Homework Answers
8. The Fourier Transform has been calculated as follow:
9. The determination of periodicity and the period of the signal
has been done as follow:
![9 9 (a) XUE 19.8 6! ( 3 2014 - -5 Periodic Signal Peried To = 32071 160 Frequency, for at TI f > f. = 160 Hz (6) x [n] = 116](http://img.homeworklib.com/questions/851d8ef0-9952-11eb-b068-9738ba8a802d.png?x-oss-process=image/resize,w_560)
10. The casual and stable nature of the system is found as
follow:
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8. Find the Fourier transform of the following signal. (5 points) x(0) 2 1 9. Determine...
QUESTIONS 1. Determine whether or not the LTI systems with the following impulse responses are causal...
QUESTIONS 1. Determine whether or not the LTI systems with the following impulse responses are causal and stable. Note that simply writing causal /noncausal, or stable /unstable is not enough, the verification of your answers are required to gain points from this question (15 puan) a. hon)-(0.5 u(n) +(1.01) u(n-1) b. h(n)-(0.5) u(n)+(1.01) u(1-n)
5- Determine whether or not each of the following LTI systems with the given impulse response...
5- Determine whether or not each of the following LTI systems with the given impulse response are memoryless: a) h(t) = 56(t- 1) b) h(t) = eT u(t) e) h[n] sinEn) d) h[n] = 26[n] 6- Determine whether or not each of the following LTI systems with the given impulse response are stable: a) h(t) = 2 b) h(t) = e2tu(t - 1) c) h[n] = 3"u[n] d) h[n] = cos(Tm)u[n] 7- Determine whether or not each of the following...
In digital signal processing. with explanation tnx will up 15. Is the function y[n]-x[n-1]-x[n-56] causal? a....
In digital signal processing. with explanation tnx
will up
15. Is the function y[n]-x[n-1]-x[n-56] causal? a. The system is non causal b. The system is causal >» c. Both causal and noncausal d. None of the above 16. Is the function y[n]x[n] stable in nature? a. It is stable - b. It is unstable c. Both stable and unstable d. None of the above 17. We define y[n] = nx[n]-(n-Dx[n]. Now, z[n] = z[n-1] + y[n]. Is z[n] a a....
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396]...
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396] Calculate the total average power of z(t). iv. [5%] If z(t) is passed through a low-pass filter and the power loss of the output signal should be optimized to be less than 5%, what should be the requirement of cutoff frequency of the low-pass filter?...
Signal system 8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the...
Signal system
8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the Fourier series coefficients for this signal. (4 points). b. If this signal passes through a LTI system with the impulse response h(t)=e* u(t), particularly, would the output signal also be a periodic signal ? If so, what would be the Fourier coefficients of the output signal ? (4 points). c. Give the mathematical expression for the output signal y(t). (2 points).
QUESTION 2 (20 MARKS) (a) A continuous time signal x(t) = 3e2tu(-t) is an input to...
QUESTION 2 (20 MARKS) (a) A continuous time signal x(t) = 3e2tu(-t) is an input to a Linear Time Invariant system of which the impulse response h(t) is shown as h(t) = { .. 12, -osts-2 elsewhere Compute the output y(t) of the system above using convolution in time domain for all values of time t. [8 marks) (b) The impulse response h[n] of an LTI system is given as a[n] = 4(0.6)”u[n] Determine if the system is stable. [3...
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t)...
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t) = 〉 1 0 < t < 1 0 t>1 Find the output y(t) of this system if the input is given by a) x(t) = 1 + cos(2nt) b) x(t)-cos(Tt) c) x(t) sin (t )l d) x(t) = 1 0 < t < 10 0 t 10 e) x(t) = δ(t-2)-5(t-4) f) a(t)-etu(t) Problem 2: For the same LTI system in Problem 1,...
2. Linearity Consider a system given with the following impulse response: (5%) h[n] 4u[1 a) Is the system LTI? b) Is it...
2. Linearity Consider a system given with the following impulse response: (5%) h[n] 4u[1 a) Is the system LTI? b) Is it causal? c) Is it stable?
2. Linearity Consider a system given with the following impulse response: (5%) h[n] 4u[1 a) Is the system LTI? b) Is it causal? c) Is it stable?
Problem 1. Determine if the LTI systems with impulse responses as given below are sta ble/unstable...
Problem 1. Determine if the LTI systems with impulse responses as given below are sta ble/unstable and causal/non-causal Note: u(t)/ ulnl represents unit-step. δ(1)/ δ[n] represents unit impulse. I. hl (t) = δ(t + 4)-5(5-t) 2. h2(l) e"cos(nt)u(-)
The given input signal for 2.7.2 is: x(t) = 3 cos(2 π t) + 6 sin(5 π t). Plz explain ...
