Complex signal example

1. What are complex signals?
2. What are real and complex signals?
3. Do complex signals exist?
4. What is a complex exponential signal?

What are complex signals?

A complex signal consists of two real signals - one for the real and one for the imaginary part. The linear processing of a complex signal, such as filtration with a time-invariant linear filter, corresponds to applying the processing both to the real and the imaginary part of the signal.

What are real and complex signals?

A real signal at any given time takes its value in the set of real numbers, and a complex signal takes its value in the set of complex numbers.

Do complex signals exist?

Also complex signal exists in electronics, where voltage is real component and current is imaginary component of complex signal. Complex signals occur with AC current and plus inductors or capacitors in electronic circuits.

What is a 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.