Engineering Help

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

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