Homework Answers
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2. Let the rectangle pulse x(n) = u(n)-u(n – 10) be an input to an LTI...
1. An LTI system has impulse response defined by h (n )={2 ,2 ,−1,−1 ,−1,−1}first 2...
1. An LTI system has impulse response defined by h (n )={2 ,2 ,−1,−1 ,−1,−1}first 2 zero . Determine the outputs when the input x(n) is (a) u(n ) ; (b) u(n−4 ) 2. Let the rectangle pulse x ( n )=u ( n ) −u (n −10 ) be an input to an LTI system with impulse response h (n )=(0.9 )n u (n ) . Determine the output y ( n ) . (Hint: You need to consider muliple...
Name: 10. [8 points] Consider a discrete-time LTI system with input x[n] and out- put y[n]....
Name: 10. [8 points] Consider a discrete-time LTI system with input x[n] and out- put y[n]. When the input signal x[n] = (6)" is applied to the system, the output signal is y[n] = 0 for all n When the input signal xn] (3)" u[n] is applied to the system, the output signal is y[n] = A 8[n] + 2 (5)" u[n] for all n, where A is a constant number a) Find A. b) Find the impulse response of...
Consider the LTI system described by the following impulse response: (a) h(n) = 2(0.5)n u(n). Determine:...
Consider the LTI system described by the following impulse response: (a) h(n) = 2(0.5)n u(n). Determine: (i) The system function representation; (ii) the difference-equation representation (Note: this is just terminology that refers to expressing the input and output time-domain signals in the form of an equation. E.g., what we did when we went over the equations for block diagrams); (iii) The pole-zero plot, sketched by hand; and (iv) the output y(n) if the input is x(n) = (0.25)n u(n) [10...
Consider an LTI system with input sequence x[n] and output sequence y[n] that satisfy the difference equation
Consider an LTI system with input sequence x[n] and output sequence y[n] that satisfy the difference equation 3y[n] – 7y[n – 1] + 2y[n – 2] = 3x[n] – 3x[n – 1] (2.1) The fact that sequences x[ ] and y[ ] are in input-output relation and satisfy (2.1) does not yet determine which LTI system. a) We assume each possible input sequence to this system has its Z-transform and that the impulse response of this system also has its Z-transform. Express the...
1. An LTI digital system with impulse response h[n] = 2(1/4)"u[n] produces an output y[n] =...
1. An LTI digital system with impulse response h[n] = 2(1/4)"u[n] produces an output y[n] = (-3)"u[n]. Determine the corresponding input x[n] using Z-transform. (30 points)
SIGNALS and SYSTEMS HOMEWORK-IV 1. Let X(t) be the input to an LTI system with unit...
SIGNALS and SYSTEMS HOMEWORK-IV 1. Let X(t) be the input to an LTI system with unit impulse response h(t), where x(t) = e-tu(t) h(t) = u(t -3). Determine and plot the output y(t) = x(t) *h(t). Both analytically and graphical method. (25 p)
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n)...
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
LTI Systems. Consider two LTI subsystems that are connected in series
(a) LTI Systems. Consider two LTI subsystems that are connected in series, where system Tl has step response s1(t)=u(t-1)-u(t-5) and system T2 has impulse response h2t = e-3tu(t). Find the overall impulse response h(t). Hint: you will need to find h1(t) first (b)Fourier Series. The input signal r(t) and impulse response h(t) of an LTI system are as follows:x(t) = sin(2t)cos(t)-ej3t +2 and h(t) = sin(2t)/t Use the Fourier Series method to find the output y(t) (c)Parseval's Identity and Theorem. Consider the system in the...
Problem 1. (10 points) The signal x()u(-2) is applied to the input of an LTI system...
Problem 1. (10 points) The signal x()u(-2) is applied to the input of an LTI system whose impulse response IS h(1)=-rect |- 4 (a) Sketch x(t), h(t) and x(r)h(t - 7) (b) Determine y)-x(i)* h() for all possible values of (interval by interval).
Problem 2: Find the impulse response h(n) of a causal LTI system if the input x(n)...
Problem 2: Find the impulse response h(n) of a causal LTI system if the input x(n) and the output y(n) are given as follows 72 42)un-1) y(n)-G)na(n) xnun)
Name: 10. [8 points] Consider a discrete-time LTI system with input x[n] and out- put y[n]. When the input signal x[n] = (6)" is applied to the system, the output signal is y[n] = 0 for all n When the input signal xn] (3)" u[n] is applied to the system, the output signal is y[n] = A 8[n] + 2 (5)" u[n] for all n, where A is a constant number a) Find A. b) Find the impulse response of...
1. An LTI digital system with impulse response h[n] = 2(1/4)"u[n] produces an output y[n] = (-3)"u[n]. Determine the corresponding input x[n] using Z-transform. (30 points)
SIGNALS and SYSTEMS HOMEWORK-IV 1. Let X(t) be the input to an LTI system with unit impulse response h(t), where x(t) = e-tu(t) h(t) = u(t -3). Determine and plot the output y(t) = x(t) *h(t). Both analytically and graphical method. (25 p)
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
Problem 1. (10 points) The signal x()u(-2) is applied to the input of an LTI system whose impulse response IS h(1)=-rect |- 4 (a) Sketch x(t), h(t) and x(r)h(t - 7) (b) Determine y)-x(i)* h() for all possible values of (interval by interval).
Problem 2: Find the impulse response h(n) of a causal LTI system if the input x(n) and the output y(n) are given as follows 72 42)un-1) y(n)-G)na(n) xnun)
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