fourier series graph interactive

What is even and odd function in Fourier series?
A function is called even if f(−x)=f(x), e.g. cos(x).
A function is called odd if f(−x)=−f(x), e.g. sin(x).
These have somewhat different properties than the even and odd numbers: The sum of two even functions is even, and of two odd ones odd.
The product of two even or two odd functions is even.
What is the introduction of the Fourier transform?
The Fourier Transform is a mathematical technique that transforms a function of time, x(t), to a function of frequency, X(ω).
It is closely related to the Fourier Series.
If you are familiar with the Fourier Series, the following derivation may be helpful.
How do you visualize Fourier transform?
The mesh plot of the magnitude is a common way to visualize the Fourier transform.
The peak at the center of the plot is F(0,0), which is the sum of all the values in f(m,n).
The plot also shows that F(ω₁,ω₂) has more energy at high horizontal frequencies than at high vertical frequencies.
One may also note that since all the Fourier coefficients are zero, the Fourier series converges boundedly to the zero function, consequently it is the Fourier series of its sum function, the zero function (obvious).
Since f is continuous, by Fejer's theorem its Fourier series is (C,1) summable to f(x) uniformly.

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