Question

The cross correlation of two real finite energy sequences x(n) and y(n) is given as __________

(a) \(r_{xy}(l)=\sum_{n=-\infty}^{\infty}x(n)y(n-l)\) where l=0,±1,±2,…

(b) \(r_{xy}(l)=\sum_{n=0}^{\infty}x(n)y(n-l)\) where l=0,±1,±2,…

(c) \(r_{xy}(l)=\sum_{n=-\infty}^{\infty}x(n)y(n-l)\) where -∞<l<∞

(d) none of the mentioned

The question was asked in a national level competition.

This is a very interesting question from Correlation of Discrete Time Signals in section Discrete Time Signals and Systems of Digital Signal Processing

Answer 1

Correct choice is (a) \(r_{xy}(l)=\sum_{n=-\infty}^{\infty}x(n)y(n-l)\) where l=0,±1,±2,…

Easy explanation: If any two signals x(n) and y(n) are real and finite energy signals, then the correlation between the two signals is known as cross correlation and its equation is given as

rxy(l)=\(\sum_{n=-\infty}^{\infty} x(n)y(n-l)\) where l=0,&pm;1,&pm;2,…