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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The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.
application of mathematics in engineering
Produce a discrete time series y(t i ) by super positioning 5 cosinusoidal components, for your own choice of the amplitudes (a j ) and frequencies (f j ). Add some Gaus
The system has a solution near (-0.5,-0.7). Set up the matrix equation Jδ = -f for Newton's method and then carry out one iteration, starting with x 0 = -0.5, y 0 = -0.7.
Use Lagrange interpolation to estimate f(3), given that f(1) = 1, f(4) = -3, f(2) = 0 and f(-1) = 3.
Parents put $1000 into a saving account at birth of their children. If the account earns interest at 7% p.a compounded yearly, how much money will be in the account when their chil
An open-loop control system has the following state-space model: (a) Find characteristic equation of the open-loop control system model. (b) What is the characteristic e
prove that A=3i+j-2k, B=-i+3j+4k ,C=4i-2j-6k and find the length of the triangle
A manager has determined the cost C, in dollars, for manufacturing is C(q) =85log 10 (10+q/2) for manufacturing, where q is the number of units produced in a given day. (a
trigonometric functions
sin2+cos2=
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