Classification of Pulse Signals:

The Classification of Pulse Signals are divided into four categories, namely

  1. Periodic signals.
  2. Aperiodic signals.
  3. Random signals.
  4. Continuous and Discrete Signals

1. Periodic Signals:

Periodic signals are those which repeat themselves at regular intervals of time say ‘T’. This time ‘T’ is referred to as the time period. Sinusoidal signals, time-base signals and rectified waveforms (i.e., the output of the rectifier circuits) etc. fall under this category of pulse signals.

A periodic signal may be expressed as

Classification of Pulse Signals

where T is the time period.

Repetition frequency fR of a periodic signal is the reciprocal of the time period T. Thus

By iteration of Eq. (28.1) we have

Classification of Pulse Signals

where n is any integer i.e., n = 1, 2, 3 ….

The average value or mean value of a repetitive signal of periodic time T is given by the following expression

The  rms value of a periodic or repetitive signal is given as

The instantaneous power, p is defined as

Classification of Pulse Signals

where v is the instantaneous voltage, i is the instantaneous current and R is the circuit resistance.

Thus average power of a voltage pulse is given as

Combining Eqs. (28.5) and (28.7) we have

Classification of Pulse Signals

2. Aperiodic Signals:

Aperiodic signals are those which occur only once in the entire time period (i.e., in the time interval from -∞ to +∞). Thus an aperiodic signal may be considered to be a periodic signal of infinite time period. Transients of different form constitute aperiodic signals. Since the aperiodic signals last for a short duration of time, our interest lies in storing it for analysis purpose. This may he accomplished by digital techniques i.e., amplitude and time quantization and digital storage.

3. Random Signals:

Random signals occur without any well defined mathematical description. At most such signals can be described by probabilistic models. Noise is one such random signal. A class of random signals which find applications in digital electronics is binary random signals. It is a two-valued random signal with random or unpredictable zero crossings. An example is a telegraph signal.

4. Continuous and Discrete Signals:

Pulse signals may be of two types, viz.; (i) continuous signal and (ii) discrete in time.

A continuous signal is one which is continuous function of independent variable “t” such as a triangular waveform or a staircase waveform, as depicted in Figs. 28.1 (a) and 28.1 (b) respectively. The signal must uniquely be defined at all values of time “t” within a given time range.

Classification of Pulse Signals

Discrete signal is defined only at a sequence of discrete val­ues of independent variable “t”. In many practical situations the instants at which signals are defined are equally spaced and may be defined by t = t± nτ where n takes only integral values (i.e., n = 1, 2, 3, …) and τ is the time duration between instants.

Classification of Pulse Signals

It is also possible to recover the original continuous signal from dis­crete signal. Discrete signals find wide applications in digital in­strumentation, digital control systems and communications.

Classification of Pulse Signals