Question

The normalized auto correlation ρxx(l) is defined as _____________

(a) \(\frac{r_{xx}(l)}{r_{xx}(0)}\)

(b) –\(\frac{r_{xx}(l)}{r_{xx}(0)}\)

(c) \(\frac{r_{xx}(l)}{r_{xy}(0)}\)

(d) None of the mentioned

I got this question by my school teacher while I was bunking the class.

My question is from Correlation of Discrete Time Signals in portion Discrete Time Signals and Systems of Digital Signal Processing

Answer 1

Right choice is (a) \(\frac{r_{xx}(l)}{r_{xx}(0)}\)

The best explanation: If the signal involved in auto correlation is scaled, the shape of auto correlation does not change, only the amplitudes of auto correlation sequence are scaled accordingly. Since scaling is unimportant, it is often desirable, in practice, to normalize the auto correlation sequence to the range from -1 to 1. In the case of auto correlation sequence, we can simply divide by rxx (0). Thus the normalized auto correlation sequence is defined as ρxx(l)=\(\frac{r_{xx}(l)}{r_{xx}(0)}\).