Answer Happy

4. [24 points] Consider the following periodic signal x(t) x(t) 1 ... t -5 -4 -3 -2 -1 0 1 2 3 4 5 a. [2 pts] Determine the period and the fundamental frequency of this signal. b. [8 pts] Determine the exponential Fourier Series coefficients, Ck, of this signal. c. [6 pts] Sketch the magnitude and phase spectra for this signal, i.e., |Ck and ZCk, for k=-3,-2,-1,0,1,2,3. Label your axes. d. [4 pts] This signal will be filtered with an ideal lowpass filter such that only the Fourier Series Coefficients Ck for k=-2,-1,0,1,2 will remain in the spectra of the filtered signal x₁(t). Find x₁(t) and express it in terms of sinusoidal eje-e-je eje te-je functions. (Hint: Euler's identity cos (0) sin 0 = -e-10). 2 2j e. [4 pts] Is the average power of filtered signal xf(t) greater or less than the average power of the original signal x(t)? Justify your answer.