Periodicity of a discrete time complex exponential signal?

1. What is the periodicity of complex exponential signal?
2. How do you find the periodicity of a discrete-time signal?
3. What is discrete-time exponential signal?

What is the periodicity of complex exponential signal?

Periodicity of complex the exponential. Recall the definition: if z = x + iy where x, y ∈ R, then ez def = exeiy = ex(cosy + i siny). It's clear from this definition and the periodicity of the imaginary exponential (§I) that ez+2πi = ez, i.e.: “The complex exponential function is periodic with period 2πi.”

How do you find the periodicity of a discrete-time signal?

A discrete-time signal is periodic if there is a non-zero integer p ∈ DiscreteTime such that for all n ∈ DiscreteTime, x(n + p) = x(n). x(n) = cos(2π f n).

What is discrete-time exponential signal?

A discrete-time real exponential sequence is defined as − 𝑥(𝑛) = 𝑎^𝑛 for all 𝑛 Depending upon the value of a the discrete time real exponential signal may be of following type − When a < 1, the exponential sequence x(n) grows exponentially. When 0 < a < 1, the exponential signal x(n) decays exponentially.