Question

a) What signal would be maximally dissimilar to this signal based on the correlation coefficient, ρ?

b) What non-zero signal would be orthogonal to this signal based on correlation coefficient? Justify your answer in both cases.

Consider the following signal 4. LAFR 1 time 10 2 6 a) What signal would be maximally dissimilar to this signal based on the correlation coefficient, p? b) What non-zero signal would be orthogonal to this signal based on correlation coefficient? Justify your answer in both cases.

Answer 1

Solution :

Correlation coefficients are used to measure the strength of the relationship between two variables.

It has a value between +1 and −1, where 1 is total positive linear correlation, 0 is no linear correlation, and −1 is total negative linear correlation. (means the two data set clearly disagree with each other)

a)

So for our given signal we can draw exactly opposite signal to get coorelation coefficient as -1.

1 time original signal 10 FUL exactly opposite version to give max dissimilarity time

b)

To get orthohogonal signal pair we need to make a signal such that its dot product in each time interval with

the given signal total add upto 0.

This is shown below :

we can see the dot product of two signal = 0 hence its orthogonal.

parent signal time 10 till one period keep signal same In the next period invert the signal New signal will have zero dot orthohogonalN signal time product with 10 parent signal