Suppose an LTI system has frequency response
. Find the system function
.
Hint: expand the cosine using Euler's formula and then do a little bit of pattern matching.
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Suppose an LTI system has frequency response
. Find the system function .
Hint: expand the...
3. Suppose that the frequency response of an LTI system is given by (a) What is...
3. Suppose that the frequency response of an LTI system is given by (a) What is the impulse response hinl) of the system? (b) Suppose that the input signal has the form zin-Ae'? n. For what values of ?0 in the range -r S will we have yn0 for all n? (c) Find the output y[n] of the system for the input x[n] = 3 + ?[n-2] cos(0.5?n 0.25m
4. LTI Systems and Erponential Response. (12 pts) (a) (2 pts) Suppose an LTI system has...
4. LTI Systems and Erponential Response. (12 pts) (a) (2 pts) Suppose an LTI system has input-output relationship y(t) 2r(t+3). What is the transfer function H(jw) of the given system. Show that H(jw)2. Hint: H(jw(tejdt (b) (5 pts) Suppose an LTI system has input-output relationship y(t)2r(t+3) as Problem 4-(a). Find the output y(t) using the complex exponential response method as discussed in lecture for the input r(t) = ej2t + 2 cos2(t). Hint: cos2(0) 1 (20 cos(26) an d 1-ejot...
A system is described by the following transfer function: A) What is the frequency response, H(f)?...
A system is described by the following transfer function:
A) What is the frequency response, H(f)?
B) What is the magnitude and phase (in degrees) of the frequency
response at a frequency of w=3 rads/sec, corresponding to
hz?
$2 + 16 H(s) = - 11s(s+2)(2+1) We were unable to transcribe this image
8) Find the output of an LTI system with the input x(t) with the sampling frequency...
8) Find the output of an LTI system with the input x(t) with the sampling frequency of fn = 10 Hz, and the filter/transfer function (el) below. x(t) = 2 + cos (2007t + ) + 2sin(1007t) Hew) = 1 + 2e1W + cos(2w)
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to...
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to e of the system to r(t)= eat cos (Bt)u (t). You have to express the response in terms of 5(t), u (t), sine function, and exponential function. (20 pts) -ly(t)), where * denotes convolution operator. (3) ()[() ]- dt d d Hint: dt
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to e of the system to...
1. An LTI system has the transfer function (or frequency response) H(u)- a) What is the...
1. An LTI system has the transfer function (or frequency response) H(u)- a) What is the magnitude of H()? b) What is the phase of H(u)? c) Determine the impulse response of this system. d) Find the differential equation between the input and output of this system. e) What is the output of the system to the input x()c
QUESTION 2 (12 marks) The step response of an LTI system is given by g(t) =...
QUESTION 2 (12 marks) The step response of an LTI system is given by g(t) = (1 - e-3t)u(t) (a) Determine the impulse response, h(t), of the system. (b) Use the linearity and time invariance properties to determine the response of the system to the input x(t) = 38(t) + 2u(t – 2). (c) Determine the frequency response of the system H(jw). [Hint: Use the tables in the formula sheet]. (d) Hence determine the output y(t) for the input signal...
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we...
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we analyce the denominator and use partial fraction expansion to write H() in the form Then we notice that each of these fraction terms is the Fourier of an exponentiol multiplied by a unit step as per the Table J (b) What is the output y(t) from the system if...
(Frequency response of CT LTI systems): You want to design a system whose unit impulse response has the form:
(Frequency response of CT LTI systems): You want to design a system whose unit impulse response has the form: h(t) =u(t) - u(t - N). Find all possible values of N >0 such that when the input signal x(t) = cos(πt), the output signal y(t) = 0 for all t.
1. Suppose that for the LTi system depicred in the following Sgure al the impulse response...
1. Suppose that for the LTi system depicred in the following Sgure al the impulse response and the transfer function ane given by The input signal it) is the square wave of Figure (bl, whare t is in seconds. Since the fundamental period isT?-2r, the fundamental frequency is ab-2s/To-1 rad/s and kas,-k. lbi (a) use the Table provided to find the exponential Fourier serias of she signal it The xpceential Fourier series for the signal may be givn by where...
3. Suppose that the frequency response of an LTI system is given by (a) What is the impulse response hinl) of the system? (b) Suppose that the input signal has the form zin-Ae'? n. For what values of ?0 in the range -r S will we have yn0 for all n? (c) Find the output y[n] of the system for the input x[n] = 3 + ?[n-2] cos(0.5?n 0.25m
4. LTI Systems and Erponential Response. (12 pts) (a) (2 pts) Suppose an LTI system has input-output relationship y(t) 2r(t+3). What is the transfer function H(jw) of the given system. Show that H(jw)2. Hint: H(jw(tejdt (b) (5 pts) Suppose an LTI system has input-output relationship y(t)2r(t+3) as Problem 4-(a). Find the output y(t) using the complex exponential response method as discussed in lecture for the input r(t) = ej2t + 2 cos2(t). Hint: cos2(0) 1 (20 cos(26) an d 1-ejot...
A system is described by the following transfer function:
A) What is the frequency response, H(f)?
B) What is the magnitude and phase (in degrees) of the frequency
response at a frequency of w=3 rads/sec, corresponding to
hz?
$2 + 16 H(s) = - 11s(s+2)(2+1) We were unable to transcribe this image
8) Find the output of an LTI system with the input x(t) with the sampling frequency of fn = 10 Hz, and the filter/transfer function (el) below. x(t) = 2 + cos (2007t + ) + 2sin(1007t) Hew) = 1 + 2e1W + cos(2w)
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to e of the system to r(t)= eat cos (Bt)u (t). You have to express the response in terms of 5(t), u (t), sine function, and exponential function. (20 pts) -ly(t)), where * denotes convolution operator. (3) ()[() ]- dt d d Hint: dt
eatu(t), (a >0), is 6(t). Find the response 5. The response of an LTI system to e of the system to...
1. An LTI system has the transfer function (or frequency response) H(u)- a) What is the magnitude of H()? b) What is the phase of H(u)? c) Determine the impulse response of this system. d) Find the differential equation between the input and output of this system. e) What is the output of the system to the input x()c
QUESTION 2 (12 marks) The step response of an LTI system is given by g(t) = (1 - e-3t)u(t) (a) Determine the impulse response, h(t), of the system. (b) Use the linearity and time invariance properties to determine the response of the system to the input x(t) = 38(t) + 2u(t – 2). (c) Determine the frequency response of the system H(jw). [Hint: Use the tables in the formula sheet]. (d) Hence determine the output y(t) for the input signal...
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we analyce the denominator and use partial fraction expansion to write H() in the form Then we notice that each of these fraction terms is the Fourier of an exponentiol multiplied by a unit step as per the Table J (b) What is the output y(t) from the system if...
1. Suppose that for the LTi system depicred in the following Sgure al the impulse response and the transfer function ane given by The input signal it) is the square wave of Figure (bl, whare t is in seconds. Since the fundamental period isT?-2r, the fundamental frequency is ab-2s/To-1 rad/s and kas,-k. lbi (a) use the Table provided to find the exponential Fourier serias of she signal it The xpceential Fourier series for the signal may be givn by where...
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