3) (25 points) Consider the following discrete-time aperiodic signals. x(n) 3 2 1 n x(n) 3...
roblem 3: (15-7+8 points) Consider the left-sided discrete-time signal a(n)42+1). a) Find the discrete Fourier transform X(eju n-2 ). (b) Find the phase (o) of the discrete Fourier transform X
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...
2) (35 points) Given the following continuous-time aperiodic signal. x(t) A t T 2 2 a. (25 points) Compute the exponential Fourier transform. b. (10 points) Plot the Fourier spectrum.
(a) Based on the following discrete-time signal x[n], [n] →n -2 -1 0 1 2 3 4 i. [5%] determine the Fourier transform (i.e., X(ein)) and sketch the magnitude spectrum. ii. [4%] Given the following signal Xp[n], which is the periodic version of x[n] with period 4. Derive the Fourier series coefficients of yn], i.e., {ax}. xp[n] -1 1 2 3 4 5 iii. [4%] Hence, derive the Fourier transform of ap[n], i.e., Xp(es"). iv. [5%] Based on the results...
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"
2. Calculate the inverse Fourier transform of X(cfw) = {2 2j 0 <W <T -2j -n<w < 3. Given that x[n] has Fourier transform X(@j®), express the Fourier transforms of the following signals in terms of X(el“) using the discrete-time Fourier transform properties. (a) x1[n] = x[1 – n] + x[-1 - n] (b) x2 [n] = x*[-n] + x[n]
Problem 1: (3 +2+3+2 10, sampling) Consider the continuous-time signal x(t) = 3 + cos(10?1+ 5) + sin(15?), t E R (a) Find the Fourier transform X-Fr. Hint: (F ejuot) (w) 2??(w-wo) (b) What is the Nyquist Frequency wn in radians/s of x? (c) Write an expression for the Fourier transform of the ideal sampling of x with sam- pling period T, = 2n/Cav.), i.e., ?00_ox(AZ)6(t-kZ) Hint: (F eiru>tz(t) (w) - X(w - rus) and recall Poisson's identity, CO eyru'st,...
The following signal's zero-point is at 2: x[n] = {1, 0, −1, 2, 3} The discrete-time Fourier Transform is expressed as X(ejw) = Xr(ejw)+jXi(ejw). Find the signal with Fourier Transform Xi(ejw) + Xr(ejw)ej2w
Matlab Question#1: Determine the discrete-time Fourier transform of x(n) (0.8y'n u(n)+(0.1)'n u(n) Evaluate Xei) at 501 equispaced. points between [0,pi] and plot its magnitude, angle, real, and imaginary parts Matlab Question#2: Determine the discrete-time Fourier transform of Evaluate Xei) at 1001 equispaced points between [0pi] and plot its magnitude, angle, real, and imaginary parts. Matlab Question#3: Compute the FT values at the prescribed frequency points and plot the real and imaginary parts and the magnitude and phase spectrums. The FT...
2. Discrete Fourier Transform.(/25) 1. N-th roots of unity are defined as solutions to the equation: w = 1. There are exactly N distinct N-th roots of unity. Let w be a primitive root of unity, for example w = exp(2 i/N). Show the following: N, if N divides m k=0 10, otherwise N -1 N wmk 2. Fix and integer N > 2. Let f = (f(0), ..., f(N − 1)) a vector (func- tion) f : [N] →...