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Digital Signal Processing Chapter 3 1. Sketch each of the following special digital sequences: (a) 58(n) (b) -2õ(n-5) (c) -5u(n) (d)5u(n-2) 2. Calculate the first cight sample values and sketch each of the following sequences: (a.) x(n)=0.5"u(n) (b. x(n)=5sin (0.2m n)u(n) 7. Sketch the following sequences: (a) x( n)=2õ(n+3) -0.56(n+1)-58(n-2)-4(6n-5) (b) x(n)=2ô(n+2) 20(n+ 1)+5u(n-3) 3.8. Given the x(n) Figures 3.26 and 1.27 write expression for each digital signal using sequence and its shifted sequences . 4 FIGURE 3.26 The first digital signal ir Problem 82 CHAPTER Digital Signals and Systems . FIGURE 3.27 The second digital signal Problem 3.8. .10. Determine which of the following systems is linear system. (a) (n) =5x(n)+2x²(n) (b)y(n)= x(n-1)+4x(n) (c) ((()) =4x³ (n- 1)-2x(n) 13. Determine which of the following linear systems is time invariant. (a)y(n)= -5x(n- 10) (b) y(n)=4x(n2) 14 Determine which of the following linear systems is causal. (a) y(n) =0 5x(n) +100x(n-2 20x(n- 10) (b) y(n): x(n+4) +0.5x(n)-2x(n-2) 16. Find the unit impulse response for each of the following linear systems. (a)y(n) 0.5x(n) 0.5x(n- 2): forn> 0,x(-2) =0,x(-1) (b)y(n) =0. 75x(n- 1)+x(n); for n> 0,y(-1)=0 Chapter 6 2. Given the difference equation y(n) =x(n) 0.5y(n- +0.6y(n- 1) (a)Calculate the system response y(n) 0,1, .4 with the input x(n)=(0.5)"u(n) and initial condition x(- 1)= and y( 1)=1, 9. A digital system is described by the following difference equation: y(n): x(n)- 0.3x (n 1) +0.28x(n-2) Find the transfer function H(z) the denominator polynomial A(z) and the numerator polynomial B(z) 10. Convert each of the following transfer functions into difference equations: (a) H(z) 550.5z (b)H(z) 1-0.3z 21. For the difference equations: (a) y(n) =0. 5x(n) +0. 5x(n- 1) (b)y(n) =0 5x(n) 5x(n- 1) (c) y(n) =0 5x(n) +0, 5x(n 2) (d)y(n) 5x(n) 5x(n-2) 1. Find H(z): 25. Given the filter H(z)= realize H(z) and develop difference equations using the following forms: a. direct form b direct -form II;

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