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In an exercise where I have to calculate the fourier series of the following function: $cos(\frac{\pi\cdot t}{2})$ I am given this question:

Write the integral of $a_0$ and calculate it. Does it match with the expected value of the DC-offset?

I calculated $a_0$ to be $a_0=4/\pi$. I also calculated the DC-offset to be $DC_{offset}=0.637$.

What do they mean by "Does it match with the expected value of the DC-offset?"

EDIT:

The function is limited to the following [-1; 1], which means my integrals are between -1 and 1:

enter image description here

I thus calculated $a_0$ the following way:

user164324
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  • What domain did you use, $[-2,2]$? The DC-offset is the mean value of the signal. What is the expected mean value of this signal? Do you expect a bias towards positive or negative values? – Winther Nov 29 '19 at 11:33
  • @Winther

    See my edit.

     – user164324 Nov 29 '19 at 11:39
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    It is hard to give a satisfactory answer without knowing what book you are reading and who "they" are. Could you please cite the reference? –  Nov 29 '19 at 14:19
  • Without a lot of context, we cannot know what the authors meant by "expected value of the DC-offset". Most likely Winther is correct that they mean "is it biased (positive or negative) in the direction you'd expect? Is the magnitude in a range that you would expect?". For example, if your calculated DC-offset had been -0.637, or had been 1.6, then you should recognize immediately that something is wrong (students often turn in ludicrous answers because they don't check it the result they got was reasonable. It may be they are training you to check yourself.) But that is a guess. – Paul Sinclair Nov 29 '19 at 20:44

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