For the signals x() given in Problems #(1-3), find the formula for the Fourier Transform X...
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)...
Find and plot the Fourier transforms of the following signals. (if the Fourier transform is a complex function, plot the magnitude absolute value) and phase (argument) parts separately) [70 points]. [Hint: You can use the time shifting property if applicable] 5, 0 <ts3 Xs(t)-〈0, otherwise
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...
Compute the Discrete-Time Fourier Transform analytically for the following signals and plot the absolute values and the phase of the DTFT from-2π to 2π x[n] αηυ[n] for α-0.7 and 0.3 x[n]-δ[n-r] for τ-2 and 3 xInrk], for r -2 and 3 a. b. C. Please show your work step by step and include the formula for finding the absolute value of DTFT and the phase of DTFT.
Find the Fourier Transform of the following signals: (a) x(t) = Sin (t). Cos (5 t) (b) x(t) = Sin (t + /3). Cos(5t-5) (c) a periodic delta function (comb signal) is given x(t) = (-OS (t-n · T). Express x(t) in Fourier Series. (d) Find X(w) by taking Fourier Transform of the Fourier Series you found in (a). No credit will be given for nlugging into the formula in the formula sheet.
Q. 2 A continuous time signal x(t) has the Continuous Time Fourier Transform shown in Fig 2. Xc() -80007 0 80001 2 (rad/s) Fig 2 According to the sampling theorem, find the maximum allowable sampling period T for this signal. Also plot the Fourier Transforms of the sampled signal X:(j) and X(elo). Label the resulting signals appropriately (both in frequency and amplitude axis). Assuming that the sampling period is increased 1.2 times, what is the new sampling frequency 2? What...
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...
Given that the Fourier transform of x(t) is 3e-jw x(jw) = (1 +ju) find the Fourier transform of the following signals in terms of X (jw). a. y(t) = e'*x(t – 2) b. y(t) = x(-3) c. y(t) = x(t)dt
For each signal x(n) in Problems #(1)-(5), use Z Transform Tables to do the following: (a) Write the formulas for its Z Transform, X(e), and Region of Convergence, RoCr (b) List the values of all poles and all zeros. (c) Sketch the pole zero diagram. Label both axes. Give key values along both axes. sin ( (-n))u-n]. (Hints: cos(π/3) (5) x1n] , 1/2, sin(π/3)-V3/2) ," For each signal x(n) in Problems #(1)-(5), use Z Transform Tables to do the following:...
(30%) Find the Fourier transform of the signals given below: 2) x(I)-e-3,Cos(10a)U(1) 3) x(t)-45(1 + 3) + 56(1) + 4δ(1-3) = 511( ) 5) x(t) = 3A(-4)e'or(1-4)