roblem 3: (15-7+8 points) Consider the left-sided discrete-time signal a(n)42+1). a) Find the discrete Fourier transform...
Consider the discrete time signal x[n]: 13 -5 10 2.5 Compute the discrete time Fourier transform (DTFT) X (A). Find the period ofX(Q). Hint: First write the x[n] showed above as two pulse functions then take the DTFT using the equation given below Express discrete Fourier transform (DFT) of x[n] using DTFT X(Q). a. b. Consider the discrete time signal x[n]: 13 -5 10 2.5 Compute the discrete time Fourier transform (DTFT) X (A). Find the period ofX(Q). Hint: First...
Consider the signal x(n-õn-4] + 2õn-5] + õn_6]. (a) Find X(el the discrete-time Fourier transform of xin]. Write expressions for the magnitude and phase of X(elu), and sketch these functions (b) Find all values of N for which the N-point DFT is a set of real numbers (c) Can you find a three-point causal signal x1n i.e., x1In] 0 for n <0 and n > 2) for which the three-point DFT of x (n] is: xn[nl (ie, xiin] O for...
Problem 2 Consider a continuous-time signal x(t), of which the Fourier transform is ( 21f # (1)= 1° X(t)e=1218i dt = le 1000 15 1 400 lo otherwise Discrete-time signal x[n] is obtained by sampling x(t) at sampling at every 1 us -i.e., x[n] = xy(10ºn). (a) Write discrete-time Fourier transform of x[n], X (elo). (b) Plot the magnitude and phase response of X (ejm).
ML 25 points) DTFT of a Signal Compute the discrete-time Fourier transform (DTFT) of the signal x[n] = {x[0],x[1], x[2], x[3]} = {1,0,-1,0} [n] = DTFT"
A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform (DFT) harmonic function is (X[0], X[7]} = [3,4 + j5,-4 -j3,1+ j5,-4,1 j5,-4 + j3, 4 - j5). Solve the following: Average value of x[n] (i) [3 marks] Signal power ofx[n]. (ii) [5 marks] [n] even, odd or neither (iii) [3 marks] A discrete-time signal xin] is periodic with period 8. One period of its Discrete Fourier Transform (DFT) harmonic function is (X[0], X[7]}...
1. (20 points) Fourier Transform and Inverse Transform Problems: (a) Compute the Discrete-time Fourier transform of signal (b) Determine the signal having the following Fourier transform X(w)cos2w.
(a) Consider a discrete-time signal v[n] satisfying vn0 except if n is a multiple of some fixed integer N. i.e oln] -0, otherwise where m is an integer. Denote its discrete-time Fourier transform by V(eJ"). Define y[nl-v[Nn] Express Y(e) as a function of V(e). Hint : If confused, start with N-2 (b) Consider the discrete-time signal r[n] with discrete-time Fourier transform X(e). Now, let z[n] be formed by inserting two zeroes between any two samples of x[n]. Give a formula...
Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n] -xs(t) -x(nTs) is created by sampling x() with sampling interval, 2it 60 a) Plot the Fourier Transform of the sampled signal, i.e. Xs (jo). b) Plot the DTFT of the sampled signal, ie, X(eja) o) Repeat (a) with 7, 2π d) Repeat (b) with , 18 Consider the continuous time signal: 2. , π (sin (2t) (Sin (8t) A discrete time signal x[n]...
Find the discrete-time Fourier transform of the signal x[n] given below. Is – uļng-u= [u]a
10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1. Sketch the Fourier transform Xr(jw) of x[n] for T-to. 2. Can x(t) be recovered for T? How? What is the maximum value of T so that r(t) can be recovered? 10ρ 18ρ A signal (t) has the Fourier transform X(jw) indicated in the figure. The signal is sampled to obtain the discrete time signal 1....