The given input signal for 2.7.2 is: x(t) = 3 cos(2
π t) + 6 sin(5 π t).Plz explain steps.Given a causal LTI system described by the differential equation find \(H(s),\) the \(\mathrm{ROC}\) of \(H(s),\) and the impulse response \(h(t)\) of the system. Classify the system as stable/unstable. List the poles of \(H(s) .\) You should the Matlab residue command for this problem.(a) \(y^{\prime \prime \prime}+3 y^{\prime \prime}+2 y^{\prime}=x^{\prime \prime}+6 x^{\prime}+6 x\)2.7.2 The signal \(x(t)\) in the previous problem is...
QUESTIONS 1. Determine whether or not the LTI systems with the following impulse responses are causal and stable. Note that simply writing causal /noncausal, or stable /unstable is not enough, the verification of your answers are required to gain points from this question (15 puan) a. hon)-(0.5 u(n) +(1.01) u(n-1) b. h(n)-(0.5) u(n)+(1.01) u(1-n)
5- Determine whether or not each of the following LTI systems with the given impulse response are memoryless: a) h(t) = 56(t- 1) b) h(t) = eT u(t) e) h[n] sinEn) d) h[n] = 26[n] 6- Determine whether or not each of the following LTI systems with the given impulse response are stable: a) h(t) = 2 b) h(t) = e2tu(t - 1) c) h[n] = 3"u[n] d) h[n] = cos(Tm)u[n] 7- Determine whether or not each of the following...
In digital signal processing. with explanation tnx
will up
15. Is the function y[n]-x[n-1]-x[n-56] causal? a. The system is non causal b. The system is causal >» c. Both causal and noncausal d. None of the above 16. Is the function y[n]x[n] stable in nature? a. It is stable - b. It is unstable c. Both stable and unstable d. None of the above 17. We define y[n] = nx[n]-(n-Dx[n]. Now, z[n] = z[n-1] + y[n]. Is z[n] a a....
(a) Given the following periodic signal a(t) a(t) -0.5 -0.25 0 0.25 0.5 0.75 1 1.25 1.5 i. [2%) Determine the fundamental period T ii. [5%] Derive the Fourier series coefficients of x(t). iii. [396] Calculate the total average power of z(t). iv. [5%] If z(t) is passed through a low-pass filter and the power loss of the output signal should be optimized to be less than 5%, what should be the requirement of cutoff frequency of the low-pass filter?...
Signal system
8. Consider the periodic signal x(t) = cos(2nt) + cos(2nt) I. a. Find the Fourier series coefficients for this signal. (4 points). b. If this signal passes through a LTI system with the impulse response h(t)=e* u(t), particularly, would the output signal also be a periodic signal ? If so, what would be the Fourier coefficients of the output signal ? (4 points). c. Give the mathematical expression for the output signal y(t). (2 points).
QUESTION 2 (20 MARKS) (a) A continuous time signal x(t) = 3e2tu(-t) is an input to a Linear Time Invariant system of which the impulse response h(t) is shown as h(t) = { .. 12, -osts-2 elsewhere Compute the output y(t) of the system above using convolution in time domain for all values of time t. [8 marks) (b) The impulse response h[n] of an LTI system is given as a[n] = 4(0.6)”u[n] Determine if the system is stable. [3...
Problem 1: Let the impulse response of an LTI system be given by 0 t< h(t) = 〉 1 0 < t < 1 0 t>1 Find the output y(t) of this system if the input is given by a) x(t) = 1 + cos(2nt) b) x(t)-cos(Tt) c) x(t) sin (t )l d) x(t) = 1 0 < t < 10 0 t 10 e) x(t) = δ(t-2)-5(t-4) f) a(t)-etu(t) Problem 2: For the same LTI system in Problem 1,...
2. Linearity Consider a system given with the following impulse response: (5%) h[n] 4u[1 a) Is the system LTI? b) Is it causal? c) Is it stable?
2. Linearity Consider a system given with the following impulse response: (5%) h[n] 4u[1 a) Is the system LTI? b) Is it causal? c) Is it stable?
Problem 1. Determine if the LTI systems with impulse responses as given below are sta ble/unstable and causal/non-causal Note: u(t)/ ulnl represents unit-step. δ(1)/ δ[n] represents unit impulse. I. hl (t) = δ(t + 4)-5(5-t) 2. h2(l) e"cos(nt)u(-)
The given input signal for 2.7.2 is: x(t) = 3 cos(2
π t) + 6 sin(5 π t).Plz explain steps.Given a causal LTI system described by the differential equation find \(H(s),\) the \(\mathrm{ROC}\) of \(H(s),\) and the impulse response \(h(t)\) of the system. Classify the system as stable/unstable. List the poles of \(H(s) .\) You should the Matlab residue command for this problem.(a) \(y^{\prime \prime \prime}+3 y^{\prime \prime}+2 y^{\prime}=x^{\prime \prime}+6 x^{\prime}+6 x\)2.7.2 The signal \(x(t)\) in the previous problem is...
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