A discrete time LTI filter at rest is given by its system function H(z), 1+z-1 H2)...
3) Given the system function of a discrete time filter 1-2z-1 10.4z-1 with R. 0. C: Iz| > 0.4 The unit sample response h[n] is a) h[n] =-58m] 6(0.4")u[n] b) h[n]- -56[n] 60-0.4)"ufn] c) h[n] = (-0.4n)2[n]-2 (-0.4n-1)u[n-1] d) h[n] = (-0.4)"u[n]-2(-0.4)"-111[n-1] e) b and c f) b and d g) a and d h) a and c i) none of the above hint: use Partial Fraction Expansion
Problem 3. See the cascaded LTI system given in Fig. 3. w in Figure 3: Cascaded LTI system Let the z-transform of the impulse response of the first block be (z - a)(z -b)(z - c) H1(2) a) Find the impulse response of the first block, hi[n in terms of a, b, c, d. Is this an FIR and IIR system? Explain your reasoning b) Find a, b, c, so that the first block nullifies the input signal c) Let...
Hint for next exercises: a) If Z{x[n]] = X(z) for a certain R.O.C Z{x[n 1]} =z1X(z) where: new R.O.C. R.O.C n2> mol b) If Z(x[n]} = X(z) for a certain R.O.C Z{x[n + 1]} z1X(z) where: new R.O.C. = R.O.C n2|< Problem #2 Fill Answer Blanks with your final answer in order to get credit. = 0.9"-3u[n-3] Given x[n] Find X(z). with R. 0.C: Answer: X(z) =
BC:9.4 A LTI discrete time system has an impulse response h[n] = (-0.8)"u[n] + (0.65)"u[n-1] Find the transfer function, #(eo), in the normalized frequency domain. Use Matlab to plot the magni- tude and phase (in degrees) of H(eo) in the range of-? < ? < ?. Attach your Matlab source code with the plots. 1212 AM ^???4/4/2013
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].
Q1) Consider an LTI system with frequency response (u) given by (a) Find the impulse response h(0) for this system. [Hint: In case of polynomial over pohnomial frequency domain representation, we analyce the denominator and use partial fraction expansion to write H() in the form Then we notice that each of these fraction terms is the Fourier of an exponentiol multiplied by a unit step as per the Table J (b) What is the output y(t) from the system if...
1-2-1 A discrete-time causal LTI system has the function of transference H(z) = The response to the inital impulse is: 7 h[n)= 3(-4)"-2-1+1 --[n] 5 a h[n)- 4-1-2-n+1 -La[n] 3 5(3-)-2-1+1 h[n]= -[n] 3 h[n)- 5(-4)-" +2-6 - + 1 --[n] 3 h[n)- 5(-4)-"-2-n+1 u[n] 3
The ROC for the causal discrete LTI system where H (2) = H(3)= (1+} = ')(1-13-) [ ] \El>$ u zl> [ ] [=> [ ] 0<1=< [ ] 0</=/<}
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...
Fill all Answer Blanks and show all calculations in a separate sheet of paper. Problem: Given the Pole-Zero Plot (one pole and one zero at the origin) of a causal filter with a normalized magnitude frequency response (max |H(w)l 1): 0.8 a) It is a FIR or IIR filter? b) what is the R.O.C of the filter ? c) Is the filter stable BIBO? Answer: Answer: Izl> Arıswer: d) The magnitude frequency response has a maximum peak at w0. Answer:...