In this lecture, we are going to learn about the definition of signal in communication and the different types of signals in communication. so let’s start with the definition of signal and then we will discuss each signal in detail.
Signal in Communication
A signal may be a function of time, temperature, position, pressure, distance, etc. Some signals in our daily life are music, speech, picture, and video signals. Systematically, we can define a signal as under:
"A function of one or more independent variables which contains some information is called a signal."
In an electrical sense, the signal can be voltage or current. The voltage or current is the function of time as an independent variable.
Classification of Signals
In daily life, we come across several electric signals such as radio signals, T.V. signals, computer signals, etc. Signals may be classified as under:
- Continuous-time and Discrete-time signals.
- Real and complex signals
- Deterministic and Random Signals
- Periodic and Non-periodic signals
- Even and Odd signals
- Energy and Power signals
- Analog and Digital signals
1. Continuous-time and Discrete-time signals
- A signal x(t) is a continuous-time signal if t is a continuous variable. This means that a continuous-time signal is defined continuously in the time domain. On the other hand, if time t is a discrete variable, i.e. x(t) is defined at discrete times, the x(t) is a discrete-time signal.
- Since a discrete-time signal is defined at discrete times, it is often identified as a sequence of numbers and is denoted by x(n), where n= an integer.
- The below figure shows the graph of continuous-time and discrete-time signals.
2. Real Signal and Complex Signals
- A signal x(t) is a real signal if its value is a real number. Similarly, a signal is x(t) is a complex signal if its value is a complex number.
3. Deterministic and Random Signals
- Deterministic signals are those signals which can be completely specified in time. The pattern of this type of signal is regular and can be characterized mathematically. In addition to this, the nature and amplitude of such a signal at any time can be predicted.
- A few examples of deterministic signals are:
(i) x(t)=bt : This is a ramp signal whose amplitude increase linearly with time and slope is b.
(ii) x(t)=a\sin \omega t : For this signal, the amplitude varies sinusoidally with time and its maximum amplitude is A.
- On the other hand, a random signal is one whose occurrence is always random in nature. the pattern of such a signal is quite irregular. Random signals are also called non-deterministic signals.
- A typical example of a random signal is thermal noise, generated in an electric circuit. Such a noise signal has probabilities behavior.
4. Periodic and Aperiodic Signals
- A periodic signal is a type of signal which has a definite pattern and repeats over and over with a repetition period of T. In other words, a signal is called periodic if it exhibits periodicity as follows:
x(t+T)=x(t), \; -\infty< t <\infty
- T is the period of the signal. The smallest value of period T which satisfies the above equation is called the fundamental period T0.
- A signal is said to be Aperiodic if it does not repeat. sometimes aperiodic signals are said to have a period equal to infinity.
- This is a decaying exponential pulse given by the equation:
x(t)=e^{-at}
Now, x(t+T_0)=e^{-a(t+T_0)}=e^{-a(t+\infty)}
x(t+T_0)=e^{-at}.e^{-\infty}
x(t+T_0)=e^{-at}.0
x(t+T_0)=0
- Which is not equal to x(t). This shows that the signal having period T_0=\infty is nothing but an aperiodic signal.
5. Even and Odd Signals
- An even signal is that type of signal which exhibits symmetry in the time domain. This type of signal is identical to the origin. Mathematically, an even signal, just satisfy the following condition:
x(t)=x(-t)
- Similarly, an odd signal is that type of signal which exhibits anti-symmetry. This type of signal is not identical to the origin. Actually, the signal is identical to its negative. Mathematically, an odd signal must satisfy the following condition.
6. Energy and Power Signals
- Signals may also be classified as energy and power signals. However, there are some signals which can neither be classified as energy signals nor power signals.
- The energy signal is one that has finite energy and zero average power.
- Hence, x(t) is an average signal, if:
\boxed{0 < E < \infty \; and \; P=0 }
- Where E is the energy and P is the power of the signal x(t).
- The power signal is one that has finite average power and infinite energy.
- Hence, x(t) is a power signal, if:
\boxed{0 < P < \infty \; and \; E=\infty }
- However, if the signal does not satisfy any of the above two conditions, then it is neither an energy signal nor a power signal.
