ECSE 303 Study Guide - Midterm Guide: Fourier Series, Linear Time-Invariant Theory, Kolmogorov Space

• School: McGill University
• Department: Electrical & Computer Engr
• Course: ECSE 303
• Professor: All

Document Summary

Note: closed book, closed notes, no calculators allowed. 4. 5 4 3. 5 3 2. 5 2 1. 5 1 0. 5: find the fourier series coefficients ofx(t). 4. 5: the signal is passed through an lti system with transfer function. Find the fourier series coefficients of the output. Solution: the signal has a fundamental period of t0 = 3. Let the fourier series coefficients be{ k}k , i. e. , x(t)= + kej 0kt: fork=0, 0= 1t0 t0/2. 3/2, k=2 (mod 6) (mod 6) (mod 6) (mod 6) (mod 6) (mod 6) (mod 3) (mod 3) (mod 3) K= (mod 6) (mod 6) (mod 6) (mod 6) (mod 6) (mod 6) (mod 6) (mod 6) k=0. 0: lety(t) denote the output and{ k}k be its fourier series coefficients. Now, note that h(j0)= 126 =2 and h(j 0k)= j k+9 k=0. Combing the two cases, we get: otherwise (mod 6) (mod 6) otherwise. Consider the following system with inputx(t) and outputy(t). y(t)=x(t2)