A sequence x[n] has a zero-phase DTFT X(e^jw) as sketched in Figure P3.3. Sketch the DTFT of the sequence x[n]e^-jπn/5
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1. Find the DTFT of the sequence x[n] = 0.5%u[n] . Express the DTFT in magnitude-phase form.
do not use z-transform, laplace transform . A DT signal is defined by Sketch the magnitude and phase of the DTFT of . A DT signal is defined by Sketch the magnitude and phase of the DTFT of
Find the DTFT X(Ω)of the following signals (The bold denote the index n = 0).Also,sketch the magnitude and the phase spectrum (you may use Matlab or other plotting software): 1.x[n]= {1,2,3,2,1}
4. a) The sequence x[n] is related to its discrete time Fourier transform (DTFT). Xeo), by the expression: 27T i) Use this expression to design a 10th order high-pass finite impulse response (FIR) filter with cut-off frequency of 7 kHz for signals sampled at 16 kHz. Perform your design using a rectangular window. ii State what improvement in the performance of the filter might be 3 obtained by the use of a Hamming window. iii) Sketch a direct form implementation...
Let x[n] be infinite-duration sequence with DTFT of 2n X(e'"), Xi[n] is an N-point finite-duration sequence whose DFT X,(e N ) was obtained by sampling X(eW) at N equally spaced points on the unit circle. Determine xl[n] in terms of x[n] Let x[n] be infinite-duration sequence with DTFT of 2n X(e'"), Xi[n] is an N-point finite-duration sequence whose DFT X,(e N ) was obtained by sampling X(eW) at N equally spaced points on the unit circle. Determine xl[n] in terms...
Consider a sequence xln] 2-"uln], with its DTFT given by xlet y[n] be a finite-duration signal of length 10. Suppose the 10-point DFT, Y[k], of y[n] is given by 10 equally-spaced samples of X(e). Determine y[n]. Hint: N-point DFT of a sequence w[n] = 2-n (u[n]-u[n-N]) is W [k] = 1-22 1wk Consider a sequence xln] 2-"uln], with its DTFT given by xlet y[n] be a finite-duration signal of length 10. Suppose the 10-point DFT, Y[k], of y[n] is given...
Lab #2 Discrete-time Fourier Transform (DTFT) OBJECTIVES: • Explore the DTFT, its meanings and concepts. • Get acquainted with Matlab/Octave 1) Start MATLAB and change the “Current Directory” in the top of the window (or type) >> cd '' (example: >> cd 'C:\NIU\lab2') Alternatively, if you don't want to use MATLAB, you can open a web-browser and go to “octave-online.net”. 2) Download and execute LAB2forStudent_A.M with >> lab2forStudent_A and observe that it produces a Discrete-Time (DT) signal xVec. 3) TO...
3.13 Determine the DTFT of the two-sided sequence y[n] = a1",jal < 1.
Q.3) 120 Marks] [8 Marks] Determine the DTFT of the following DT signals i) x[n] = (0.5)" [u[n]-n(n-3)) a) ii) ? [n] = n (0.5)" u[n-2] b) [8 Marks] Consider the following CTFT pair: jw x(t) ?? (-v^2 + 5 i) e -/00t x(t) 6) using the CTFT properties determine the Fourier transform (CTFT) of: i x(3t-6) e) [4 Marks] Prove the Parseval's relationship for a CT signal x e
Define the rectangular window as follows: wlnl otherwise (a) Show that its DTFT has the following expression: W(eju)-e-jaa, sin Me Find out what the constant α is. sin(?) (b) Make a sketch of IW(ejoj as a function of ω for the case of M-4, and show where the zero crossings are. (c) Now, consider the Hann window defined as follows, πη 2M 0, otherwise. Make a sketch of wH[n] Define the rectangular window as follows: wlnl otherwise (a) Show that...