - 1)". 3- It transforms the periodic sequence X[n]shown below into a constant sequence. What must be the...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
4. Consider a certain system defined by impulse response h(n) such that calculate the following: i....
4. Consider a certain system defined by impulse response h(n) such that calculate the following: i. transfer function ii. magnitude response of the filter i phase response of the filter iv. sketch magnitude and phase response of the filter at intervals (π/10) radians (13 Marks) (3 Marks) (3 Marks) (6 Marks)
Consider an impulse response h(t) = 5e-Stu(t) and if the system is causal, what is the...
Consider an impulse response h(t) = 5e-Stu(t) and if the system is causal, what is the unit step response s(t)? [Hint: for a causal system, hít – 1) = 0 for 1> 5(1 +e+St)uce) O re-** - 1) (t) O(1-* Xu(t) (1+e-su(t)
Problem ↑ h[n] 0.5 0.25t r0.25 Consider the impulse response h|n] shown in the figure. (i)...
Problem ↑ h[n] 0.5 0.25t r0.25 Consider the impulse response h|n] shown in the figure. (i) Show that the impulse response corresponds to a lowpass filter by determining its magnitude response |H(e ) (ii) What is the phase response of the filter? How can you obtain a linear-phase filter from this hn? (iii) Obtain a three-tap linear-phase highpass filter by suitably modifying the coef- ficients of h|n]. Verify your answer by plotting the magnitude response of the new filter.
Given the constraints: 1) frequency response: H(ejw) = 0 at w = 0 and w =...
Given the constraints:
1) frequency response: H(ejw) = 0 at w = 0 and w =
.
2)
What are the impulse response coefficients h[0],h[1],h[2] that
is length 3 causal and finite impulse response filter . Sketch
phase and magnitude of frequency response.
We were unable to transcribe this image1 H(eju)|dw = 2 27 J-
2. Consider a system described by Determine the system function H(z), the impulse response and the...
2. Consider a system described by Determine the system function H(z), the impulse response and the region of convergence of the system for all possible regions of convergence.
Consider a discrete-time LTI system with impulse response
Sketch the magnitude of the frequency response
of the system. Provide enough details in your sketch to convey the
pattern.
sin((2n/3)n hln h[n] =
Question 1 (10 pts): Consider the continuous-time LTI system S whose unit impulse response h is given by Le., h consists of a unit impulse at time 0 followed by a unit impulse at time (a) (2pts) Obtain and plot the unit step response of S. (b) (2pts) Is S stable? Is it causal? Explain Two unrelated questions (c) (2pts) Is the ideal low-pass continuous-time filter (frequency response H(w) for H()0 otherwise) causal? Explain (d) (4 pts) Is the discrete-time...
Consider a real LTI system with the following properties. 1 - Its frequency response H(w) is real and linear on [0, 1] (and therefore on ( - 11,0] by symmetry) as illustrated below (warning: the true values and signs of Q and b may not be those shown in the graph which is only for illustration). 2. It preserves the input ( - 1)". 3- It transforms the periodic sequence X[n]shown below into a constant sequence. What must be the...
(e) Consider an LTI system with impulse response h(t) = π8ǐnc(2(t-1). i. (5 pts) Find the frequency response H(jw). Hint: Use the FT properties and pairs tables. ii. (5 pts) Find the output y(t) when the input is (tsin(t) by using the Fourier Transform method. 3. Fourier Transforms: LTI Systems Described by LCCDE (35 pts) (a) Consider a causal (meaning zero initial conditions) LTI system represented by its input-output relationship in the form of a differential equation:-p +3讐+ 2y(t)--r(t). i....
4. Consider a certain system defined by impulse response h(n) such that calculate the following: i. transfer function ii. magnitude response of the filter i phase response of the filter iv. sketch magnitude and phase response of the filter at intervals (π/10) radians (13 Marks) (3 Marks) (3 Marks) (6 Marks)
Consider an impulse response h(t) = 5e-Stu(t) and if the system is causal, what is the unit step response s(t)? [Hint: for a causal system, hít – 1) = 0 for 1> 5(1 +e+St)uce) O re-** - 1) (t) O(1-* Xu(t) (1+e-su(t)
Problem ↑ h[n] 0.5 0.25t r0.25 Consider the impulse response h|n] shown in the figure. (i) Show that the impulse response corresponds to a lowpass filter by determining its magnitude response |H(e ) (ii) What is the phase response of the filter? How can you obtain a linear-phase filter from this hn? (iii) Obtain a three-tap linear-phase highpass filter by suitably modifying the coef- ficients of h|n]. Verify your answer by plotting the magnitude response of the new filter.
Given the constraints:
1) frequency response: H(ejw) = 0 at w = 0 and w =
.
2)
What are the impulse response coefficients h[0],h[1],h[2] that
is length 3 causal and finite impulse response filter . Sketch
phase and magnitude of frequency response.
We were unable to transcribe this image1 H(eju)|dw = 2 27 J-
2. Consider a system described by Determine the system function H(z), the impulse response and the region of convergence of the system for all possible regions of convergence.
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