Howtosignalprocessing
- How do you find the period of a complex exponential function?
- What is complex exponential signal?
- Are all complex exponential signals periodic?
- What is harmonically related complex exponentials?
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.”
What is complex exponential signal?
A complex exponential is a signal of the form. (1.15) where A = ∣A∣ej 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 eat equals. We will see later that complex exponentials are fundamental in the Fourier representation of signals.
Are all complex exponential signals periodic?
For discrete Page 2 Signals and Systems 2-2 time the complex exponential may or may not be periodic depending on whether the sinusoidal real and imaginary components are periodic. In addition to the basic signals discussed in this lecture, a number of ad- ditional signals play an important role as building blocks.
What is harmonically related complex exponentials?
Mouaaz Nahas To Page 5 Signal Analysis (802321) That is, a harmonically related set of complex exponentials is a set of periodic exponentials with fundamental frequencies that are all multiple of a single positive frequency o.. at x(t) = C e Dr.
