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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The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.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) For a given integer n, if n 2 is divisible by 4, then n2 4 is divisible by 16. State the hypothesis of this sentence and the conclusion. Give a direct proof of the statement
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
Below are the conditions specified by the institution: a) If the temperature sensor shows 30 degree Celsius or higher, the air-conditioner will be turned ON regardless of the othe
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.
integral dx/root of sinx using beta and gamma functions
From this point on it is assumed that any problem amenable to solution with the aid of the Discrete Fourier Transform (or DFT) will in fact be treated computationally with a fast r
trigonometric functions
simple problems on partial derivatives
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
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
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