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3. Find the discrete-time Fourier series (DTFS) and the corresponding spectra D, and ZD, for the...
1. Find the discrete-time Fourier series (DTFS) and sketch their spectra D. and ZD, for 05rs N. -1 for the following periodic signal: x[n] = 4 cos 2.41en+ 2 sin 3.2an 2. If x[n] = [0, 1, -2, 3, 4, 5, -6], determine No and 120 for this sequence.
Find the discrete-time Fourier series (DTFS) and sketch their spectra IDI and LD for 0 No-1 for the following periodic signal: f[k] 2 cos 3.2r(k-3).
Consider the discrete-time periodic signal n- 2 (a) Determine the Discrete-Time Fourier Series (DTFS) coefficients ak of X[n]. (b) Suppose that x[n] is the input to a discrete-time LTI system with impulse response hnuln - ]. Determine the Fourier series coefficients of the output yn. Hint: Recall that ejIn s an eigenfunction of an LTI system and that the response of the system to it is H(Q)ejfhn, where H(Q)-? h[n]e-jin
Prob. 2 Discrete-Time Fourier Series (DTFs) (a) A periodic signal, rin] is shown below. Use the analysis equation to determine the discrete-time Fourier Series (DTFS) coefficients, a. Express the a in terms of cosines [72] -2 N= -3 (b) Sketch the spectrum, as vs. k for -5Sk s5. Please note each value. ak 2 5 Prob. 2 (cont.) -Discrete-Time Fourier Series (CTFS) (c) A periodic signal rafnl is given below. a2In] 2 1 E -3 what is the fundamental period...
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1. Convolution and Discrete-Time Fourier Series (DTFS) (a) Generate a periodic signal r2[n] with the fundamental period N ralla-sin(2nn/ İ0) + sin(2m, 2 ) + sin(2nn/30) for 0 < n < N-1 Find the fundamental frequency Ω0-2, N, with the fundamental period N. (b) Generate a periodic signal h2[n] with the fundamental period N haln] = (1/2)", for 0 < n < N-1 (e) Using the com ftuction n Matab, compute the compvolution (d) Using the...
/lay Figure 9.1: Discrete-time sinusoid sin 0.11 n and its Fourier spectra. x[n] = sin Olan= (010.17n – e-O.lan) (9.15) From the spectra in Fig. 9.1 write the Fourier series corresponding to the interval - 10 2r> -30 (or-T2N>-37). Show that this Fourier is equivalent to that in Eq. (9.15).
Objective Conduct DTFT, DTFS on a periodic discrete signal. Task: Consider the system with impulse response Tth sin 8 h(n) S(n) Tn (1) Find the Fourier-series representation for the output y(n) when the input x(n) is the periodic extension of the sequence 3/2, -1,0, -3/2, 1,0 Plot the x(n), h(n), y(n) and Fourier coefficient bk using Matlab or handwriting (Example 7.2.6 irse material) in cour (2) Find the output y(n) of the system with the input 1 Tn Tn x(п)...
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...
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
Find the discrete time Fourier series of the following periodic signal x[n] = 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3... Verify using Parseval's Theorem