Question

What is the relation between cross correlation and auto correlation?

(a) |rxy(l)|=\(\sqrt{r_{xx}(0).r_{yy}(0)}\)

(b) |rxy(l)|≥\(\sqrt{r_{xx}(0).r_{yy}(0)}\)

(c) |rxy(l)|≠\(\sqrt{r_{xx}(0).r_{yy}(0)}\)

(d) |rxy(l)|≤\(\sqrt{r_{xx}(0).r_{yy}(0)}\)

I got this question during an internship interview.

The query is from Correlation of Discrete Time Signals topic in division Discrete Time Signals and Systems of Digital Signal Processing

Answer 1

Correct option is (d) |rxy(l)|≤\(\sqrt{r_{xx}(0).r_{yy}(0)}\)

For explanation: We know that, a^2rxx(0)+b^2ryy(0)+2abrxy(l) ≥0

=> (a/b)^2rxx(0)+ryy(0)+2(a/b)rxy(l) ≥0

Since the quadratic is nonnegative, it follows that the discriminate of this quadratic must be non positive, that is 4[r^2xy(l)- rxx(0) ryy(0)] ≤0 => |rxy(l)|≤\(\sqrt{r_{xx}(0).r_{yy}(0)}\).