Problem 2: (10 points) Determine the Fourier coefficient for the following periodic signals. (1) x(t) =...
3.12. Determine the exponential Fourier series for the following periodic signals: sin 2t + sin 3t (a) x(t) = 2 sint (b) x(t)-Σ δ(t-kT) k-00
Problem .2 Determine the Fourier transform of the following signals and plot the spectrum C. X(t) = (2+ cos211000t) cos 275000t
Signals and systems Problem 2 (20 points) Let -S2t+1, Osts1 x(t) = -t +4, 1sts 3 be a periodic signal with fundamental period T=3 and Fourier coefficients ar a. Determine the value of ao. b. Determine ak, k = 0, by: 1. first finding the Fourier coefficients of ii.then using the appropriate property of the continuous-time Fourier series. c. Use the result of part (b) to express the Fourier transform of x().
Problem 7.3 r(t) has the Fourier transform Xjw Determine the Fourier transforms of the following signals. (a) Fal)-5r(3t -2) (b) r(t)(t 1)sin(2t) (c) elt)5) HINT: Find the value of r(t) first. (d) ralt) (t)cos(2mt
1. Determine the Fourier transforms X) of the following signals and plot the spectrum a x( ) = 4 sin 2.1 4000cos2x 2000 b. x(t) = (2+2 cos 2 x 20007) cos 2.5000
Find the Fourier Transform of the following signals: (a) x(t) = Sin (t). Cos (5 t) (b) x(t) = Sin (t + /3). Cos(5t-5) (c) a periodic delta function (comb signal) is given x(t) = (-OS (t-n · T). Express x(t) in Fourier Series. (d) Find X(w) by taking Fourier Transform of the Fourier Series you found in (a). No credit will be given for nlugging into the formula in the formula sheet.
Let x(t) and y(t) be periodic signals with fundamental period T and Fourier coefficients αn and βn, respectively. Use the properties of Fourier series and find the Fourier series coefficients of the following signals in terms of@n, βn, or both. a) V,(t) = x(t-to) + x(t + to) b) yb (t) = 2x(t-1) + 3y(t-1) c) ye(t) = x(-t) + x(-t-to) d) ya(t)=x(t)y(t) 1.
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...
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...
Chapter 1: Problem 1. Determine whether or not each of the following signals is periodic. In case a signal is periodic, specify its fundamental period. a.X (n) = 3 cos (5n + 4) b. x(n) = 2 exple-t) C. x(n) = cos () cos (4) d. "(m) = cos (3)- sin (a) + 3 cost 8 cos )