1) (40 points) Given the following continuous-time periodic signal. x(t) Тр To TO 2 a. (20...
1) (40 points) Given the following continuous-time periodic signal. x(t) -To To τ TO To 2 2 a. I (20 points) Compute the exponential Fourier series. b. (10 points) Plot the Fourier spectrum for n=...-3,-2,-1,0,1,2,3... Assume A=1. c. (10 points) Using mathematical expressions, explain the existing of negative frequencies.
2) (35 points) Given the following continuous-time aperiodic signal. x(t) A t T 2 2 a. (25 points) Compute the exponential Fourier transform. b. (10 points) Plot the Fourier spectrum.
Problem 1: Consider the continuous-time signal r(t) as shown in Figure 1. r(t) Figure 1: A continuous-time signal r(t) (a) Determine the fundamental period and the fundamental angular frequency of r(). 5 (b) Write down the equation for z(0) as the Fourier Series in exponential form and identify (c) Sketch the spectrum of this signal indicating the complex amplitudes and the frequen- points the Fourier Series coefficients. (15 points cies. [10 points
A periodic signal, x(t) is shown below. A = 10, T-4 sec. -T Write a MATLAB script to plot the signal, using enough points to get a smooth curve. Compute the Fourier series coefficients for the signal (if you can find them in the text, that is ok). Plot the single-sided or double-sided spectra for each signal. Include enough frequencies in the plots to adequately represent the frequency content of the signals. Plot partial sums of the Fourier series for...
1. (25 points) A continuous-time periodic signal x (t) is real valued and has a fundamental period T-8. The nonzero Fourier series coefficients for x(t) are Express x(t) in the fornm
2. A continuous-time periodic signal with Fourier series coefficients c^ = and period T, 0.1sec pass through an ideal lowpass filter with cut off frequency =102.5Hz. The resulting signal y, (t) is sampled periodically with T 0.005 sec determine the spectrum of the sequence y(n) = ya(nT)
Problem (3) a) A periodic square wave signal x(t) is shown below, it is required to answer the below questions: x(t) 1. What is the period and the duration of such a signal? 2. Determine the fundamental frequency. 3. Calculate the Trigonometric Fourier Series and sketch the amplitude spectrum and phase spectrum of the signal x(t) for the first 5 harmonics. b) Find the Continuous Time Fourier Series (CTFS) and Continuous Time Fourier Transform (CTFT) of the following periodic signals...
Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients as Do = 1, Dn = 2 (1 + j(-1)") Sketch the magnitude and phase spectral-line up to the a) b) Estimate the signal's power from the 1t four h c) Write the math ematical expression for the complex exponential Fourier series expansion form. 12) Solution: Problem 4: [8 Points] x(t) is a continuous periodic signal that has complex exponential Fourier series coefficients...
(1) Consider the following continuous-time signal: (1) 2ua(-t+t)ua(t), where its energy is 20 milli Joules (2 x 103Joules). The signal ra(t) is sampled at a rate of 500 samples/sec to yield its discrete-time counter part (n) (a) Find ti, and hence sketch ra(t). (b) From part (a), plot r(n) and finds its energy (c) Derive an expression for the Fourier transform of a(n), namely X(ew). (d) Plot the magnitude spectrum (1X(e)) and phase spectrum 2(X(e). (e) Consider the signal y(n)...
problem E 1. 20 points Consider the signal g(t) = t2 over the interval (-1,1) and it's periodic extension. (a) Find the exponential Fourier series (F.S.) for this signal. (b) Find the compact trigonometric Fourier series. (c) From the exponential F.S., plot the amplitude and phase spectrum. (d) Plot the approximated signal you obtain via the Fourier Series with (i) the DC component only; (ii) up to the first harmonic, and (iii) up to the second harmonic e) Using Parseval's...