The frequency response Hf(w) of a discrete-time LTI system is as shown.
The frequency response Hf(w) of a discrete-time LTI system is as shown.
Hf(w) is real-valued so the phase is 0.
Find the output y(n) when the input x(n) is
x(n) = 1+cos(0.3πn).
Put y(n) in simplest real form (your answer should not contain j)
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The frequency response Hf(w) of a discrete-time LTI system is as shown.
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)...
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients o...
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients of the output of this system when the input is x[n] = cos(n+π)
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients of the output of this system when the input is x[n] = cos(n+π)
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...
A discrete-time LTI system with a cumpling frequency of 8kHz is shown in Figure 4.1. The...
A discrete-time LTI system with a cumpling frequency of 8kHz is shown in Figure 4.1. The rectangular boxes with the label z provide one sample period delay to their input signals. The circular components are adders or subtractors. The triangular components provide linear gain factors of or by, where i is 0, 1 or 2 a) Derive the system transfer function H(z). b) Find the difference equation relating the output y[n) and input x[n). c) Given that the gain values...
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
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) -...
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) - et u(t). (a) What is the frequency response H (w) of this system? (b) Find and sketch H(w). (c) Is this a lowpass, bandpass, or highpass filter, or none of those? 2.7.6 The impulse response of a continuous-time LTI system is given by h(t) = S(t – 2). (This is a delay of 2.) (a) What is the frequency response H (w) of this...
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
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].
Bonus Question) A discrete-time LTI system with a sampling frequency of Ukm2 is shown in the...
Bonus Question) A discrete-time LTI system with a sampling frequency of Ukm2 is shown in the following Figure. The rectangular boxes with the label z provide one sample period delay to their input signals. The circular components are adders or subtractors. The triangular components provide linear vain factors of ar or bi where i is 0,1 or 2. i) Derive the system transfer function H(2). ü) Find the difference equation relating the output y[n] and input x[n]. iii) Given that...
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...
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients of the output of this system when the input is x[n] = cos(n+π)
Problem 1 You are given the discrete-time LTI system with impulse response, Calculate the Fourier series coefficients of the output of this system when the input is x[n] = cos(n+π)
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...
A discrete-time LTI system with a cumpling frequency of 8kHz is shown in Figure 4.1. The rectangular boxes with the label z provide one sample period delay to their input signals. The circular components are adders or subtractors. The triangular components provide linear gain factors of or by, where i is 0, 1 or 2 a) Derive the system transfer function H(z). b) Find the difference equation relating the output y[n) and input x[n). c) Given that the gain values...
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
2.7.5 The impulse response of a continuous-time LTI system is given by h(t) = f(t) - et u(t). (a) What is the frequency response H (w) of this system? (b) Find and sketch H(w). (c) Is this a lowpass, bandpass, or highpass filter, or none of those? 2.7.6 The impulse response of a continuous-time LTI system is given by h(t) = S(t – 2). (This is a delay of 2.) (a) What is the frequency response H (w) of this...
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
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].
Bonus Question) A discrete-time LTI system with a sampling frequency of Ukm2 is shown in the following Figure. The rectangular boxes with the label z provide one sample period delay to their input signals. The circular components are adders or subtractors. The triangular components provide linear vain factors of ar or bi where i is 0,1 or 2. i) Derive the system transfer function H(2). ü) Find the difference equation relating the output y[n] and input x[n]. iii) Given that...
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...
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