2 (20 marks) Consider the signals: x(t)=u(1+1)-n(1-1), a) Plot x(20) andrespectively (b) Calculate the following convolution,...
Find the convolution of the following two signals: X(t) ylt). Plot the resulting signal. 1. 0 x (t) y (t)
2(a). Compute and plot the convolution of ytryh)x where h(t) t)-u(t-4), x(t)u(t)-u(t-1) and zero else b). Compute and plot the convolution y(n) h(n)*x (n) where h(n)-1, for 0Sns4, x(n) 1, n 0, 1 and zero else.
8) Convolution Integral (7 points). Given the following signals x(t) and h(t), compute and plot the convolution y(t) = x(t) *h(t). x(t) = u(t+2) - u(t – 4) h(t) = 5u(t)e-2t
signal and systems 9. Consider the convolution of two of the following signals : | att) ht) le(n) 力。 2.5 1015年9 L. -3-2-10 2-1012 (5 points cach). a. Determine the convolution of act) and (t) : x(t)= a(t) * b(t). b. Determine the convolution of c(n) and dén): y(n)= e(n) * dín). c. Give the MATLAB code for the convolution of e(n) and dín).
Calculate the convolution sum x{n]=x[n]*x,[n]: 3. a). xn] S[n]+36[n-1]+28[n-2], x,[n]- u[n]- u[n-3) b). [n]- S[n]+ d[n=1]+S[n-2]+0.58[n-3]+ S[n-51,x,[n]- x,[2n] 4. An LTI system is described with the following LCCDE: In]=x[n]+2y[n-1] a). Plot a block diagram to show the input-output relationship. b).With the input x[n]= S[n], and known y[0] = 0 . Find out the output sequence In] using recursive calculation. 5. A system is described with the following figure, find out a suitable LCCDE to express the input-output relationship y[n] [n]...
how to calculate the convolution Calculate the convolution of the following sequences: x[n] (n +1 )R, [n] and h = u [n-2] Answer: Note that the convolution of any sequence with u[n] is the sum of all the components (an integrator) 2. x[n]=仁1,-2-3-4) 1 vl n | =.xln|>k 11 | n | = 〈ー1, 2(00.-1,-3.-6.-10-10. Calculate the convolution of the following sequences: x[n] (n +1 )R, [n] and h = u [n-2] Answer: Note that the convolution of any sequence...
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
(1) Consider the following continuous-time signal: (1) 2ua(-t+t)ua(t), where its energy is 20 milli Joules (2 x 103Joules). The signal ra(t) is sampled at a rate of 500 samples/sec to yield its discrete-time counter part (n) (a) Find ti, and hence sketch ra(t). (b) From part (a), plot r(n) and finds its energy (c) Derive an expression for the Fourier transform of a(n), namely X(ew). (d) Plot the magnitude spectrum (1X(e)) and phase spectrum 2(X(e). (e) Consider the signal y(n)...
Q1-20 points) a) Find the transform of the following signals and plot the ROC. 1 x(n)=(-0,357u(n-4)+(0.25?u(n+2) IL- x(n)=-cu-n-1) b) Find the Inverse Z-transform of: z(2-1.5) for (2-0.33)(2-0.5) ROC: z>0.5
(a) Determine the Fourier transform of x(t) 26(t-1)-6(t-3) (b) Compute the convolution sum of the following signals, (6%) [696] (c) The Fourier transform of a continuous-time signal a(t) is given below. Determine the [696] total energy of (t) 4 sin w (d) Determine the DC value and the average power of the following periodic signal. (6%) 0.5 0.5 (e) Determine the Nyquist rate for the following signal. (6%) x(t) = [1-0.78 cos(50nt + π/4)]2. (f) Sketch the frequency spectrum of...