Struggling to understand why Fourier basis is orthogonal

1. Why are Fourier basis orthogonal?
2. Are Fourier bases orthogonal?
3. How is Fourier series orthogonal?
4. Is the Fourier transform orthogonal?

Why are Fourier basis orthogonal?

Orthogonality suggests the dot product of any 2 of the Fourier basis functions is 0. E.g., ∫ sin(mx) * sin(nx) dx = 0, where (n,m) are integers. Because n,m are integers and we integrate from [0,2π], the basis functions are 2π periodic. This means they all integrate to 0 over the range [0,2π].

Are Fourier bases orthogonal?

The Fourier series will provide an orthonormal basis for images.

How is Fourier series orthogonal?

The orthogonal system is introduced here because the derivation of the formulas of the Fourier series is based on this. So that does it mean? When the dot product of two vectors equals 0, we say that they are orthogonal.

Is the Fourier transform orthogonal?

in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions.