![2. (Combining systems (30 Pts)] Hi and H2 be continuous-time LTI systems respectively with impulse responses hi and h2. (a) Provide the expression of Hi(r) (t) for all t using the impulse response h (5 Pts) (b) Provide the expression of H21r)(t) for all t using the impulse response h2 (5 Pts) (c)Let Hs be the serial connection of H1 and H2, i.e Draw a block diagram for the above equation 5 Pts). Show that H3 is another LTI system. Justify your answer (5 Pts). Hint: Can you represent Hs with a convolution? (d) Let H4 be the parallel connection of Њ and H2, ie, Draw a block diagram for the above equation 5 Pts). Show that Hs is another LTI system. Justify your answer (5 Pts). Hint: Can you represent Hs with a convolution?](http://img.homeworklib.com/questions/5d9dfbc0-0ed2-11ec-810e-e91ded5f473f.png?x-oss-process=image/resize,w_560)
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2. (Combining systems (30 Pts)] Hi and H2...
signals and systems Question 1 (30%): Consider a LTI systern which is comprised of four subsystems...
signals and systems
Question 1 (30%): Consider a LTI systern which is comprised of four subsystems whose impulse responses are hi(t), h2(t). ha(t), and ha(t). u(t) f(t) hi(t) h2(t) 13 ha(1) Where: hi (t) = δ(t + 1) h2(t) = 2(u(t)-u(t-1)] hs(t) = 201t-2) h1(t) = u(t + 2)-u(t) a) (8%) Compute the overall impulse response htotal(t) of the system comprised of hi(t), h2(t), hs(t), and h4(t). Sketch and write the expression for htotai(t) b) (4%) Is the total system...
2. Consider the following interconnection of four LTI systems where each system is described by its...
2. Consider the following interconnection of four LTI systems where each system is described by its impulse response, denoted by h,(t) for i E (1,2,3,4): i (t) hi(t) r(t) z(t) (t)h) но hs(t) alt) h4(t) 2(t) It is not hard, but is tedious, to show that an interconnection of LTI systems is LTI. Assuming this result, consider the system a(t) b(t) where r(t) and b(t) are the same signals in the two block diagrams and h(t) is the impulse response...
3. Impulse Response and Step Response. (25 pts) Consider the following LTI systems: • T1: Has...
3. Impulse Response and Step Response. (25 pts) Consider the following LTI systems: • T1: Has input-output relationship yı(t) = -X1(t – 5) 1<t<4 • T2: Has impulse response hz(t) = { therwise • T3: Has step response s3(t) = -4u(t + 3) • T4: Has step response s4(t) = -tu(t) (a) (5 pts) What is the impulse response hi(t) of system Tj? (b) (10 pts) What is the step response sz(t) of system T2? Write it in terms of...
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...
(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....
a = 3 signals and systems 1) [10 pts. Let a system be defined as ta...
a = 3
signals and systems
1) [10 pts. Let a system be defined as ta y(t) x(31 - 2a)dt 2a Is this system b) No b) No b) No vii) memoryless? a) Yes viii) Linear? a) Yes ix) Time invariant? a) Yes x) Causal? a) Yes xi) BIBO stable? a) Yes 2) [5 pts. What is the impulse response h(t)? 3) [10 pts.] Let a signal in s domain b) No b) No 2 Y(S) Sa What is the...
2. (30 pts) A signal 7: n İs applied lo an ll.l system I (hi [n) outputting y1,,,and il is also a...
2. (30 pts) A signal 7: n İs applied lo an ll.l system I (hi [n) outputting y1,,,and il is also applied to an LTI system 2 (h2n) outputng Then te sum of nnl and s applied to an LTI systcm 3 (hsln) oulputting n The relationships are given in the following cquations. Assume thaforn < 0 (a) (15 pts) Find the valo e impulse respsofte system 3 (b) (15 pts) Find the valucof the impulse response of the t...
Problem 4 (30 pts) This problem explores the sampling theorem and its consequences. Consider the system...
Problem 4 (30 pts) This problem explores the sampling theorem and its consequences. Consider the system shown in the figure below, where the two input signals are given to be xi(t) = sinc(10t) and x2(t) = sinc(6t). ylt) z(t) LTI →2;(+) ht) Xalt) P(+) - E81-nt) a) State the sampling theorem. Be sure to include all conditions for its validity. (5 pts) b) What is the minimum frequency at which y(t) must be sampled such that it could be completely...
(a) x(t) undergoes impulse train sampling through the following system below: x(t) 20 n=-00 3 i. (5 pts) What is the s...
(a) x(t) undergoes impulse train sampling through the following system below: x(t) 20 n=-00 3 i. (5 pts) What is the sampling frequency w used by this system? What is the equation for the output Fourier Transform X,(jw) in terms of X(jw)? ii. (5 pts) Using your equation from (i), sketch the output spectrum X, (jw) vs. w. Make sure to label all critical points iii. (5 pts) Using your sketch from (ii), determine if there is aliasing or not....
Problem 2. (35 marks) Time-Domain Analysis of Systems (a) (10 marks) x(t) = u(t – 3)...
Problem 2. (35 marks) Time-Domain Analysis of Systems (a) (10 marks) x(t) = u(t – 3) – u(t – 5) and h(t) = E=-1 8(t - k). Determine y(t) = x(t) * h(t). (b) (25 marks) An LTID system is specified by the following equation: 2y[n + 1] – 3y[n] + y[n – 1] = 4.x[n + 1] – 3x[n]. i) [8 marks] Draw a schematic diagram for the LTID system in terms of delay compo- nents "D". ii) [12...
signals and systems
Question 1 (30%): Consider a LTI systern which is comprised of four subsystems whose impulse responses are hi(t), h2(t). ha(t), and ha(t). u(t) f(t) hi(t) h2(t) 13 ha(1) Where: hi (t) = δ(t + 1) h2(t) = 2(u(t)-u(t-1)] hs(t) = 201t-2) h1(t) = u(t + 2)-u(t) a) (8%) Compute the overall impulse response htotal(t) of the system comprised of hi(t), h2(t), hs(t), and h4(t). Sketch and write the expression for htotai(t) b) (4%) Is the total system...
2. Consider the following interconnection of four LTI systems where each system is described by its impulse response, denoted by h,(t) for i E (1,2,3,4): i (t) hi(t) r(t) z(t) (t)h) но hs(t) alt) h4(t) 2(t) It is not hard, but is tedious, to show that an interconnection of LTI systems is LTI. Assuming this result, consider the system a(t) b(t) where r(t) and b(t) are the same signals in the two block diagrams and h(t) is the impulse response...
3. Impulse Response and Step Response. (25 pts) Consider the following LTI systems: • T1: Has input-output relationship yı(t) = -X1(t – 5) 1<t<4 • T2: Has impulse response hz(t) = { therwise • T3: Has step response s3(t) = -4u(t + 3) • T4: Has step response s4(t) = -tu(t) (a) (5 pts) What is the impulse response hi(t) of system Tj? (b) (10 pts) What is the step response sz(t) of system T2? Write it in terms of...
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...
(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....
a = 3
signals and systems
1) [10 pts. Let a system be defined as ta y(t) x(31 - 2a)dt 2a Is this system b) No b) No b) No vii) memoryless? a) Yes viii) Linear? a) Yes ix) Time invariant? a) Yes x) Causal? a) Yes xi) BIBO stable? a) Yes 2) [5 pts. What is the impulse response h(t)? 3) [10 pts.] Let a signal in s domain b) No b) No 2 Y(S) Sa What is the...
2. (30 pts) A signal 7: n İs applied lo an ll.l system I (hi [n) outputting y1,,,and il is also applied to an LTI system 2 (h2n) outputng Then te sum of nnl and s applied to an LTI systcm 3 (hsln) oulputting n The relationships are given in the following cquations. Assume thaforn < 0 (a) (15 pts) Find the valo e impulse respsofte system 3 (b) (15 pts) Find the valucof the impulse response of the t...
Problem 4 (30 pts) This problem explores the sampling theorem and its consequences. Consider the system shown in the figure below, where the two input signals are given to be xi(t) = sinc(10t) and x2(t) = sinc(6t). ylt) z(t) LTI →2;(+) ht) Xalt) P(+) - E81-nt) a) State the sampling theorem. Be sure to include all conditions for its validity. (5 pts) b) What is the minimum frequency at which y(t) must be sampled such that it could be completely...
(a) x(t) undergoes impulse train sampling through the following system below: x(t) 20 n=-00 3 i. (5 pts) What is the sampling frequency w used by this system? What is the equation for the output Fourier Transform X,(jw) in terms of X(jw)? ii. (5 pts) Using your equation from (i), sketch the output spectrum X, (jw) vs. w. Make sure to label all critical points iii. (5 pts) Using your sketch from (ii), determine if there is aliasing or not....
Problem 2. (35 marks) Time-Domain Analysis of Systems (a) (10 marks) x(t) = u(t – 3) – u(t – 5) and h(t) = E=-1 8(t - k). Determine y(t) = x(t) * h(t). (b) (25 marks) An LTID system is specified by the following equation: 2y[n + 1] – 3y[n] + y[n – 1] = 4.x[n + 1] – 3x[n]. i) [8 marks] Draw a schematic diagram for the LTID system in terms of delay compo- nents "D". ii) [12...
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