Periodic and non-periodic Signals,
Deterministic and Random Signals,
Energy and Power Signals:,
CT Systems and DT Systems,

**Classification of CT and DT
signals:**

**Periodic and non-periodic Signals**

A
periodic function is one which has been repeating an exact pattern for an
infinite period of time and will continue to repeat that exact pattern for
aninfinite time. That is, a periodic function x(t) is one for which

x (t) =
x(t+nT)

for any
integer value of n, where T >0 is the period of the function and − ∞ < t
<∞ . The signal repeats itself every T sec. Of course, it also repeats every
2 T,3T and nT. Therefore, 2T, 3T and nT are all periods of the function because
the function repeats over any of those intervals. The minimum positive interval
over which a function repeats itself is called the fundamental period T0.T0 is
the smallest value that satisfies the condition x ( t ) = x ( t+T0). The
fundamental frequency f _{0} of a periodic function is the reciprocal
of the fundamental period f_{0}=1/T_{0}. It is measured in
Hertz and is the number of cycles (periods) per second. The fundamental angular
frequency ω_{0} measured in radians per second is ω_{0}=2πT_{0}=
2πf_{0}. A signal that does not satisfy the condition in (2.1) is said
to be a periodic or non-periodic.

**Deterministic and Random Signals**

Deterministic
Signals are signals who are completely defined for any instant of time, there
is no uncertainty with respect to their value at any point of time. They can
also be described mathematically, at least approximately. Let a function be
defined as

A random
signal is one whose values cannot be predicted exactly and cannot be described
by any exact mathematical function, they can be approximately described.

**Energy and Power Signals:**

Consider
v(t) to be the voltage across a resistor
R producing a current i(t). The instantaneous power p(t) per ohm is defined as,
Total energy E and average power P on a per-ohm basis are

For an
arbitrary continuous-time signal x (t), the normalized energy content E of x(t)
is defined as,

The
normalized average power P of x (t) is defined as,

Similarly,
for a discrete-time signal x[n], the normalized energy content ** E**
of x[n] is defined as,

The normalized
average power P of x[n] is defined as,

**CT Systems and DT Systems:**

A system
is defined as a physical device which contains set of elements or functional blocks
and that generates a response or output signal for a given input.

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