Pave- 1. Solve the following problems and show all steps if you want partial credit, please encircle the answer with a box. Problem #1: (30 points) Consider the following periodic signal y(t). Periodic Waveform 35 05 5 10 15 20 30 1. Determine the Fourier series expression of y(t) using exponential format. 2. Find mathematical expression of the Fourier Transform of the periodic signal y(t). 3. Plot the power-spectral density of the signal from 0 sf (Hz) s 1/6 4. Find the average power from the PSD of part 3. 5. Determine the error in average power in percent x 100 PO = y*(t)dt Fade error = Ideal que pleni Problem #2: (30 points) Using the following FT pair: g(0) GC) Acos(w.t) [19) = (sinc{t(s f)) + sinc(rcs + )}] Determine the Fourier Transform for the following expressions using the Fourier- transform theorems and pairs (assume that A = 8, r = 2 s and wo = 12rt rad/s): a) y(t) = g(t - 2) + g(t + 2) b) yz(t) = 29 () c) y(t) = g(t)ell d) y(t) (g(t)) dta Problem #1: (30 points) Consider the following periodic signal y(t). Periodic Waveform 3 2.5 Amplitude (V) 1.5 + 05 385045 2018 0 10 15 20 25 30 35 40 45 80 85 60 time(s 1. Determine the Fourier series expression of y(t) using exponential format. 2. Find mathematical expression of the Fourier Transform of the periodic signal y(t). 3. Plot the power-spectral density of the signal from 0 sf (Hz) 1/6 4. Find the average power from the PSD of part 3. 5. Determine the error in average power in percent - ideal Pave = Syy(t)dt Pave - Pave x 100, error = -Ideal Pave Pave- 1. Solve the following problems and show all steps if you want partial credit, please encircle the answer with a box. Problem #1: (30 points) Consider the following periodic signal y(t). Periodic Waveform 35 05 5 10 15 20 30 1. Determine the Fourier series expression of y(t) using exponential format. 2. Find mathematical expression of the Fourier Transform of the periodic signal y(t). 3. Plot the power-spectral density of the signal from 0 sf (Hz) s 1/6 4. Find the average power from the PSD of part 3. 5. Determine the error in average power in percent x 100 PO = y*(t)dt Fade error = Ideal que pleni Problem #2: (30 points) Using the following FT pair: g(0) GC) Acos(w.t) [19) = (sinc{t(s f)) + sinc(rcs + )}] Determine the Fourier Transform for the following expressions using the Fourier- transform theorems and pairs (assume that A = 8, r = 2 s and wo = 12rt rad/s): a) y(t) = g(t - 2) + g(t + 2) b) yz(t) = 29 () c) y(t) = g(t)ell d) y(t) (g(t)) dta Problem #1: (30 points) Consider the following periodic signal y(t). Periodic Waveform 3 2.5 Amplitude (V) 1.5 + 05 385045 2018 0 10 15 20 25 30 35 40 45 80 85 60 time(s 1. Determine the Fourier series expression of y(t) using exponential format. 2. Find mathematical expression of the Fourier Transform of the periodic signal y(t). 3. Plot the power-spectral density of the signal from 0 sf (Hz) 1/6 4. Find the average power from the PSD of part 3. 5. Determine the error in average power in percent - ideal Pave = Syy(t)dt Pave - Pave x 100, error = -Ideal Pave
