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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The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.
The following are 8 data points that shows the relationship between the number of fishermen and the amount of fish they can catch a day. (Let the number of fishermen be X and the a
The integral has an exact answer, viz., sinc(pfT). As T®¥ the sinc function tends to zero. Divide the region from -T/2 to T/2 into N equal parts and sum the rectangles on b
what are the uses of laplace transformation?
The number ways of choosing 2 boys and 2 girls in a class for a game of mixed doubles is 1620. Then, what is the number of ways of choosing 2 students in the class?
A research analyst for an oil company wants to develop a model to predict miles per gallon based on highway speed. An experiment is designed in which a test car is driven at speeds
A house wall may be approximated as two 1.2 cm layers of fiber insulating board, a 8 cm layer of loosely packed asbestos, and 10 cm layer of common brick. Assuming convective heat
a) Use divided differences to ?nd the polynomial (in nested form) that interpolates the data b) Add the data point x = 6, y = -20 and hence estimate y for x = 2.
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
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.
A stone weighing 50 newton is tied to one end of a cord 0.90 meter long. the stone is then whirled in a vertical circle. if the breaking strength of the cord in tension is 60 newto
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