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

 

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Derive state equation and output equation for direct II form. Let a discrete-time system have the state-variable description given by 2 0 b= [2], c= [1 -1], D= [0] Define new states qi'[n] =2q;[n] and 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(eº) = ex (e) (b) d x(e) y(em)= ΦΩ 2. Find DTFT of the following signals using its properties (1) x[n] = n( ²3 ) *u{n+2] (2) x[n] = cos(n) (u[n-2] 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 Derive state equation and output equation for direct II form. Let a discrete-time system have the state-variable description given by 2 0 b= [2], c= [1 -1], D= [0] Define new states qi'[n] =2q;[n] and 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(eº) = ex (e) (b) d x(e) y(em)= ΦΩ 2. Find DTFT of the following signals using its properties (1) x[n] = n( ²3 ) *u{n+2] (2) x[n] = cos(n) (u[n-2] 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

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