4- Find the auto-correlation function of the signal g(t) = e-at
u(t). From this determine the energy
spectrum density of g(t).
4- Find the auto-correlation function of the signal g(t) = e-at u(t). From this determine the...
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.
Please answer questions step by step solution in details with clear handwriting, please. 2 Using the time shifting properties, prove the following: g(t) sin - wo) - G(w+w.)] Ig(t +T) - g(1 - 1)]=G(w)sin Tw Using the letter result, find the Fourier transform of the following signal: 2 3 3 4 Determine the maximum bandwidth of signal that can be transmitted through low pass RC filter as shown in figure where R=1000, and C= 109, If over this bandwidth, the...
A signal has auto-correlation Find the total power.
Given an energy signal x(t) = (t-5T)e-t-T) , where T-0.1 compute its energy spectrum density in Matlab 1. use two different methods to a. Get its spectrum using Fourier transformation, follovfed by the squaring its amplitude. Plot its Fourier transformation and its energy spectrum density. Get its autocorrelation function, followed by its Fourier transformation. Plot its autocorrelation function and its energy spectrum density. b. 2. In a multipath channel, the received signal y (t) x(t) 0.15x(t -6T) +0.09x(t 10.5T), plot...
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
Problem 3 (Some parts borrowed from Mitra, Ch.4). The cross-correlation function ray(t) between two real-valued CT signals r(t) and y(t) is given by We use the cross-correlation to detect whether two signals are related to each other by delay. The autocor- relation function rt) of a real-valued CT signal r(t) is given by One use of the autocorrelation function is to detect the period of the signal. 1. Find the autocorrelation of z(t)-e-at u(t) for α > 0. 2. Find...
Given an input signal (t)nd the output signal is y(t)-(e2 e)u(t), compute the transfer function H(s). Determine whether the system is stable and causal or not.
(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...
4. (a) Consider a continuous-time signal given by j101 f(t)= e ' [u(t) - u(t – 2)] (i) Find the Fourier transform of f(t) using the properties listed in the Appendix on page 6. (ii) If the signal f(t) is sampled in the time domain, what is the Nyquist rate (in Hertz) of f(t)? Comment on your result. (8 Marks)
6.(20%) Given a filter with frequency response function 5 F[h(t)=H=4+j(2f) 3 and given an input x(t) eu(t) with its Fourier transform by 1 = *U)-3+ j(27f) F[x()] (10%) (a) Obtain the energy spectral density G,(f) for the input signal x(t) (10%) (b) Obtain the energy spectral density G.(f) for the output signal y(t) 6.(20%) Given a filter with frequency response function 5 F[h(t)=H=4+j(2f) 3 and given an input x(t) eu(t) with its Fourier transform by 1 = *U)-3+ j(27f) F[x()]...