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Produce a discrete time series y(ti) by super positioning 5 cosinusoidal components,
for your own choice of the amplitudes (aj) and frequencies (fj).
Add some Gaussian noise to each digitised value. Experiment with amplitudes (including that of the noise term), and frequencies, showing results graphically. Then smooth your noisy time series with at least two different filters, e.g., a simple moving average smoother and an order two binomial filter.
Discuss the relative performance of the smoothers. You should consider quantifiable parameters such as; variance, r.m.s. deviations from the noise-free time series, and signal attenuation. Comment on the validity of the expression below, for your chosen smoother.
As an engineering student, the ministry of energy and minerals has tasked you to help them model equation(s) that can estimate the amount of crude oil in a reservoir. The governmen
1. (i) How many digits does the number 101000 have when written to base 7 ? (ii) Use the prime number theorem to estimate the proportion of prime numbers among the positive inte
A Pew Research poll was conducted to investigate opinions about global warming. The respondents who answered yes when asked if there is solid evidence that the earth is getting wa
In the case of Castenedav . Partida , it was found that during a period of 11 years in Hilda County, Texas, 870 people were selected for grand jury duty, and 39% of them were Ame
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
You are working as an engineer on a project that involved being able to accurately measure the fluid level change in a large outdoor holding tank. The fluid level rises and falls a
a^n * n *u[n-1]
Evaluate the expression below for various smoothers, plot and compare the results, making appropriate comments.
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
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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