![1. (25 points) Consider the discrete-time LTI “at resť system described by In+ 2] + 5y[n+ 1] + 6y[n] = x[n + 1] Use the itera](http://img.homeworklib.com/questions/7c272380-e5a2-11ea-8d23-cd6ade7f8e21.png?x-oss-process=image/resize,w_560)
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1. (25 points) Consider the discrete-time LTI “at resť system described by In+ 2] + 5y[n+...
For a causal LTI discrete-time system described by the difference equation:
For a causal LTI discrete-time system described by the difference equation: y[n] + y[n – 1] = x[n] a) Find the transfer function H(z).b) Find poles and zeros and then mark them on the z-plane (pole-zero plot). Is this system BIBO? c) Find its impulse response h[n]. d) Draw the z-domain block diagram (using the unit delay block z-1) of the discrete-time system. e) Find the output y[n] for input x[n] = 10 u[n] if all initial conditions are 0.
Discrete-time convolution. Use of shift invariance for LTI systems. A discrete-time LTI system is described the...
Discrete-time convolution. Use of shift invariance for LTI systems. A discrete-time LTI system is described the its impulse response h[n]. h[n] = (5)"u[n]. n-3 1 An input x[n] = u[n – 4) is applied. The output of the system y[n] is given by: x[r] – 54 G)" ()") un 14 The correct answer is not provided gắn] = [16(5)” – 54(5) ] n] y[n] = [16()" – 54(+)"] uſn – 4
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n)...
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1 system #1 system #2...
Consider the cascade of LTI discrete-time systems shown in Figure P2.37. LTI System 1 hi[n], H...
Consider the cascade of LTI discrete-time systems shown in Figure P2.37. LTI System 1 hi[n], H (el) LTI System 2 h2[n], H2(eje) Figure P2.37 The first system is described by the frequency response Hi(j =c-joo < 0.25% 11 0.25% < and the second system is described by <A hain) = 2 Sin(0.57) (a) Determine an equation that defines the frequency response, H(e)®), of the overall system over the range -- SUSA. (b) Sketch the magnitude. He"), and the phase, ZH(e)),...
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 a discrete-time LTI system with impulse response hn on-un-1), where jal < 1. Find the...
Consider a discrete-time LTI system with impulse response hn on-un-1), where jal < 1. Find the output y[n] of the system to the input x[n] = un +1].
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n...
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n] and output y[n] described by bx[n-21- ax[n-3 for n 2 0, where a and b are real-valued positive coefficients. A) Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? B) What are the initial conditions and their values? Why? C) Draw the block diagram of the filter relating input x[n] and output y[n] D) Derive a formula for the transfer function in...
Consider an LTI discrete-time system that has impulse response h n Tn-12) 1 if otherwise a) Deter...
Consider an LTI discrete-time system that has impulse response h n Tn-12) 1 if otherwise a) Determine the magnitude H(Q and the phase response LH(D for-r < Ω < π Enter Ω as "and enter the piecev se function Η Ω using the hea side function b)Determine the output of the system, rn, if the input is given by z n-Sn-9 +com( ) Enter your answer in terms of hin y[n] = In your answers, enter 2(n) for a discrete-time...
6) Consider a discrete-time LTI system with impulse response h[n] = response h[n] = ( 1)...
6) Consider a discrete-time LTI system with impulse response h[n] = response h[n] = ( 1) u[n]. Use Fourie transforms to determine the response of this system to the input x[n] = ml + un).
A causal discrete-time LTI system is described by the equation
A causal discrete-time LTI system is described by the equationwhere z is the input signal, and y the output signal y(n) = 1/3x(n) + 1/3x(n -1) + 1/3x(n - 2) (a) Sketch the impulse response of the system. (b) What is the dc gain of the system? (Find Hf(0).) (c) Sketch the output of the system when the input x(n) is the constant unity signal, x(n) = 1. (d) Sketch the output of the system when the input x(n) is the unit step signal, x(n)...
Discrete-time convolution. Use of shift invariance for LTI systems. A discrete-time LTI system is described the its impulse response h[n]. h[n] = (5)"u[n]. n-3 1 An input x[n] = u[n – 4) is applied. The output of the system y[n] is given by: x[r] – 54 G)" ()") un 14 The correct answer is not provided gắn] = [16(5)” – 54(5) ] n] y[n] = [16()" – 54(+)"] uſn – 4
(2) Consider the causal discrete-time LTI system with an input r (n) and an output y(n) as shown in Figure 1, where K 6 (constant), system #1 is described by its impulse response: h(n) = -36(n) + 0.48(n- 1)+8.26(n-2), and system # 2 has the difference equation given by: y(n)+0.1y(n-1)+0.3y(n-2)- 2a(n). (a) Determine the corresponding difference equation of the system #1. Hence, write its fre- quency response. (b) Find the frequency response of system #2. 1 system #1 system #2...
Consider the cascade of LTI discrete-time systems shown in Figure P2.37. LTI System 1 hi[n], H (el) LTI System 2 h2[n], H2(eje) Figure P2.37 The first system is described by the frequency response Hi(j =c-joo < 0.25% 11 0.25% < and the second system is described by <A hain) = 2 Sin(0.57) (a) Determine an equation that defines the frequency response, H(e)®), of the overall system over the range -- SUSA. (b) Sketch the magnitude. He"), and the phase, ZH(e)),...
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 a discrete-time LTI system with impulse response hn on-un-1), where jal < 1. Find the output y[n] of the system to the input x[n] = un +1].
Q8) Consider the following causal linear time-invariant (LTI) discrete-time filter with input x[n] and output y[n] described by bx[n-21- ax[n-3 for n 2 0, where a and b are real-valued positive coefficients. A) Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? B) What are the initial conditions and their values? Why? C) Draw the block diagram of the filter relating input x[n] and output y[n] D) Derive a formula for the transfer function in...
Consider an LTI discrete-time system that has impulse response h n Tn-12) 1 if otherwise a) Determine the magnitude H(Q and the phase response LH(D for-r < Ω < π Enter Ω as "and enter the piecev se function Η Ω using the hea side function b)Determine the output of the system, rn, if the input is given by z n-Sn-9 +com( ) Enter your answer in terms of hin y[n] = In your answers, enter 2(n) for a discrete-time...
6) Consider a discrete-time LTI system with impulse response h[n] = response h[n] = ( 1) u[n]. Use Fourie transforms to determine the response of this system to the input x[n] = ml + un).
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