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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.
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
Let z 0 = a + ic, z 1 = b + id, z 2 = -id, and z = [z 0 + z 1 ]. Let z 0 be the apex of the wedge with one ray passing through z 1 and the other passing through z 2 , and
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
What, to 3 decimal places, is the principal value of [a - ic] (b + id)/10 (real and imaginary parts)? Call the real part, and the imaginary part. Give one (any) other value of th
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
elongation of conical bar under its own weight is what fraction of rectangular bar
trigonometric functions
Below are items that affected the 2011 accounting records for Darwin Adaptions Inc. The annual accounting period ended December 31, 2011. No adjusting entries were made during the
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
Evaluate the expression below for various smoothers, plot and compare the results, making appropriate comments.
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