Consider a discrete-time system described by the following difference equation. y(n) = y(n−1)−.24y(n−2) + 2x(n−1)−1.6x(n−2) Find...
- Consider a discrete-time system described by the following difference equation.
y(n) = y(n−1)−.24y(n−2) + 2x(n−1)−1.6x(n−2)
- Find the transfer function H(z).
- Find the zero-state response to the causal exponential input x(k) = .8nµ(n). This means that given H(z), we can calculate Y(z) and subsequently the output, y(n) with all initial conditions presumed to be zero. Hence the term, zero-state.
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Consider a discrete-time system described by the following
difference equation.
y(n) = y(n−1)−.24y(n−2) +
2x(n−1)−1.6x(n−2)
Find...
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.
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)...
1) A causal discrete-time system is described by the difference equation, y(n) = x(n)+3x(n-1)+ 2x(n-4) a)...
1) A causal discrete-time system is described by the difference equation, y(n) = x(n)+3x(n-1)+ 2x(n-4) a) What is the transfer function of the system? b) Sketch the impulse response of the system
(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...
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...
6. (15) Consider the following causal linear time-invariant (LTT) discrete-time filter with input in and output...
6. (15) Consider the following causal linear time-invariant (LTT) discrete-time filter with input in and output yn described by y[n] = x[n] – rn - 2 for n 20 . Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? • What are the initial conditions and their values for this causal and linear time-invariant system? Why? • Draw the block diagram of the filter relating input x[n) and output y[n] • Derive a formula for...
If the input to the system described by the difference equation y(n+1) (1/2)x(n+) -x(n) is a)...
If the input to the system described by the difference equation y(n+1) (1/2)x(n+) -x(n) is a) Does it matter what are the initial conditions for nc0 in order to find y(n) for n20? Explain your b) x(n) -u(n) answer. (3 points). Determine the transfer function H(z) and the Frequency Response (H(est) (10 points). Find the amplitude lH(epT)I and the phase He*') as a function of co. Evaluate both for normalized frequency ω T=z/4. ( 10 points) c) Find the steady...
2. A discrete time LTI system is described by the difference equation (assume initial conditions are...
2. A discrete time LTI system is described by the difference equation (assume initial conditions are zero) y[n] + y[n – 1] = x[n] + 1/4x[n – 1] – 1/8x[n – 2] a) Find the transfer function of the system H(z). b) If you take the inverse of the transfer function (1/H(z)), is the system stable? Prove yes or no.
Please solve using the Discrete-Time Fourier Transform: Given a filter described by the difference equation y[n]...
Please solve using the Discrete-Time Fourier Transform: Given a filter described by the difference equation y[n] = x[n] + 2x[n - 1] + x[n - 3] where x[n] is the input signal and y[n] is the output signal. a) Find H[n] the impulse response of the filter. b) Plot the impulse response c) Find the value of H( Ω) for the following values of Ω = 0, pi, pi/2, and pi/4
3.21. Given a filter described by the difference equation y[n] = 2x[n] + 3x[n - 1]...
3.21. Given a filter described by the difference equation y[n] = 2x[n] + 3x[n - 1] + 2x[n - 2] where x[n] is the input signal and y[n] is the output signal. (a) Find and plot h[n] the impulse response of the filter. (b) find and plot H(Ω).
1) A causal discrete-time system is described by the difference equation, y(n) = x(n)+3x(n-1)+ 2x(n-4) a) What is the transfer function of the system? b) Sketch the impulse response of the system
(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...
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...
6. (15) Consider the following causal linear time-invariant (LTT) discrete-time filter with input in and output yn described by y[n] = x[n] – rn - 2 for n 20 . Is this a finite impulse response (FIR) or infinite impulse response (IIR) filter? Why? • What are the initial conditions and their values for this causal and linear time-invariant system? Why? • Draw the block diagram of the filter relating input x[n) and output y[n] • Derive a formula for...
If the input to the system described by the difference equation y(n+1) (1/2)x(n+) -x(n) is a) Does it matter what are the initial conditions for nc0 in order to find y(n) for n20? Explain your b) x(n) -u(n) answer. (3 points). Determine the transfer function H(z) and the Frequency Response (H(est) (10 points). Find the amplitude lH(epT)I and the phase He*') as a function of co. Evaluate both for normalized frequency ω T=z/4. ( 10 points) c) Find the steady...
2. A discrete time LTI system is described by the difference equation (assume initial conditions are zero) y[n] + y[n – 1] = x[n] + 1/4x[n – 1] – 1/8x[n – 2] a) Find the transfer function of the system H(z). b) If you take the inverse of the transfer function (1/H(z)), is the system stable? Prove yes or no.
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