What are the Different Types of Signals?

By Aina Parasher|Updated : August 26th, 2022

Different Types of Signals: The signals are classified into several types depending on the criteria used for their classification. This classification aims to exploit the basic properties of the signals to our advantage in the analysis of signals and systems. In this article, we will discuss the types of signals those are useful in the analysis of signals and systems, namely

  • Continuous-Time and Discrete-Time Signals
  • Even and Odd signals
  • Periodic and Aperiodic Signals
  • Energy and Power signals
  • Deterministic Signals and Random signals
  • Causal and Non-causal Signals
  • Analog and Digital Signals

Continuous-Time and Discrete-Time Signals

If a signal value is defined for every instant of time in a considered interval however small the interval is, it is called a “continuous-time signal”. A discrete-time signal is derived from a continuous-time signal through a process called uniform sampling, hence it is defined for discrete values of the time.

For a discrete-time signal module f(n), the argument ‘n’ must be an integer, in contrast, the argument ‘t’ of the continuous-time signal can be any real value.

If a continuous-time signal time signal f(t) is uniformly sampled to form a discrete-time signal f(nTs) such that t=nTs

f(nTs) = f(t), n = 0, ±1, ±2, ±3,….

where Tis the sampling period (sec/sample).

If Ts = 1 sec/sample, then f(nTs)=f(n)

The below figure shows a continuous-time signal f(t)=sin t and its discrete-time version f(nTs)

Continuous-Time and Discrete-Time Signals

Continuous-Time and Discrete-Time Signals 2

The continuous-time signal f(t) can be defined either in the form of a mathematical equation or in a graphical form. On the other hand, along with mathematical form, and a graphical representation, the discrete-time signal f(n) can be represented in the set of values as shown below.

Here the arrow indicates the amplitude of the sample at the origin, and the values right to the arrow represent the amplitude of the sample for the positive values of ‘n’ and the values to its left will be the sample amplitudes for the negative values of ‘n’.

Even and Odd Signals

Even Signal

If f(t) is a continuous-time signal, that is symmetric about the vertical axis such that it appears visually identical to its time-reversal version, such signal is known as an even signal.

f(−t) = f(t)

For a discrete-time signal

f(−n) = f(n)

Example:

Even Signals

Even Signals 2

Odd Signal

If f(t) is a continuous-time signal, it will be called an odd signal, if it is anti-symmetric about its vertical axis, such that

f(−t)=−f(t)

For a discrete-time signal to be an odd signal

f(−n)=−f(n)

Example:

Odd Signals

Odd Signals 2

But in practice, most of the signals are neither even nor odd, for such signals we can find even and odd parts such signals to exploit the symmetry in the analysis of signals and systems. If

f(t) is any continuous-time signal that is neither an even signal nor an odd signal, then

  • Even part of the signal is
  • The odd part of the signal is

Then f(t) is representable as the sum of its even component (fe(t))and its odd component(fo(t)).

f(t) = (fe(t))+(fo(t))

Periodic and Aperiodic Signals

If any signal has a definite pattern, that repeats itself at a regular interval, such signal is known as a periodic signal. If it does not have such a pattern, then it is known as an aperiodic signal. If f(t) is a continuous-time periodic signal, then

f(t)= f(t±kT)

Where ‘T’ is the fundamental time period of the signal f(t), and ‘k’ is an integer.

T=1/frequency(f)=2π/ω

Where, ωis the angular frequency, ω=2πf, and don’t be confused with signal f(t) and frequency ‘f’.

If f(n) is a discrete-time signal,

f(n) = F(n+N)

Where ‘n’ is an integer and ‘N’ is the fundamental time period. Here N is the number of samples taken by the signal to repeat the same pattern, it is an integer, in contrast ‘T’ can be any real value for a continuous-time signal.

Consider the following example for a better understanding.

Periodic Signals

>Periodic Signals

Energy Signals and Power Signals

If the total energy of the signal is finite, such signals are called energy signals, power of such signals is zero. The signals having infinite energy and finite power are known as power signals. To have precise clarity on this we have to know how to calculate the power and energy of the signal, for this understanding consider an electric circuit having a resistor of resistance (R), applied voltage v(t), and the current flowing through the resistor i(t). The instantaneous power is given by

To calculate the normalized power let us assume the resistance R=1

By accumulating the instantaneous power over an interval [Equation] to [Equation], we can obtain the energy dissipated in that interval E(t).

Hence by using this example we can generalize the energy of any continuous-time signal f(t)

Total normalized energy
Then we will calculate the power

Hence we have to calculate the energy first, if the energy of the signal is finite then it is an energy signal, the power of an energy signal is almost negligible hence we can consider it as zero.

If the energy of the signal is infinite, then we can’t calculate the power of such a signal directly since

For such signals, we have to calculate the power indirectly as shown below

If the signal has infinite energy and finite power such signal can be called the power signal. If the signal has infinite energy and infinite power, such signals are neither energy nor power signals.

  • In general, the power signals are having an infinite duration with their value tending to a non-zero constant value as time tends to infinity. Hence periodic signals are power signals in general.
  • The signals having infinite duration with their values also tend to infinity, such signals are called neither energy nor power signals.

If f(n) is a discrete-time signal, then the energy and power of the signal are given by

Deterministic and Random Signals

If a signal’s future value is known exactly at present, such signal is called a deterministic signal.

Example: f(t) = 3t + 6

At t=0; f(t) = 3(0) + 6 = 6 (present value)

At t=10; f(t) = 3(10) + 6 = 36 (future value)

If the future value of the signal cannot be determined at present, such signals are called random signals, such signals can only be expected or estimated.

Causal and Non-causal Signals

If f(t) is a signal such that

f(t)= 0; t<0

Then f(t) is known as a causal signal.

Example:

If f(t) is a signal that has a defined value in the interval t<0; such signals are known as non-causal signals.

f(t) ≠ 0; t < 0

Example:

Causal and Non-causal Signals

Non-causal Signals

Analog and Digital Signals

Concerning time, the signals are classified into continuous-time signals and discrete-time signals. Similarly based on the value the signals are classified into analog and digital. If the value of the signal can be any real value in its dynamic range such signals are known as analog signals. Whereas if the signal is allowed to consider the specific values in its dynamic range such signals are known as digital signals.

Analog and Digital Signals

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FAQs on Different Types of Signals

  • Every signal can be decomposed into the sum of its even and odd components. If xe(t) is the even component of the signal x(t) and xo(t) is its odd component, the x(t) can be written as-

    x(t) = xe(t)+xo(t)

    Here, xe(t)= [x(t)+x(-t)]/2

    xo(t)= [x(t)-x(-t)]/2

  • Visually it appears like a periodic signal, but we cannot find its period. Let the signal f(t)=A=Acos(0t).

    Here angular frequency 𝜔=0, hence frequency f=0, but the time period T=1/0=undefined. So, the DC or constant signal is a periodic signal with a nondefinable period.   

  • The signals having finite energy and almost negligible or zero power are known as energy signals. Whereas the signal that contains infinite energy and finite power is known as a power signal. The energy and power of the continuous-time signal x(t) can be calculated using the below formulas.

  • The sum of two continuous-time periodic signals may or may not be periodic, but the sum of two discrete-time signals is always periodic. That is the reason while adding two discrete-time phasors we will check whether they are individually periodic or not, if they are individually periodic, it is obvious that their sum is a periodic signal.

  • Concerning the value on its vertical axis signals can be classified into digital and analog signals. If the value of the signal can be any real value in its defined range, such signals are known as analog signals. If the value of the signal is confined to the specific values in a defined range, then it is known as a digital signal. 

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