- #1
izen
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Homework Statement
these two functions will give the same Fourier series? because when I write the graph they look the same?
Homework Equations
The Attempt at a Solution
in the picture
thank you
jbunniii said:The series coefficients are defined by an integral. If you change the value of a function at a finite number of points, can the integral give you a different result?
No, you can change a function at a finite number of points, and the integral will still be the same. So your Fourier coefficients will be the same for both functions.izen said:I think integral give a different result so they are different ? not 100% sure
jbunniii said:No, you can change a function at a finite number of points, and the integral will still be the same. So your Fourier coefficients will be the same for both functions.
A Fourier series is a mathematical representation of a periodic function as a sum of sine and cosine functions with different frequencies and amplitudes. It is used to approximate any periodic function with a combination of simpler trigonometric functions.
The main purpose of using Fourier series is to analyze and model periodic phenomena in various fields such as physics, engineering, and mathematics. It allows us to decompose complex functions into simpler components, making it easier to study and understand them.
A Fourier series is used to represent a periodic function, while a Fourier transform is used to analyze a non-periodic function. Additionally, a Fourier series uses discrete frequencies, while a Fourier transform uses continuous frequencies.
No, a Fourier series can only accurately represent functions that are periodic. Non-periodic functions cannot be represented using a Fourier series, but they can be analyzed using a Fourier transform.
The coefficients of a Fourier series can be calculated using the Fourier series formula, which involves integrating the function over one period and dividing by the period. Alternatively, there are also tables and software programs available that can calculate the coefficients for more complex functions.