2. Consider a system described by Determine the system function H(z), the impulse response and the...
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...
Consider the system function (z - 1) 2 H(z) = (z+1)(z-2)(z+D a) Find the (causal) difference equation for the system specified by H(z) b) Assuming the system is causal, determine the impulse response hln]. c) Is it possible to find an h[n] that is stable? If not, explain why. If it is possible, determine h[n] for this case.
A discrete-time LTI system has the system function \(H(z)\) given below:$$ H(z)=\frac{z^{2}}{z^{2}-\frac{1}{4}} $$(a) Sketch the pole-zero plot for this system. How many possible regions of convergence (ROCs) are there for \(H(z)\). List the possible ROCs and indicate what type of sequence (left-sided, right-sided, two-sided, finite-length) they correspond to.(b) Which ROC (or ROCs) correspond to a stable system? Why?(c) Which ROC (or ROCs) correspond to a causal system? Why?(d) Write a difference equation that relates the input to the output of...
1 Find the impulse response of H(z), where H(z) is the system 1-2+2 function of the difference equation of the 2nd-order IIR filter given by the block diagram Y(z) X(z) + X + +
1. A discrete-time LTI system has the system function H(z) given below: H(2)1 2 (e) Determine the impulse response hin] associated with the stable system defined by this system function. (f) Make a careful sketch of the frequency response magnitude, i.е., IH(ew), of this system for lwl S T. Label your sketch! 1. A discrete-time LTI system has the system function H(z) given below: H(2)1 2 (e) Determine the impulse response hin] associated with the stable system defined by this...
QUESTION 1 Consider a system of impulse response h[n] of transfer function H(z) with distinct poles and zeros. We are interested in a system whose transfer function G(z) has the same poles and zeros as H(z) but doubled (meaning that each pole of H(z) is a double pole of G(z), and same for the zeros). How should we choose g[n]? g[n]=h[n]+h[n] (addition) g[n]=h[n].h[n] (multiplication) g[n]=h[n]th[n] (convolution) None of the above
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 for which the input rn] and the output yin] satisfy the linear onstant-coefficient difference equation 2 Please determine the algebraic equation system function H(). (5 points) 2. Please determine the poles and zeros. (5 points) 3. Please determine the impulse response hin]. (Hint: Please discuss two cases de pending on the region of convergence. (10 points) Consider an LTI system for which the input rn] and the output yin] satisfy the linear onstant-coefficient difference equation 2...
Determine the impulse response h[n] of the LTI system described by the difference equationy[n] - 0.35y[n-1] = x[n]
A linear time invariant system has an impulse response given by h[n] = 2(-0.5)" u[n] – 3(0.5)2º u[n] where u[n] is the unit step function. a) Find the z-domain transfer function H(2). b) Draw pole-zero plot of the system and indicate the region of convergence. c) is the system stable? Explain. d) is the system causal? Explain. e) Find the unit step response s[n] of the system, that is, the response to the unit step input. f) Provide a linear...