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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The time interval [0,T] has been marked out in equal steps T/N, and frequency fn = n/T has been replaced by the dimensionless quantity n/N.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 wire of 3mm diameter and 5 m long has a load of 100g suddenly applied to its ends. calculate stress and extension produced. also show that these are twice the static values
The table summarizes results from a clinical trial (based on data from Pfizer, Inc). Use a 0.05 significance level to test the claim that experiencing nausea is independent of whet
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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
In the x,y plane, divide up the x-axis by placing marks at x=a, x=b, and x = -2. Suppose φ is harmonic in the upper half plane and on the segments of the x-axis defined by your mar
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
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
Prove that the Lagrangian coef?cient polynomials for p n (x) satisfy ∑ n k=0 l k (x) = 1. Hint: It is only a 3-line proof. Consider the interpolating polynomial for a constan
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In an article in Marketing Science , Silk and Berndt investigate the output of advertising agencies. They describe ad agency output by finding the shares of dollar billing volume
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