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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»

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)|≤\(\sqrt{r_{xx}(0).r_{yy}(0)}\).


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