Test: Introduction to Signals

All bounded periodic signals are power signals, because they do not converge to a finite value so their energy is infinite and their power is finite.

The autocorrelation function of a signal is defined as the measure of similarity or coherence between a signal and its time delayed version. Thus, autocorrelation is the correlation of a signal with itself.

Property of autocorrelation function:

• The autocorrelation function of energy signals exhibits complex conjugate symmetry, which means the real part of autocorrelation function R(τ) is an even function of delay parameter ( τ) and the imaginary part of R(τ) is an odd function of the parameter τ. Thus,

R(τ)=R∗(−τ)

Because f_s ≤ 2f₀,

Ts ≤ _.

and 

⇒  

x(t) = u(t) - u(-t)

u(t) = 

u(-t) = 

-u(-t) = 

Hence, 

x(t) = u(t) - u(-t)

even part = [u(t) + u(-t)] / 2 = 1/2

odd part = [u(t) - u(-t)] / 2 = 1/2[x(t)]