Find the discrete-time Fourier Series for the following periodic signals: 3. 4 cos 2.4n n +...
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.
Determine whether the following discrete-time signals are periodic or not? For the periodic ones, find their fundamental period. 2. (5 points each) a. x1 [n] =sin(0.5n +z/4) c. x1n] = cos (tn/3) + sin(nn/5)-2cos(tn/10) d. x4[n]- sin(tn/12) cos(tn/3) (Hint: use trigonometric identities to write the signal as a sum of sinusoids)
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.
3.11-For each of the following signals compute the complex exponential Fourier series by using trigonometric identities,and then sketch the amplitude and phase spectra for all values of k (a) x(t)-cos(5t-π/4) (b) x(t) sint+ cos t 756 Chapter & The Series and fourier Translorm 023 4 5 ibi FIGURE Pa P33 3.13 Problems 157 in 0 14 12 3 I) ain FIGURE ,3.3 (antísndj (c) sti)-cos(1-1) + sin(,-%) 3.12. Determine the exponential Fourier series tor the Following periodic signals
3.11-For each...
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
Solution required in MATLAB
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...
Signals and Systems: Discrete time Fourier Series: If: 1. Please find the F.S. representation of x[n] 2. Please plot the amplitude spectrum 3. What is the fundamental frequency of x[n]? 4. How many distinct harmonics can be present in x[n]?--for this fundamental frequency. 5. How many harmonics are actually in x[n]? Trying to prepare for finals, its crunch time, thank you for your help! r[n] = 2sin(n-) + cos(n-) r[n] = 2sin(n-) + cos(n-)
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
2. Determine whether the following discrete-time signals are periodic or not? For the periodic ones, find their fundamental period. (5 points each) n12 c. z[n] sin (3rn7)2sin(n/10)
3. [45] Compute the exponential Fourier series representation for the following signals and sketch the amplitude and phase spectra. x(t) -7 -6 -2 -1 4 5 6 x(t) b) c) x(t) periodic with period 4 and (sin(at),0 <t<2 x(0) = { 0,2 <t 54