Out of these two methods, which one is computationally intensive and why?

I have a signal, let's say A6. It has 300 sample points. There are two different methods to estimate the magnitude of the signal. I want to know which method is computationally intensive.

The steps of the first method are as followed,

Step1: A = A6 - mean(A6);

Step2: B = A .* A;

Step3: C = cumsum(B);

Step4: D = trapz(C);

D represents the magnitude of the signal in terms of area under the curve.

The steps of the second method are as followed,

Step1: A = A6 .* A6;

Step2: B = cumsum(A);

Step3: Mean Square Error (MSE) between B and fitted straight line.

The value of the MSE represents the magnitude of the signal.

Thanks,

Irtaza

[James Tursa]

Why don't you code both of them up and then run the profiler?

[Syed Haider]

Thanks for the suggestion but I am looking for the theoretical explanation. Step4 of the first method vs. Step3 of the second method.

Answer 1

[Walter Roberson]

trapz should have a lower constant of proportion because it is sum(C) - (C(1)+C(end)) /2 whereas mse requires sqrt(sum((C-B).^2)). Both are linear in size but one requires squaring as well as sum.

[Syed Haider]

Thanks Walter for the explanation. Is there a method faster than trapz to calculate the area under the curve.

[Walter Roberson]

Unless you have a formula for the curve, there would be no way to calculate the area without examining each value at least once, which is all that trapz requires.