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In the two problems below find the expotential Fourier Transform of the given f(x) and write f(x) as a Fourier integral.
A study was done with a group of university students to determine if there was a correlation between the amounts of sleep they got and their academic performanc
The question is the example on page 2 of the attachment (entitled 'Uniform Transducer'). it states that the center of the finger is at z'=L/4.
Perform a linear-regression analysis of the data to find the line of best fit and the correlation coefficient.
Using an alpha value of 0.05, which variables are significant (size, bath, bed, garage)?
Circularity of the DFT/FFT. Using the same x[n] (shown below):
Is the statistical significance of the model as a whole less than the desired statistical significance for the regression model?
Consider a periodic function f(x) with period L.
Perform a residual analysis on your results and determine the adequacy of the fit of the model.
Calculate by hand the X(omega), DTFT of the sequence x[n]=[1 1 1 1 0 0 0 0] for n=0:7, zero else.
The sum of the infinite series, 1/2^2 - 2/3^2 + 3/4^2 - 4/5^2 + ... is given as pi^2/12 - log 2 on pages 64-65 in the book "Summation of Series" by L. B. W.
Using the Fourier transform integral, find Fourier transforms of the following signals.
Find A1 such that f1(t) is normalized to unity on (0, infinity). Call this function PHI_1(t).
Forecast the annual maintenance cost for a police car that is 5 years old and will be driven 10,000 miles in 1 year.
If the company does not sell a single e-reader, how much is lost in sales? Mathematically, what is this value called in the equation?
We use the Fourier expansions of certain poynomial functions to compute the sum of some useful numerical series.
Show that this series can be differentiated term by term to yield the Fourier expansion of f'(x) on [-1,1].
A manager wishes to determine the relationship between the number of miles (in hundreds of miles) the manager's sales representatives travel per month .
Given the function below: Expand the function in an Fourier integral and determine what this integral converges to.
Find the exponential Fourier series for x(t), y(t) and z(t). In each of three cases it is not necessary to do any integration.
Expand the function in a sine-cosine series and Computer plot on the interval.
What is the Fourier Transform for the convolution of sin(2t)*cos(2t) .
Describe the general behavior of the solution over time: what happens?
How might a regression analysis be used to formulate strategies?
Take your data and arrange it in the order you collected it. Count the total number of observations you have, and label this number N.