Correlation between Signals

Correlation is a measure of similarity between two signals and forms the foundations for most detection and estimation problems in signal processing. In our everyday life, we recognize something by correlating it with what we already know. Correlation plays a crucial role in many areas of our life such as economics, marketing, and psychology.

The algorithm

As described in the beginning, the objective of correlation between two signals is to measure the degree to which those two signals are similar to each other. Mathematically, correlation between two signals $x[n]$ and $h[n]$ is defined as

$$y[n] = \sum \limits _{m = -\infty} ^{+\infty} x[m] h[m-n]$$

where the above sum is computed for each $n$ from $-\infty$ to $+\infty$.

The process of correlation can be understood by reading the following steps:

1. Select the time shift:

Observe that there are two indices, ...