2. Consider the following interconnection of four LTI systems where each system is described by its...
signals and systems
Question 1 (30%): Consider a LTI systern which is comprised of four subsystems whose impulse responses are hi(t), h2(t). ha(t), and ha(t). u(t) f(t) hi(t) h2(t) 13 ha(1) Where: hi (t) = δ(t + 1) h2(t) = 2(u(t)-u(t-1)] hs(t) = 201t-2) h1(t) = u(t + 2)-u(t) a) (8%) Compute the overall impulse response htotal(t) of the system comprised of hi(t), h2(t), hs(t), and h4(t). Sketch and write the expression for htotai(t) b) (4%) Is the total system...
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2. (Combining systems (30 Pts)] Hi and H2 be continuous-time LTI systems respectively with impulse responses hi and h2. (a) Provide the expression of Hi(r) (t) for all t using the impulse response h (5 Pts) (b) Provide the expression of H21r)(t) for all t using the impulse response h2 (5 Pts) (c)Let Hs be the serial connection of H1 and H2, i.e Draw a block diagram for the above equation 5...
12 • 171 T- (6) Figure 1 (b) Consider the interconnection of the LTI systems shown in Figure 2 below. (1) Find the impulse response h[n] of the total system. (ii) Determine and sketch the total impulse response h[n] if ht[n]= 8[n-1], h2[n] = 3u[n+4], h3[n] = -3u[n-2], and he[n] = 8[n+4]. xin that the syn] - Paragraph -
(a) LTI Systems. Consider two LTI subsystems that are connected in series, where system Tl has step response s1(t)=u(t-1)-u(t-5) and system T2 has impulse response h2t = e-3tu(t). Find the overall impulse response h(t). Hint: you will need to find h1(t) first (b)Fourier Series. The input signal r(t) and impulse response h(t) of an LTI system are as follows:x(t) = sin(2t)cos(t)-ej3t +2 and h(t) = sin(2t)/t Use the Fourier Series method to find the output y(t) (c)Parseval's Identity and Theorem. Consider the system in the...
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2. Given the following z-transform of the impulse response h [n], of a causal LTI system Ti H1 (z) = (,-1)(z-0.5) (a) Find hin (b) Verify the first three non-zero values of hi[n] using long division. (c) Find the z transform Hs(z) of hs[n]-2"hi[n], and specify the ROC. (d) Find thez transform H4() of han+n -1], and specify the ROC. e) Find the impulse response, hs[n], of the system Ts, which is the...
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Consider the cascade of a LTI system witlh impulse response h()-"u() ith the LTI system whose impulse response is h2 () ao(t) where δ(1) φ . Find the overall impulse response.
Consider a LTI system with impulse response h[n] = u[n]*a^n, where |a| < 1. a) Determine the frequency response of the system. b) Find the magnitude response and the phase response, given a = 1/2. No plots. c) Consider a LTI system whose impulse response h1[n] is a time-shifted version of h[n], i.e., h1[n] = h[n − n0]. Compute the frequency response H1(e^(jΩ)), and represent H1(e^(jΩ)) in terms of H(e^(jΩ)).
2. Consider the interconnection of the following three systems depict hi In x[n] Assume han , otherwise (a) Determine the overall impulse response hin). (b) Determine the frequency response H(e). (c) Find the output vin), when the input zn-unl is applied.
3. Impulse Response and Step Response. (25 pts) Consider the following LTI systems: • T1: Has input-output relationship yı(t) = -X1(t – 5) 1<t<4 • T2: Has impulse response hz(t) = { therwise • T3: Has step response s3(t) = -4u(t + 3) • T4: Has step response s4(t) = -tu(t) (a) (5 pts) What is the impulse response hi(t) of system Tj? (b) (10 pts) What is the step response sz(t) of system T2? Write it in terms of...
LTI Systems-Stability Consider an LTI system with system function: s-1 H (s) = If the system is non-causal and un-stable, determine the time domain impulse response