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QUESTION Derive state equation and output equation for direct II form. Let a discrete-time system...

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QUESTION Derive state equation and output equation for direct II form. Let a discrete-time system have the state-variable description given by 1 2-12 b= c = [1 -1}, D= [0] Define new states q'[n] =2q[n] and 5 q2'[n] = 3q2|n). (i) Find the new state variable description given by A, b', c' and D'. (ii) Draw a block diagram corresponding to the new state-variable description computed in (i). Section - II Answer the following questions Answer the following questions 1. You are given x[n]= u[n] => x(e). Find y[n] if (a) y(e)=e14x(e!) (b) d x(el) d92 2. Find DTFT of the following signals using its properties (1) x[n]=n + 2] - yle= - (1). (5) Ma - 21 (2) x[n] = cos(n) Using convolution property (frequency domain) determine the convolution y[n]=x[n]*h[n] of the sequence x[n] = {1 1 1}, h[n]=8[n+1]+8[n] +8[n-1). OR Derive exponential FS form from the trigonometric form of FS. Determine the complex exponential Fourier series representation for the following signal x(t) = cos (4t) + sin(6t)

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