Consider h(n)=[0.5^n * cos((pi*n)/2)]*u(n)
a. find transfer function H[Omega]
b. If x(n)= cos((pi*n)/2), find system output y[n] using H(Omega) from part a
Consider h(n)=[0.5^n * cos((pi*n)/2)]*u(n) a. find transfer function H[Omega] b. If x(n)= cos((pi*n)/2), find system output...
Given a system magnitude and phase frequency response below, and an input signal x(n) = cos(2*pi*n/3), find the output y(n) from the system. (25 pts) Magnitude Response Omega pi2 atomegapi Phase Response -pv2 at omega-pl omega
Find transfer function of h(n) = cos(n) u(n)
[2 Marks] 18. If (z) and u[n]-cos(2n)지지 the correct value of V(z) will be (2z-1) js 2 2zei5-1 2ze-15-1 2 2zel5-12ze-15-1 19. Determine the Z-transform of x[n]. [2 Marks each] n] sinl0n)u[n]0.3" n] 0.5" cos (10n)u[n] In]-(0.3) u[/n] The transfer function of a discrete time system is H(z)- 20. 1+2z3z Use the inverse Z-transform to determine the system difference equation [4 Marks] 21. An LTI system is described by the following input/output difference equation: yln] 0.12yln x[n] (assume zero initial...
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 the following wave function: y(x, t) = cos(kx - omega t). a. Show that the above function is an eigenfunction of the operator partialdifferential^2/partialdifferential x^2[...] and determine its eigenvalue. b. Show that the above function is a solution of the wave equation expressed as partialdifferential^2 y(x, t)/partialdifferential x^2 = 1/v^2 partialdifferential^2 y(x, t)/partialdifferential t^2, given the wave velocity is v = omega/k (where omega = 2 pi V and k = 2pi/lambda).
7. A causal LTI system has a transfer function given by H (z) = -1 (1 4 The input to the system is x[n] = (0.5)"u[n] + u[-n-1] ) Find the impulse response of the system b) Determine the difference equation that describes the system. c) Find the output y[n]. d) Is the system stable?
- A causal system has input x[n] and output y[n]. Use the transfer function to determine the impulse response of this system. (a) x[n] = [[n]+} \n - 1]- 38[n – 20, x[n] = [[n] - [n – 1] (b) x[n] = (-3)" u[n], y[n] = 4(2)"u[n] – (7)" u[n]
(42)1+ (z-0.5)z-0.9)(z-0.8) 3. The transfer function of a system is H(z) = a) Compute an analytical expression for the response y[n] if x[n] = u[n]. . Use Matlab to calculate the coefficients b) Simulate the response using Matlab (stem plot). Generate 50 points. (enter transfer function into Matlab and apply step input) (42)1+ (z-0.5)z-0.9)(z-0.8) 3. The transfer function of a system is H(z) = a) Compute an analytical expression for the response y[n] if x[n] = u[n]. . Use Matlab...
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...
(3) For the system modeled by with output defined as a) Find the system's transfer function(s) E(t) +3z(t) +2x(t)-Sult) b) Find the system's pole(s) (if any) and zero(s) (if any) c) Find n(t →x) if u(t)-G 120) 0 t<0 e) Find the frequency response function corresponding to output y 1) Find steady-state ya(t) if u(t) 3sin(21)