Question

Why addition of periodic discrete signals is always periodic

Answer 1

A real function is said to be periodic if there exists a real number

so that

for all

. The number

is said to be a period of the function. The most familiar examples of periodic functions are the trigonometric functions sine, cosine, and tangent.

Note that if

is a period of a function, then

are also periods. If a periodic function is continuous and nonconstant, then it has a least period, and all other periods are positive integer multiples of the least period.