The unit sample is a signal which is zero everywhere except when its argument is zero, then it is equal to 1. Mathematically
unit sample: δ=ì
a)1ifn=0
b)0 otherwise
The unit sample function is very useful in that it can be seen as the elementary constituent in any discrete signal. Let x be a sequence. Then we can express x as follows (using the unit sample definition and the delay operation)
x=∑ (x(k)δ(n−k)) (1)
k=−∞