SOME SPECIAL SIGNALS AND THEIR GRAPHS?

When we study the analysis of the transient state and steady state response of control system it is very essential to know a few basic terms and these are described below. 

Standard Input Signals : 

These are also known as test input signals. The input signal is very complex in nature, it is complex because it may be a combination of various other signals. Thus it is very difficult to analyze characteristic performance of any system by applying these signals. So we use test signals or standard input signals which are very easy to deal with. We can easily analyze the characteristic performance of any system more easily as compared to non standard input signals. Now there are various types of standard input signals and they are written below:

Unit Impulse Signal : In the time domain it is represented by ∂(t). The Laplace transformation of unit impulse function is 1 and the corresponding waveform associated with the unit impulse function is shown below.  

Unit Step Signal :

 In the time domain it is represented by u (t). The Laplace transformation of unit step function is 1/s and the corresponding waveform associated with the unit step function is shown below.  

Unit Ramp signal :

 In the time domain it is represented by r (t). The Laplace transformation of unit ramp function is 1/s2 and the corresponding waveform associated with the unit ramp function is shown below.  

Parabolic Type Signal : 

In the time domain it is represented by t2 / 2. The Laplace transformation of parabolic type of the function is 1 / s3 and the corresponding waveform associated with the parabolic type of the function is shown below.  

Sinusoidal Type Signal :

 In the time domain it is represented by sin (ωt).The Laplace transformation of sinusoidal type of the function is ω / (s2 + ω2) and the corresponding waveform associated with the sinusoidal type of the function is shown below.  

impulse,unit and ramp signals

Cosine Type of Signal : 

In the time domain it is represented by cos (ωt). The Laplace transformation of the cosine type of the function is ω / (s2 + ω2) .

Transient Response of Control System

As the name suggests transient response of control system means changing so, this occurs mainly after two conditions and these two conditions are written as follows- 

•  Condition one : Just after switching ‘on’ the system that means at the time of application of an input signal to the system. 

•  Condition second : Just after any abnormal conditions. Abnormal conditions may include sudden change in the load, short circuiting etc.

Steady State Response of Control System

Steady state occurs after the system becomes settled and at the steady system starts working normally. Steady state response of control system is a function of input signal and it is also called as forced response.

Now the transient state response of control system gives a clear description of how the system functions during transient state and steady state response of control system gives a clear description of how the system functions during steady state. Therefore the time analysis of both states is very essential. We will separately analyze both the types of responses. 

Analog signals

An analog signal is any continuous signal for which the time varying feature (variable) of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal. For example, in an analog audio signal, the instantaneous voltage of the signal varies continuously with the pressure of the sound waves. It differs from a digital signal, in which the continuous quantity is a representation of a sequence of discrete values which can only take on one of a finite number of values. The term analog signal usually refers to electrical signals; however, mechanical, pneumatic, hydraulic, human speech, and other systems may also convey or be considered analog signals.

An analog signal uses some property of the medium to convey the signal's information. For example, an aneroid barometer uses rotary position as the signal to convey pressure information. In an electrical signal, the voltage, current, or frequency of the signal may be varied to represent the information.

Any information may be conveyed by an analog signal; often such a signal is a measured response to changes in physical phenomena, such as sound, light, temperature, position, or pressure. The physical variable is converted to an analog signal by a transducer. For example, in sound recording, fluctuations in air pressure (that is to say, sound) strike the diaphragm of a microphone which induces corresponding fluctuations in the current produced by a coil in an electromagnetic microphone, or the voltage produced by a condenser microphone. The voltage or the current is said to be an "analog" of the sound.

An analog signal has a theoretically infinite resolution. In practice an analog signal is subject to electronic noise and distortion introduced by communication channels and signal processing operations, which can progressively degrade the signal-to-noise ratio (SNR). In contrast, digital signals have a finite resolution. Converting an analog signal to digital form introduces a constant low-level noise called quantization noise into the signal which determines the noise floor, but once in digital form the signal can in general be processed or transmitted without introducing additional noise or distortion. In analog systems, it is difficult to detect when such degradation occurs. However, in digital systems, degradation can not only be detected but corrected as well.

Advantages and disadvantages

The primary disadvantage of analog signals is that any system has noise – i.e., unwanted variation. As the signal is copied and re-copied, or transmitted over long distances, or electronically processed, the unavoidable noise introduced by each step in the signal path is additive, progressively degrading the signal-to-noise ratio, until in extreme cases the signal can be overwhelmed. This is called generation loss. Noise can show up as "hiss" and intermodulation distortion in audio signals, or "snow" in video signals. This degradation is impossible to recover, since there is no sure way to distinguish the noise from the signal; amplifying the signal to recover attenuated parts of the signal amplifies the noise (distortion/interference) as well. Digital signals can often be transmitted, stored and processed without introducing noise. Electrically, analog noise can be diminished by shielding, good connections and several cable types such as coaxial or twisted pair.

See also

Ampex
Analog audio
Analog device
Analog signal processing
Analog sound vs. digital sound
Analog video
Analog-to-digital converter
Digital audio
Digital video
Magnetic tape

Magnetic recording
Courtesy wikipedia...