Converting complex sum of exponential signal to real signal

1. What is a complex exponential signal?
2. What is the difference between real and complex signals?
3. What should be the condition for the signal to be decaying in real exponential signal?
4. Are complex signals real?

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.

What is the difference between 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.

What should be the condition for the signal to be decaying in real exponential signal?

Discrete-Time Real Exponential Signal

When 0 < a < 1, the exponential signal x(n) decays exponentially.

Are complex signals real?

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.