| Line 8: | Line 8: | ||
Solution: <br /> | Solution: <br /> | ||
(1) <math>e^{j ω_0 n}</math> --> <div style="font-family: Verdana, sans-serif; font-size: 12px; text-align: justify; width: 2%; margin: auto; border: 1px solid #aaa; padding: 3em;"> LTI </div> --><math>{\mathcal H}(ω_0)e^{j ω_0 n}</math> where <math>{\mathcal H}(\omega)</math> is DTFT of unit impulse response h[n] <br /> | (1) <math>e^{j ω_0 n}</math> --> <div style="font-family: Verdana, sans-serif; font-size: 12px; text-align: justify; width: 2%; margin: auto; border: 1px solid #aaa; padding: 3em;"> LTI </div> --><math>{\mathcal H}(ω_0)e^{j ω_0 n}</math> where <math>{\mathcal H}(\omega)</math> is DTFT of unit impulse response h[n] <br /> | ||
| − | (2)y[n] = x[n] * h[n] <br /> | + | (2)y[n] = x[n] * h[n] <br /><br /> |
| − | (3)<math>{\mathcal y}(\omega)</math>=<math>{\mathcal X}(\omega)</math><math>{\mathcal H}(\omega)</math> | + | |
| + | (3)<math>{\mathcal y}(\omega)</math>=<math>{\mathcal X}(\omega)</math><math>{\mathcal H}(\omega)</math><br /> | ||
| + | <br /> | ||
| + | (4)Y(z) = X(z)H(z) | ||
(20 pts)2. For each ROAC, determine which of these system properties apply. (Just list the letters of the properties that apply.) Below we describe the ROAC of the transfer function of an LTI system. | (20 pts)2. For each ROAC, determine which of these system properties apply. (Just list the letters of the properties that apply.) Below we describe the ROAC of the transfer function of an LTI system. | ||
Revision as of 15:22, 14 November 2016
Sample Midterm Examination 2
ECE 438
Fall 2016
Instructor: Prof. Mimi Boutin
(15 pts)1. List at least three properties of an LTI system.
Solution:
LTI
-->$ {\mathcal H}(ω_0)e^{j ω_0 n} $ where $ {\mathcal H}(\omega) $ is DTFT of unit impulse response h[n] (2)y[n] = x[n] * h[n]
(3)$ {\mathcal y}(\omega) $=$ {\mathcal X}(\omega) $$ {\mathcal H}(\omega) $
(4)Y(z) = X(z)H(z)
(20 pts)2. For each ROAC, determine which of these system properties apply. (Just list the letters of the properties that apply.) Below we describe the ROAC of the transfer function of an LTI system.
