Discontinuity in the angle of a complex exponential signal

1. What is complex exponential signal?
2. How do you find the period of a complex exponential function?
3. Why is complex exponential periodic?
4. What is exponential signal?

What is complex exponential signal?

A complex exponential is a signal of the form. (1.15) where A = ∣A∣e^{j θ} and a = r + j Ω 0 are complex numbers. Using Euler's identity, and the definitions of A and a, we have that x(t) = A e^at equals. We will see later that complex exponentials are fundamental in the Fourier representation of signals.

How do you find the period of a complex exponential function?

II. 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.”

Why is complex exponential periodic?

When the magnitude of the complex exponential is a constant, then the real and imaginary parts neither grow nor decay with time; in other words, they are purely sinusoidal. In this case for continuous time, the complex exponential is periodic.

What is exponential signal?

An exponential signal or exponential function is a function that literally represents an exponentially increasing or decreasing series.