How do you convert a function defined over a periodic interval other than 2π into an interval of 2π for Fourier series representation?

To convert a function defined over a periodic interval other than 2π into an interval of 2π for Fourier series representation, change the units of the independent variable. For example, if the function has a period T, you can express the Fourier series using the angular frequency ω, where ω = 2π/T, and rewrite the function in terms of ω and time.

When dealing with functions that have a period T, the conversion to an interval of 2π involves defining the angular velocity ω as 2π divided by the period T. The Fourier series can then be expressed in terms of ω, allowing the coefficients to be calculated over the interval that covers one complete period. This method is particularly useful in practical applications where the independent variable is time.