The values of some variable s are recorded at equally spaced times t, (i= 1, 2,...,...

  

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The values of some variable s are recorded at equally spaced times t₁, (i= 1, 2,..., 201) so that t₁ =0 and the time interval between any two consecutive measurements is t₁+1 ti = a, where a is the last non-zero integer, taken from your student ID. For example, if your ID is 103838497, then a = = 7, if your ID is 103838490, then a = 9. The recorded values of s are stored in the file "TimeSeries.dat" available on Canvas in the column format. It is known that the variable s can be represented in the form s(t) = t + n(t), where n(t) is some irregular and bounded function, which can be associated with random noise present in the data. In this case, we say that the data is noisy and it contains a linear trend, i.e. the value s(t) increases on average with time. It is known that a linear trend can be removed from the data by differentiation. In other words, by applying the derivative s(t)' = (t+n(t))' = 1+n(t)', the linear trend will be removed so that the differentiated data s(t)' doesn't increase with time. The following step-by-step instructions are to be implemented in a single Matlab script. • Use importdata() command to import the data file "TimeSeries.dat" into Matlab. • Calculate the vector that contains the values of the first derivative s(t)'. Use the following method: Use first-order forward differences if the first letter of your Surname is A-H Use first-order backward differences if the first letter of your Surname is I-P, Use central differences if the first letter of your Surname is Q-Z, • Plot the detrended data as a function of time. • Use the max() function to find the maximal value of the first derivative and the corresponding value of time when this maximal value occurs. The values of some variable s are recorded at equally spaced times t₁, (i= 1, 2,..., 201) so that t₁ =0 and the time interval between any two consecutive measurements is t₁+1 ti = a, where a is the last non-zero integer, taken from your student ID. For example, if your ID is 103838497, then a = = 7, if your ID is 103838490, then a = 9. The recorded values of s are stored in the file "TimeSeries.dat" available on Canvas in the column format. It is known that the variable s can be represented in the form s(t) = t + n(t), where n(t) is some irregular and bounded function, which can be associated with random noise present in the data. In this case, we say that the data is noisy and it contains a linear trend, i.e. the value s(t) increases on average with time. It is known that a linear trend can be removed from the data by differentiation. In other words, by applying the derivative s(t)' = (t+n(t))' = 1+n(t)', the linear trend will be removed so that the differentiated data s(t)' doesn't increase with time. The following step-by-step instructions are to be implemented in a single Matlab script. • Use importdata() command to import the data file "TimeSeries.dat" into Matlab. • Calculate the vector that contains the values of the first derivative s(t)'. Use the following method: Use first-order forward differences if the first letter of your Surname is A-H Use first-order backward differences if the first letter of your Surname is I-P, Use central differences if the first letter of your Surname is Q-Z, • Plot the detrended data as a function of time. • Use the max() function to find the maximal value of the first derivative and the corresponding value of time when this maximal value occurs.