Question

6. Alinear interpolator is a system that takes an input x[n] and produces an output y{n} defined by y[2n]=x[n] y[2n+1]= |_ x[n]+x[n+1] 2 + b. a. Find the frequency response, H (ei"), of the system that produces this result. What is the impulse response of that system? Demonstrate that the system defined by part b when operating on a signal in which a zero is inserted between each of the data point, produces an output that is a linearly interpreted signal by a factor of 2. c.

Answer 1

Solution The interpolator System that takes. Input x [n] output yin y (2n) 2x [n] x (n) + X(n+1) y Canti) 잇 for y (an) = y(0) (nh= (1+46) h = y (2n) = 4 (2) ay (2nt) :y (3) - n22 -y (21) = y(4) y (2n+1)= y(5) (2n) = y(6) ay (2n+1) = y (7) n. 3 9 y (n) .yo) tyl17 +42) ty (3) ry (4) +y (5) y can] ty (anti) * H)+ (n+1) in) + 2 yon) - 3 / з у. (n) + 2 x (n+1) reiw) = 1.571ejw) +0-sejw xierw

y lejun Xew) 2 [3 reiw) Hew) = + [3r eje if(3) = ( 3 + 2011] sin) at no it ý defined impulse respons mean giving sing as input. # (W) 22. out x ola for no even let us Surpose signal sito defined as 567 2a, bo cd, c. f] Considen to be acorate. Now when we insert Zero in blow each point blw

we get s't) - 20.0.6.0.0, 0, d. 0,0,0,f) Hence we can write 5(6) 25'(26). This į basically scumpling by factor of a in the input į fincanly in térented signal by a factor de டு irulse வெச, 41 hen] 1 TFT I's laredo = 1. OFT [15+0.5 54.56 m2 70.5 8(n+1) h[n] 1.58 in) +0.5 (SH+i) h [n 2 1.58 (n) to.sg -58 (nry)