2. For a system with impulse response h(n) = (,"u(n) (a) determine the output sequence of the sys...
(20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input signal is x[n] = 2e-n + sin(nn)- 2, -co <n< 0o. 7. (20 pts.) Determine the response of the system described by the difference equation 1 1 y(n)y(n1)n2)x(n 8 7 for input signal x(n) u(n) under the following initial conditions 1, y(-2) 0.5 y(-1) (20 pts.) Determine the output sequence of the system with impulse response h[n] 6. u[n] when the input...
4. The impulse response of a system is given by h[n]=(0.3)"u[n]. If the input to the system is x[r]=(-0.6)" u [n], giving an output of y[n]=[n]*x[n]: a. (5 pts) Find the spectrum of the output, Y(e/2/). b. (10 pts) Use partial fraction decomposition to rewrite Y (e/2*) as a sum of two terms then take the inverse DTFT to find the output, y[n]
Determine the output response y[n] of a causal LTI digital system with an impulse response h[n]=2(0.2)n μ[n] for an input sequence x[n] = 4(0.3)n μ[n]
1. An LTI digital system with impulse response h[n] = 2(1/4)"u[n] produces an output y[n] = (-3)"u[n]. Determine the corresponding input x[n] using Z-transform. (30 points)
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 that a CT system with unit impulse response h(t)=u(t) is excited by the input signal defined as 0,<-3 t +3,-3<t < 0 x(t) = { t -- +3,0 < t < 6 0,t> 6 Find the output of the system and plot it. (10 points)
1. An LTI system has impulse response defined by h (n )={2 ,2 ,−1,−1 ,−1,−1}first 2 zero . Determine the outputs when the input x(n) is (a) u(n ) ; (b) u(n−4 ) 2. Let the rectangle pulse x ( n )=u ( n ) −u (n −10 ) be an input to an LTI system with impulse response h (n )=(0.9 )n u (n ) . Determine the output y ( n ) . (Hint: You need to consider muliple...
CONVOLUTION - Questions 4 and 5 4. Consider an LTI system with an impulse response h(n) = [1 2 1] for 0 <n<2. If the input to the system is x(n) = u(n)-un-2) where u(n) is the unit-step, calculate the output of the system y(n) analytically. Check your answer using the "conv" function in MATLAB. 5. Consider an LTI system with an impulse response h(n) = u(n) where u(n) is the unit-step. (a) If the input to the system is...
The unit impulse response and the input to an LTI system are given by: h(t) u(t) - u(t - 4) x(t) e2[u(t)-u(t - 4)] x(t) 1 y(t) h(t) 1. Determine the output signal, i.e.y(t), you may use any method. 2. Is this system memoryless? Why? 3. Is this system causal? Why? 4. Is this system BIBO stable? Why?
1. The signal x(t)- expl-a)u(t) is passed as the input to a system with impulse response h(t) -sin(2t)/(7t (a) Find the Fourier transform Y() of the output (b) For what value of α does the energy in the output signal equal one-half the input signal energy? Hint: use the duality property of Fourier Transform to obtain H(a