"ASSIGNMENT FOR DIGITAL SIGNALPROCESSINGProf. Rashmi PatilAssignment No: 3Questions: Answer the following multiple choice questions.Q1 The cross correlation of two real finite energy sequences x(n) andy(n) is given as:d) None of the mentionedQ.2 What is the cross correlation sequence of the following sequences?x(n)={….0,0,2,-1,3,7,1,2,-3,0,0….}y(n)={….0,0,1,-1,2,-2,4,1,-2,5,0,0….}a) {10,9,19,36,-14,33,0,7,13,-18,16,7,5,-3}b) {10,-9,19,36,-14,33,0,7,13,-18,16,-7,5,-3}c) {10,9,19,36,14,33,0,-7,13,-18,16,-7,5,-3}d) {10,-9,19,36,-14,33,0,-7,13,18,16,7,5,-3}Q.3 What is the energy sequence of the signal ax(n)+by(n-l) in terms ofcross correlation and auto correlation sequences?2 2 a) a r (0)+b r (0)+2abr (0)xx yy xy 2 2 b) a r (0)+b r (0)-2abr (0)xx yy xy 2 2 c) a r (0)+b r (0)+2abr (1)xx yy xy 2 2 d) a r (0)+b r (0)-2abr (1)xx yy xy Q.4 The normalized auto correlation ?xx(l) is defined as:a) (r (l))/(r (0))xx xx b) -(r (l))/(r (0))xx xx c) (r (l))/(r (0))xx xy d) None of the mentionedn Q.5 What is the auto correlation of the sequence x(n)=a u(n), 0<a<l?2 l a) 1/(1-a )a (l=0) 2 -l b) 1/(1-a )a (l<0)2 |l| c) 1/(1-a )a (-8<l<8)d) All of the mentionedQ.6 Which of the following parameters are required to calculate thecorrelation between the signals x(n) and y(n)?a) Time delayb) Attenuation factorc) Noise signald) All of the mentionedQ.7 Which of the following relation is true?a) r (l)= r (-l)xy xy b) r (l)= r (l)xy yx c) r (l)= r (-l)xy yx d) None of the mentionedQ.8 Which of the following is the auto correlation of x(n)?a) r (l)=x(l)*x(-l)xy b) r (l)=x(l)*x(l)xy c) r (l)=x(l)+x(-l)xy d) None of the mentionedQ.9What is the relation between cross correlation and auto correlation?a) |r (l)|=v(r (0).r (0))xy xx yy b) |r (l)|=v(r .r (0))xy xx(0) yy c) |r (l)|?v(r .r (0))xy xx(0) yy d) |r (l)|=v(r .r (0))xy xx(0) yy Q.10 Auto correlation sequence is an even function.a) Trueb) False ASSIGNMENT SOLUTIONS FOR DIGITALSIGNAL PROCESSINGProf. Rashmi PatilAnswer key to assignment No.31 aExplanation: If any two signals x(n) and y(n) are real and finiteenergy signals, then the correlation between the two signals is knownas cross correlation and its equation is given as2 b 3 cExplanation:The energy signal of the signal ax(n)+by(n-l) is4 aExplanation: If the signal involved in auto correlation is scaled, theshape of auto correlation does not change, only the amplitudes of autocorrelation sequence are scaled accordingly. Since scaling isunimportant, it is often desirable, in practice, to normalize the autocorrelation sequence to the range from -1 to 1. In the case of autocorrelation sequence, we can simply divide by r (0). Thus thexx normalized auto correlation sequence is defined as ? (l)=xx (r (l))/(r (0)).xx xx"