Problem (1) Find the equivalent sampled impulse response sequence and the equivalent z-transfer f...
3. (10 points) Two linear time invariant (LTI) systems with impulse response hi(k) and h2(k) are connected in cascade as shown in Figure 1. Let x(k) be the input, yı(k) be the output of the first LTI, and y2(k) be the output of the second LTI. Let hi(k) = k(0.7)k u(k), h2(k) = ku(k), and x(k) = (0.3)k u(k). Use z-transform to (a) find yı(k). (b) find y2(k). x(k) yi(k) y2(k) hi(k) h2(k)
Problem 1: The impulse response ht) for a particular LTI system is shown below hit) Be5e (4 cos(3t)+ 6 sin(3t) e. u(t) 1. Plot the impulse response for h(t) directly from the above equation by creating a time vector 2. Use the residue function to determine the transfer function H(s). Determine the locations of the poles and zeros of H(s) with the roots function, and plot them in the s-plane (x for poles, o for zeros). Use the freas function...
3.(10 points) Two linear time invariant (L TI) systems with impulse response hy(k) and h2(k) are connected in cascade as shown in Figure 1. Let x(k) be the input, yı(k) be the output of the first LTI, and yz(k) be the output of the second LTI. Let h;(k) = k(0.5)* u(k), hz(k)= ku(k), and x(k) = (0.7)* u(k). Use z-transform to (a) find yı(k). (b) find y2(k). x(k) yi(k) h;(k) h2(k) ya(k)
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...
2. For the transfer functions in problem 1 (a)(d)(e), find the corresponding impulse response functions h(t) using partial fraction expansion and determine the value of lim h(t) if the limit exists. Verify that lim- n(t)-0 for stable systems. (optional) After performing the partial fraction expansion by hand (required), yoiu are encouraged to use MATLAB to verify your results. MATLAB has a function called 'residue' that can calculate poles (pi) and residues (ci). For example, the following line will calculate the...
(c) A digital filter has transfer function 1 Н(2) z 1/2 Evaluate the response function of the filter, Y(z)= X(z)H(z), for the sequence (i 2* x(n)a. (Use the geometric series 1-c k 0 (ii By using partial fractions, determine the response of the filter, y(n), to the input x(п) %— а". (iii What is the response to the input data x(n) (1)"? [Note: the Z- transform of a sequence x(n) is defined as X(z) x(n)z. The n-0 inverse Z- transform...
Consider the convolutional encoder shown in Figure 2. (a) Find the impulse response of the encoder (b) Find the output codeword if the input sequence is all 1’s (1 1 1 1 1 1 . . .) (c) Discuss the result of (b) (d) Find the polynomial representation of the encoder (e) Sketch the state diagram of the encoder Consider the convolutional encoder shown in Figure 2 (a) Find the impulse response of the encoder (b) Find the output codeword...
Can you please show all the steps to arrive to the equations D_ZOH(z) and D_TOTAL(z)? Suppose that a discrete-time signal x(n) is processed by the system with transfer function 0.01 before sent to a ZOH at 100Hz and then a continuous time filter with transfer Нpт(2) z-0.99 function HcT(s) 1 vlDetemine the DT transfer function of the system when the ) output is also sampled at 100Hz The sampled output will be given by the ZOH equivalent transfer function of...
Consider the convolutional encoder shown in Figure 2 (a) Find the impulse response of the encoder (b) Find the output codeword if the input sequence is all 1's (111111...) (c) Discuss the result of (b) (d) Find the polynomial representation of the encoder (e) Sketch the state diagram of the encoder 2. Output input Figure 2 Consider the convolutional encoder shown in Figure 2 (a) Find the impulse response of the encoder (b) Find the output codeword if the input...
2. Consider a linear time-invariant system with transfer function H(s)Find the (s + α)(s + β) impulse response, h(t), of the system 2. Consider a linear time-invariant system with transfer function H(s)Find the (s + α)(s + β) impulse response, h(t), of the system