Chapter: Digital Signal Processing - Signals and System

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Classification of Signals

1. Single channel and Multi-channel signals 2. Single dimensional and Multi-dimensional signals 3. Continuous time and Discrete time signals. 4. Continuous valued and discrete valued signals. 5. Analog and digital signals. 6. Deterministic and Random signals 7. Periodic signal and Non-periodic signal 8. Symmetrical(even) and Anti-Symmetrical(odd) signal 9. Energy and Power signal

CLASSIFICATION OF SIGNALS

 

1.       Single channel and Multi-channel signals

 

2.       Single dimensional and Multi-dimensional signals

 

3.       Continuous time and Discrete time signals.

 

4.       Continuous valued and discrete valued signals.

 

5.       Analog and digital signals.

 

6.       Deterministic and Random signals

 

7.         Periodic signal and Non-periodic signal

 

8.       Symmetrical(even) and Anti-Symmetrical(odd) signal

 

9.       Energy and Power signal

 

 1. Single channel and Multi-channel signals

 

If signal is generated from single sensor or source it is called as single channel signal. If the signals are generated from multiple sensors or multiple sources or multiple signals are generated from same source called as Multi-channel signal. Example ECG signals. Multi-channel signal will be the vector sum of signals generated from multiple sources.

 

2. Single Dimensional (1-D) and Multi-Dimensional signals (M-D)

 

If signal is a function of one independent variable it is called as single dimensional signal like speech signal and if signal is function of M independent variables called as Multi - dimensional signals. Gray scale level of image or Intensity at particular pixel on black and white TV is examples of M-D signals.

 

3. Continuous time and Discrete time signals.

 


Continuous Time (CTS)

 

1.        This signal can be defined at any time instance & they can take all values in the continuous interval(a, b) where a can be -∞ & b can be ∞

2.        These are described by differential equations.

3.        This signal is denoted by x(t).

4.        The speed control of a dc motor using a tacho generator feedback or Sine or exponential waveforms.

 

Discrete time (DTS)  

    

1.        This signal can be defined only at certain specific values of time. These time instance need not be equidistant but in practice they are usually takes at equally spaced intervals.

2.        These are described by difference equation.

3.        These signals are denoted by x(n)  or notation x(nT) can also be used.

4.        Microprocessors and computer based systems uses discrete time signals.

 

4. Continuous valued and Discrete Valued signals.


Continuous Valued

 

1.        If a signal takes on all possible values on a finite or infinite range, it is said to be continuous valued signal.

2.        Continuous Valued  and continuous time   signals are basically analog signals. 

 

Discrete Valued

 

1.        If signal takes values from a finite set of possible values, it is said to be discrete valued signal.

2.        Discrete time signal with set of discrete amplitude are called digital signal.

 

 5. Analog and digital signal


Analog signal

 

1.        These are basically continuous time & continuous amplitude signals.

2.        ECG  signals,  Speech  signal,  Television signal etc. All the signals generated from various  sources   in  nature  are analog.

 

Digital signal

 

1.        These are basically discrete time signals & discrete amplitude signals. These signals are basically  obtained  by  sampling & quantization process.

2.        All signal representation in computers and digital signal processors are digital.

 

Note: Digital signals (DISCRETE TIME & DISCRETE AMPLITUDE) are obtained by sampling the ANALOG signal at discrete instants of time, obtaining DISCRETE TIME signals and then by quantizing its values to a set of discrete values & thus generating DISCRETE AMPLITUDE signals.

 

Sampling process takes place on x axis at regular intervals & quantization process takes place along y axis. Quantization process is also called as rounding or truncating or approximation process.

 

6. Deterministic and Random signals


Deterministic signals

1.        Deterministic  signals  can  be  represented  or described by a mathematical equation or lookup table.

2.        Deterministic signals are preferable because for analysis and processing of signals we can use mathematical model of the signal.

3.        The value of the deterministic signal can be evaluated at time (past, present or future) without certainty.

4.        Example Sine or exponential waveforms.

 

Random signals

1.        Random  signals  that  cannot  be represented or  described by  a mathematical equation or lookup table.

2.        Not Preferable. The random signals can be described with the help of their statistical properties.

3.        The value of the random signal can not be evaluated at any instant of time.

4.        Example Noise signal or Speech signal 

 

7. Periodic signal and Non-Periodic signal

 

The signal x(n) is said to be periodic if x(n+N)= x(n) for all n where N is the fundamental period of the signal. If the signal does not satisfy above property called as Non-Periodic signals.

 

Discrete time signal is periodic if its frequency can be expressed as a ratio of two integers. f= k/N where k is integer constant.


 

8. Symmetrical(Even) and Anti-Symmetrical(odd) signal

 A signal is called as symmetrical(even) if x(n) = x(-n) and if x(-n) = -x(n) then signal is odd. X1(n)= cos(ωn) and x2(n)= sin(ωn) are good examples of even & odd signals respectively. Every discrete signal can be represented in terms of even & odd signals.


Ex. 1.:Test whether the following CT waveforms is periodic or not. If periodic find out the fundamental period.

a) 2 sin(2/3)t + 4 cos (1/2)t + 5 cos((1/3)t                      Ans: Period of x(t)= 12 b)

a) cos(t 2) + b sin(t/4)                                                  Ans: Non-Periodic

Find out the even and odd parts of the discrete signal x(n)={2,4,3,2,1}

Find out the even and odd parts of the discrete signal x(n)={2,2,2,2}

 

9. Energy signal and Power signal

 

Discrete time signals are also classified as finite energy or finite average power signals. The energy of a discrete time signal x(n) is given by


The average power for a discrete time signal x(n) is defined as


If Energy is finite and power is zero for x(n) then x(n) is an energy signal. If power is finite and energy is infinite then x(n) is power signal. There are some signals which are neither energy nor a power signal.

 

a)     Find the power and energy of u(n) unit step function.

 

b)    Find the power and energy of r(n) unit ramp function.

 

c)     Find the power and energy of an u(n).

 

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