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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The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.
There are many situations which call for the replacement of an integral by a sum, or vice versa. In the former case the highest accuracy is sometimes required. This means that in t
WHY IS SINp = 0
prove that A=3i+j-2k, B=-i+3j+4k ,C=4i-2j-6k and find the length of the triangle
A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i
MA for pulling a 1500 gram cart up a 20 degree plane up a 1 meter ramp using a wheel and axel. Wheel diameter is 8 cm
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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.
Compute the (real and imaginary parts of the) principal value of the eighth root of (a + ib) to 3 decimal places (accurate to 10 -3 ). Call the real part "m 7 ", and the imagina
discussion
The data in this exam are a set of 6 integers a through f, based on your social security number. Write the LAST 6 digits of your social security or ID number in the spaces below, t
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