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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The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.
Question 1 Find all solutions of the following equations in the interval [0, 2π) (a) sin(2x) = √2 cos(x). (b) 2 cos 2 (x) + 3 sin(x) = 3. 2. Sketch the graph of the ci
-20+i,-20-i
This is a pen and paper exercise, you are expected to provide a detailed derivation. Follow the procedure outlined in the lectures for construction of a simple averaging by thr
for what values of (a,b) does the point P (0,a,b) lie on the line through Q (1,-1,4) and R (2,3,5)?
how much for small assigment question ? differentation ?
Find the quadratic that interpolates f(x) = 2x 3 - x + 1 at the nodes x 0 = 0, x 1 = 2, x 2 = 3, a) by solving a set of three equations for the coefficients of p 2 (x) = a 2
in the diagram shown below, the fuel tank which is of uniform cross section and of length 8m is position so that the rear of the tank is 19 metres from the datum. the mass of the f
. The Government of Uganda wants to locate a refinery plant that will annually receive crude oil from two wells in Bunyoro region, F1 and F2. The refinery plant will process the cr
A researcher is interested in comparing the Christian maturity level of students who volunteer for community service versus those who do not. The researcher suppose that those who
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
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