Similarity

Similarity between Discrete-Time Signals and is computed by summing the element-wise product of their Samples

$$S(x,y)=\sum _{i}x[i]\cdot y[i]$$

• Similarity is only defined for two signals of exactly the same length
• Similarity is a fold, unlike a Convolution

Alternatively, if you want to think of the signals as finite 1 dimensional vectors,, similarity is just the Dot Product of the two signals of the same length

$$S(\vec{x},\vec{y})=\vec{x}\cdot \vec{y}$$

For Continuous-Time Signals you just slightly adjust it to a continuous land sum (Integral)

$$S(x,y)=\int x(t)\cdot y(t)dt$$