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Sampling

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Sampling  is defined as, “The process of measuring the instantaneous values of continuous-time signal in a discrete form.” Sample  is a piece of data taken from the whole data which is continuous in the time domain. When a source generates an analog signal and if that has to be digitized, having  1s  and  0s  i.e., High or Low, the signal has to be discretized in time. This discretization of analog signal is called as Sampling. The following figure indicates a continuous-time signal  x (t)  and a sampled signal  x s  (t) . When  x (t) is multiplied by a periodic impulse train, the sampled signal  x s  (t)  is obtained. Sampling Rate To discretize the signals, the gap between the samples should be fixed. That gap can be termed as a  sampling period T s . SamplingFrequency=1Ts=fsSamplingFrequency=1Ts=fs Where, TsTs is the sampling time fsfs is the sampling frequency or the sampling rate Sampling frequency  is the reciprocal of the sampling period. This samplin
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Mathematical Modelling

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Why mathematical modeling? Mathematical modeling is the art of translating problems from an application area into tractable mathematical formulations whose theoretical and numerical analysis provides insight, answers, and guidance useful for the originating application. Mathematical modeling is indispensable in many applications is successful in many further applications gives precision and direction for problem solution enables a thorough understanding of the system modeled prepares the way for better design or control of a system allows the efficient use of modern computing capabilities Learning about mathematical modeling is an important step from a theoretical mathematical training to an application-oriented mathematical expertise, and makes the student fit for mastering the challenges of our modern technological culture. 2  A list of applications In the following, I give a list of applications whose modeling I understand, at least in some detail. All areas mentioned hav
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Laplace Transform

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INTRODUCTION:                A basic result  is that the response of an LTI system is given by convolution of the input and the impulse response of the system. In this chapter and the following one we present an alternative representation for signals and LTI systems. In this chapter, the Laplace transform is introduced to represent continuous-time signals in the s-domain (s is a complex variable), and the concept of the system function for a continuous-time LTI system is described. Many useful insights into the properties of continuous-time LTI systems, as well as the study of many problems involving LTI systems, can be provided by application of the Laplace transform technique. THE LAPLACE TRANSFORM : we know that for a continuous-time LTI system with impulse response h(t), the output y(t) of the system to the complex exponential input of the form e st  is where Definition: The function H(s) in  the above Eq is referred to as the Laplace transform of h(t). For a general con
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Unit Step Signal

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Introduction:          This section explains the unit step signal and also derives the unit step signal in the following way. The unit step signal: A well known discontinuous function is the unit step function u 0 * (t) which is defined as It is also represented by the waveform of Figure given below In the waveform of Figure above, the unit step function u 0 (t)  changes abruptly from 0 to 1 at t = 0. But if it changes at  t = t 0 instead, it is denoted as u 0 (t-t 0 ) . In this case, its waveform and definition are as shown in Figure given below If the unit step function u 0 (t)  changes abruptly from 0 to 1 at  t = -t 0 , it is denoted as u 0 (t  t 0 ) . In this case, its waveform and definition are as shown in Figure given below.
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Fourier Transform

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Introduction: This section will discuss the fourier transform and explains the graphical representation of the fourier transform. The fourier transform: Let X( t ) be a nonperiodic signal of finite duration, that is, Such a signal is shown in Fig. (a). Let x T 0 (t) be a periodic signal formed by repeating x(t) with fundamental period T 0  as shown fig (b ). If we let T o  -  , we have The complex exponential Fourier series of x T 0 (t)  is given by The above equ can be written as Let us define X(w) as the complex Fourier coefficients c k , can be expressed as Cosine and sine  Function Introduction: This section describes the cosine and sine function Pair mathematically and also explains this in detail.   The cosine function pair: Proof:   The f(t) - F(w) correspondence is also shown in fig given below We know that Cos w 0 t is real and even function of time, and we found out that its Fourier transform is a real and even function of frequency. The Sine Function Pair: Pro
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Remote sensing Sensor

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INTRODUCTION: Sensors:  Sensors can be classified as passive or active.  Sensors, which sense natural radiations, either emitted or reflected from the Earth, are called passive sensors.  It is also possible to produce electromagnetic radiation of a specific wavelength or band of wavelengths and illuminate a terrain on the Earth’s surface. The interaction of this radiation with the target could then be studied by sensing the scattered radiation from the targets.  Such sensors, which produce their own electromagnetic radiation, are called active sensors. A photographic camera, which uses only sunlight, is a passive sensor; whereas the one, which uses a flashbulb, is an active sensor.  Again, sensors (active or passive) could be either imaging, like the camera, or non-imaging, like the non scanning radiometer.   Sensors are also classified on the basis of range of electromagnetic region in which they operate such as optical or microwave. The major sensor parameters which have bearing o
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Web Mapping

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INTRODUCTION:            The term "Web mapping" constitutes both the technology and art of sharing maps on the Internet. The simplest Internet-based maps are static, such as images (i.e., jpegs or tiffs) that do not allow users to change the components, extent, or appearance of the map. These maps are the easiest and simplest to share because all that is required is placing the image on a Web server and telling others where to find it. At the opposite end of the spectrum are customizable, interactive Web-based maps. These maps are usually created with the use of modern hardware, complex software. In addition, these initiatives require human expertise for successful implementation. The advantage of developing and implementing interactive maps is that they give the user the ability to customize the map to meet this own specific needs. Possible user interactions include adjusting the extent of the map by zooming in or out, turning on and off features displayed within the map,
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