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Signal and Systems
A signal is an impulse (magnetic field, voltage or current) or a detectable physical quantity that transmits a message or information. A signal can also be termed as functions of independent variables which carry some information. A signal is often an abstract notion. For example a flashing light in front of the car bumper can be a turn signal or an umpire’s fingered gesturing can be a no ball signal in cricket game. There can be two types of signals continuous time or discrete time.
A physical set of components which produce or receive a signal is termed as a system. In engineering terms the input is in the form of an electrical signal X which leads to the creation of an output signal Y. For example in a household thermostat, the turning of a knob or switch is the input signal while the controlling of the furnace is done by the output signals.
Various aspects of signals and systems
The complex signals are further simplified as linear combinations containing certain basic functions. Some examples of these functions are the unit step function and impulse function which are also considered the fundamentals in engendering of signals and systems. The systems are analyzed in the time domain by the various tools available. These tools are use to study the linear systems and signals. The LTI or linear time invariant system is one such example.
The digital systems and signal also often produce noise. The noise is the biggest enemy of the electrical engineer. The noise can be of various types such as white noise, colored noise or thermal noise. The white noise affects all the frequency components of a signal in equal proportions where as the colored noise effects the components of a system in an unequal manner. The thermal noise is produced because of heating of components which leads to change in resistance of resistors. The energy storage element’s inductance and capacitance also changes. These changes contribute to the noise reduction in the output of the circuit.
The various types of noises produced have a certain amount of energy which is associated with them. Higher the energy and transmitted power of the system, greater the interference of noise in the transmitted data signal.
The Fourier series and Laplace transform
The specialized tool of Fourier series helps in decomposing of periodic signals into an infinite sum of everlasting sinusoids whereas the rectangular series represents all signals as a sum of sine and cosine functions. The systems respond in a different way to each frequency. They can either amplify or attenuate the component of frequencies. The frequency response of the system is the way in which the system output is related to the input of the signal for various different frequencies. Through the usage of filter system certain frequency ranges can be selectively attenuated or amplified. The Laplace transform is the most preferred tool for the analysis and development of certain circuits such as filters. Laplace transform can be considered the extension of Fourier transform to the complex plane.
Probability basics and Filters
The probability basics of signals and systems include probability (that a function will occur), random variable (whose value is not fixed but depends on chance), mean(the average, more precise value of the random variable), standard deviation(measurement of deviation of the signal from the man), variance (the square of standard deviation), probability function (the probability of the occurrence of a certain event), probability density function (the random variable’s values description of the distribution) and cumulative distributive function(describes the probability of a certain value below or at a certain threshold). The filter design is done by finding the proper transfer function for amplifying selected parts of a system and also to damp other signals as function of their frequency. Various type of filters are brick wall filters, analog filters etc.
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