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An experiment conducted over time T necessarily produces a windowed view of the phenomenon generating the data. It is a useful strategy to regard the windowed data as one period of a periodic function. Then one may write
and seek to calculate the Fourier coefficients cn from the integral expression
Large values of cn will be regarded as a quantitative indication of a genuine periodic change in the phenomenon under study. In digital form the relevant equations are
The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.
what are the applications of integration?
a restrained steel bar is heated from 20 degrees to 194 degrees and not permitted to expand. the bar is 10mm diameter, determine the thermal stress in the bar
a^n * n *u[n-1]
If x and y are two independent random variables then their joint density function is given by The density function f z of the sum of these two variables is given by the c
1. (i) How many digits does the number 101000 have when written to base 7 ? (ii) Use the prime number theorem to estimate the proportion of prime numbers among the positive inte
Ask questioA mass on a spring vibrates. Its position at time t from its starting point is x(t) = 2 cos(t) e t Find the velocity and acceleration at time t. What is the behavior of
As with the first order system, there is a general differential equation that governs the response of a second order system. The equation is of the form: Where: So
As an engineering student, the ministry of energy and minerals has tasked you to help them model equation(s) that can estimate the amount of crude oil in a reservoir. The governmen
what are median,mode,aveage,mode
Values from the iteration x = cos(x) are: x 0 = 0.8, x 1 = 0.696707, x 2 = 0.766959, x 3 = 0.720024, x 4 = 0.751790, x 5 = 0.730468. a) Calculate the sequence {y n } fr
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