ECE130B: Homework 8 - Preparing Cheat Sheets for Final Exam, Assignments of Criminal Justice

Download ECE130B: Homework 8 - Preparing Cheat Sheets for Final Exam and more Assignments Criminal Justice in PDF only on Docsity! ECE130B: Home Work 8 Due on March 13, 2009. Prolems marked reading assignment don’t have to be turned in. Remember to prepare the following cheat sheets for your final exam: 1. table of convolution formulas 2. table of z-transform pairs (Table 10.2 from the text book) 3. table of z-transform properties (Table 10.1 from the text book) 4. table of discrete-time Fourier transform pairs (Table 5.2 from the text book) 5. table of discrete-time Fourier transform properties (Table 5.1 from the text book) 6. table of discrete-time Fourier series pairs 7. table of discrete-time Fourier series properties (Table 3.2 of the text book). You can augment these tables with additional entries, but they must belong to the table. 1. Reading assignment: Sections 3.6, 3.7 and 7.5. 2. A discrete-time periodic signal x[n] is real-valued and periodic with period 5 (that is, x[n + 5] = x[n] for all n). Some of the Fourier series coefficients (based on a period of 5) for x[n] are a0 = 1, a1 = 2e jπ/3, a2 = e jπ/4. Express x[n] in the form x[n] = A0 + 4∑ k=1 Ak sin ( k 2π 5 n+ φk ) , where Ai and φi are real numbers. Hint: What is the value of a−1 and a−2? Then use the Fourier synthesis formula x[n] = 2∑ k=−2 ake jk 2π 5 n. 3. Find the Fourier series coefficients of the periodic function x[n] = ∞∑ m=−∞ (4 δ[n− 5m]− 4 δ[n− 1− 5m]) . 4. When the impulse train x[n] = ∞∑ k=−∞ δ[n− 4k] is input to a particular LTI system with frequency response H(ω), the output of the system is found to be y[n] = cos ( π 4 − 3π 2 n ) . Find H(0), H(π/2), H(π) and H(3π/2). Is it possible to find the value of H(ω) for any other values of ω from the given information (0 ≤ ω ≤ 2π)? 5. Reading assignment. Problems 3.11, 3.12, 3.16, 3.18, 3.27, 3.28, 3.29, 3.30.(a), 3.30.(b), 3.31, 3.36–3.39. 1