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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The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.
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
Two boys A and B are at two diametrically opposite points on a circle. At one instant the two start running on the circle; A anticlockwise with constant speed v and B clockwise wit
A company manufactures an assembly consisting of a frame, a shaft, and a ball bearing. The company manufactures the shafts and frames but purchases the ball bearings from a ball be
a^n * n *u[n-1]
First systems were described as systems that had one method of storing energy. Second order systems; wait for it.... have two methods of storing energy. Using a similar mechanica
Draw parallel lines with slope +1.05; one passes through (0,a), and the other passes through (0,b). Suppose φ is a harmonic function between the two lines, with φ = 0 on the line t
If a temperature function is given in the x,y plane by T(x,y) = x+y, what is the value, to 3 decimal places, of the corresponding temperature function T1(u,v) at the point (u,v) =
If V is the initial speed of the ball at angle of elevation a , if the origin of the coordinate system is chosen to coincide with the propulsion device, then the initial conditi
integral dx/root of sinx using beta and gamma functions
change each of the following propositions into symbolic form. De ne the universe of discourse and the predicates you use. (i) Some children are afraid of snakes. (ii) All com
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