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1. Determine the DTFT of each of the following sequences: TL (c) zelrnl - \o. otherwise
1. Determine the DTFT of each of the following sequences. a) X[n]=δ[n-1]+6[n-6] c) xt[n]= (-3)" (u[n-1]-u[n-10]) d) x.[n]=0.5a cos(nn/2)u[n] e) 2n-2 u[-n+41 Xcn
Assume that a sequence an has the spectrum (DTFT) A(f)- 0 otherwise within fl s l/2 Stetch the spectrum of each of the following sequences a) aln] cos(n) b) a[n] cos(11??) c) ancos(n)
Question 3]: Determine the DTFT of the following sequences over 0 SW S1, then plot the corresponding magnitude, angle, real part and imaginary part in one figure window. 1. x(n) = (0.3)"u(n) 2. x(n) = (0.5)"u(n-10) 3. x(n) = (0.9)" [u(n)-un-21)]
7. Determine the DTFT of the sequence [n]-, where N is 1S 0 otherwise a positive integer. Plot it for No 4 and No 20
Problem 5 Discuss the convergence of the following sequences: (a) an - 7 TL = n -1)n sin(n n3+1 (d) dn Vn TL
3. For each of the following discrete-time sequences: (i) Find the Z-transform (ZT), if it exists, and plot the region of convergence (ROC) in the Z-plane (ii) Find the poles and zeros and plot them in the 2-plane (iii) Determine whether the DTFT of the sequence exists (a) x[n] = 8[n – 1] + 28[n – 3] (b) [n] = (0.9e-j*)" u[n + 2] – 2-ul-n - 1] (c) x[n] = 2-" un + 1]
1. For each of the following sequences, determine whether it converges. If so, find the limit. 2n+1 5n-2 a. b. 4. =(-1)"." 2n 2"-1 c. n
Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convolution of two signals. Q5. Consider an L'TI system with input x (o] and impulse response h (o] specified as follows. x [n] = 2"u [-n] h [n] -u [n] Find the output y [n] using convolution sum. Q4. Consider the two sequences x [n] = [0 otherwise h[n] = {00 otherwise α>1 calculate the convolution of two signals. Q5. Consider an L'TI...
7. (25) Solve the following problems. (a) Find the limit (b) Find the interval of convergence of the following power series 0O TL Tl n-1 (c) Find the sum of the following power series and determine the largest set on which your formula is valid n= 1 (d) Let f(x) = cosa. Find T6(2), the Taylor polynomial of f at zo = 0 with degree 6 (e) Calculate the Maclaurin series for the following functio f(x) = In 7. (25)...
3.13 Determine the DTFT of the two-sided sequence y[n] = a1",jal < 1.