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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 routine (or FFT), and that the data sets are of length N = 2n, unless noted otherwise. The DFT pair will be written
In this formulation, Y0 represents the average value of the data, the so-called DC term. In addition, |Yn|2 represents the contribution that frequencies near n/N make to total data variance.
(Note: Some FFT routines require that the data first be made complex.)
Experiment with some versions of the FFT available to you, first using a digitised sinusoid as input. Then attempt to duplicate the figure below, comment on variance normalisation.
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A researcher is interested in comparing the Christian maturity level of students who volunteer for community service versus those who do not. The researcher suppose that those who
Values from the iteration x = cos(x) are: x 0 = 0.8, x 1 = 0.696707, x 2 = 0.766959, x 3 = 0.720024, x 4 = 0.751790, x 5 = 0.730468. a) Calculate the sequence {y n } fr
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.
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
i have a wav file which consists of a number of hammer impact noises. i want to break up each impact into and individual wav file. i want to ignore the first 40ms of the impact and
Use Lagrange interpolation to estimate f(3), given that f(1) = 1, f(4) = -3, f(2) = 0 and f(-1) = 3.
Question 1 Find all solutions of the following equations in the interval [0, 2π) (a) sin(2x) = √2 cos(x). (b) 2 cos 2 (x) + 3 sin(x) = 3. 2. Sketch the graph of the ci
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