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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.
What is the total energy of the rectangular pulse shown in figure below?
The autocorrelation function R_{x}(τ) satisfies which one of the following properties?
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:
R(τ)=R∗(−τ)
The autocorrelation function R_{x}(τ) of the signal x(t) = V sinωt is given by:
The sampling of a function f(t) = sin(2πf_{0}t) starts from zerocrossing. The signal can be detected, if sampling time T is:
Because f_{s} ≤ 2f_{0},
Ts ≤ _{.}
What is the power and energy of the unit step sequence u(n) respectively?
Let δ(f) is the delta function the value of integral
If a signal f(t) has energy ‘E’ the energy of the signal f(2t) is equal to:
and
⇒
Consider the sequence: x[n] = [ 4  j5, 1 + j2, 4], the conjugate antisymmetric part of the sequence is:
The function x(t) is shown in the figure. Even and odd parts of a unit step function u(t) are respectively:
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)]
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