Given the following noisy measurement from an analogue sensor whose sampling per

Question

Given the following noisy measurement from an analogue sensor whose sampling period is 0.0025 seconds. The measurement starts from t = 0. It s known that the data belongs to a periodic function n the form y = c_1 cos(t) + c_2 cos (2t) + c_3 cos (3t) + s _1 sin(t)+ s_2 sin (2t) + s_3 sin (3t) Use least squares regression to find coefficients c_1, c_2, c_3, s_1, s_2 and s_3 Use the coefficients calculated in part(a) to reconstruct the original signal Subtract the reconstructed signal from the given noisy measurement and find the existing noise on the measurement

Explanation / Answer

After performing a regression analysis on the given regressors vs noisy measurement, we can get the following values of corresponding coefficients,

Now by using the coefficients obtained we can predict the original value for measurement signal by simply plugging the values of coefficient in the given equation y = c1 * cos(t) + c2 * cos(2t) + c3 * cos(3t) + s1 * sin(t) + s2 * sin(2t) + s3 * sin(3t) we will get the required result

Variable Coefficients Values Intercept Intercept -109869 cost c1 137878.8 cos2t c2 -22202 cos3t c3 -5803.6 sint s1 -102986 sin2t s2 75033.23 sin3t s3 -15711.5

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