5. Given the Fourier transform of the signal g(t) 9(0) = jo -02 + 5jo +6...
Please finish these questions. Thank you Given find the Fourier transform of the following: (a) e dt 2T(2 1) 4 cos (2t) (Using properties of Fourier Transform to find) a) Suppose a signal m(t) is given by m()-1+sin(2 fm) where fm-10 Hz. Sketch the signal m(t) in time domain b) Find the Fourier transform M(jo) of m(t) and sketch the magnitude of M(jo) c) If m(t) is amplitude modulated with a carrier signal by x(t)-m(t)cos(27r f,1) (where fe-1000 Hz), sketch...
(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...
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...
4. (25 pt) Given a signal, g(t) 10eStu(t) (a) Find the Fourier transform of the signal, G(). (b) What is the Energy Spectral Density (ESD) of the signal, e().Plot the variation of ESD with frequency using the frequency range of [-3,3]. (c) Determine the signal energy Eg of the signal using Parseval's Theorem.
5. Fourier Transform and System Response (12 pts) A signal æ(t) = (e-t-e-3t)u(t) is input to an LTI system T with impulse response h(t) and the output has frequency content Y(jw) = 3;w – 4w2 - jw3 (a) (10 pts) Find the Fourier transform H(jw) = F{h(t)}, i.e., the frequency response of the system. (b) (2 pts) What operation does the system T perform on the input signal x(t)?
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)...
6) Answer the following questions: a) (5 points) Using the Fourier transform, find the value of the following integral S. sinc(Be)dt b) (5 points) Find the Amplitude and phase spectra of the following signal x(t) Ae=sin(5t), t20, t<0. 10. c) (5 points) Find the Fourier transform of v(t) 1
8. (a) Find the Fourier transform of the signal by direct integration. f(t) = ((t-5)+e-Y(-5))u(t-5) (5 points) (b) Use the convolution theorem of Fourier transform, find the convolution of the following signals: (5 points) x(t) = 5e-4tu(t) and h(t) = 7e-3tu(t)
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
Determine Fourier Transform of f(t) = u(t - 2) + 8(t - 6) Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )