1.12. The Fourier transform of a signal x(t) is defined by X(f) = sincf, where the sinc func- tion is as defined in Equ...
g(t) Given the signal g(t) = cos(t)), (1) Using the frequency-shifting property, find Fourier Transform G(f)in "sinc" format. (2) Find the Energy Spectrum Density (ESD): Sgf) = 1G(f)12 (3) Find and sketch the Autocorrelation R,(t) by Wiener-Khintchine Theorem. -210 210
Let x(t) denote a signal and X(f) denote the corresponding Fourier transform which is given in the graph below. Given this graph, sketch the Fourier transforms of the following signals: -2 2 a, x b.x) Cos(8m) c. x(t) sinc (t) 2/ Let x(t) denote a signal and X(f) denote the corresponding Fourier transform which is given in the graph below. Given this graph, sketch the Fourier transforms of the following signals: -2 2 a, x b.x) Cos(8m) c. x(t) sinc...
2) (Fourier Transforms Using Properties) - Given that the Fourier Transform of x(t) e Find the Fourier Transform of the following signals (using properties of the Fourier Transform). Sketch each signal, and sketch its Fourier Transform magnitude and phase spectra, in addition to finding and expression for X(f): (a) x(t) = e-21,-I ! (b) x(t)-t e 21 1 (c) x(t)-sinc(rt ) * sinc(2π1) (convolution) [NOTE: X(f) is noLI i (1 + ㎡fy for part (c)] 2) (Fourier Transforms Using Properties)...
The Fourier transform of the following signal 2(t) = cos (F.) () is X(s) 47 cos(278) 772 – 167232 where II is the rectangle function defined in A2 (a)(iii). Determine the Fourier transform of the function 47 Cos (2) y(t) 72 – 16722
Introduction to Wireless Digital Communication 44. Consider the following passband sinc pulse signal: (t) = 2sind(2x 107t) cos (4.8 × 10-t) (a) Determine and plot p()l, where Xpf) is the continuous-time Fourier trans (b) Find the complex baseband equivalent signal a() of p(t). Plot x(f)I, where zp 3.540) where sinc(a)) form of rp(t). Do not forget to label correctly. x(f) is the continuous-time Fourier transform of r(t). Do not forget to label correctly (c) Determine the absolute bandwidth of the...
Given LTI system with following input response (can use properties of the Fourier transform like, sinc(x) = sin(πx)/πx ): h(t) = 8/π sinc(8t/π) where input x(t) of the LTI system is the following continuous-time signal x(t) = cos(t) cos(8t) a) find the Fourier transform of x(t) b) find the Fourier transform of h(t) c) Is this LTI system BIBO stable? Prove d) find the output y(t) of the LTI system
(b) The signal f(t) is shown in the figure below 3 2 f(t) _ 0 I 1 -4 -3 -2 -1 0 1 2 3 4 5 6 7 t and is given by 21 (1) + 3A (132), where A is the triangle function defined as 10-{ It a It <a It > a 0 Write the Fourier transform F [A(t)] (s) of f(t) exploiting the fact that FA(t)](s) = sinc-(s) where sin(TTS) sinc(s) ITS and the theorem for...
P7. Use the Fourier transform of the signal (t) and Parseval's theorem to: duw that「.sinc.(ka)dz-t; determine sinc(t - 2)dt
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal x(t) is X(f) - rect(f/ 2), find the Fourier Transform of the following signals using properties of the Fourier Transform: (a) d(t) -x(t - 2) (d) h(t) = t x( t ) (e) p(t) = x( 2 t ) (f) g(t)-x( t ) cos(2π) (g) s(t) = x2(t ) (h)p()-x(1)* x(t) (convolution) 3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal...
SHOW STEP BY STEP SOLUTION. THIS IS LINEAR SYSTEM ANALYSIS. a) Find frequency response, x (Fourier Series), where k is frequency index -Sksoo b) Find values of x when k1, 0, 1, 2 4 2 46 a) A Fourier Transform of rectangle is defined as T=11 2.4.2 sinc (2.2.f) 16-sinc(4.f) a) 16 4 b)-1.0000 0 1.0000 2.0000 -0.2773-0.17821 2.9091 -0.2773 0.17821 -0.3835 0.83981 So the Fourier series is x =-| 16-sincl 4-1-e , r + 16 . sinc! 4-1-e -16-sinc...