- #1

QuantumCuriosity42

- 79

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- TL;DR Summary
- Investigating if sines and cosines are the only orthogonal basis for periodic functions that generate the entire function space.

Hello everyone,

I've been delving deep into the realm of periodic functions and their properties. One of the fundamental concepts I've come across is the use of sines and cosines as an orthogonal basis for representing any functions. This is evident in Fourier series expansions, where any function can be represented as a sum of sines and cosines of different frequencies.

However, this leads me to a question: Are sines and cosines the

Would love to hear insights and if there are any relevant literature or studies that have explored this topic further.

Thank you in advance!

I've been delving deep into the realm of periodic functions and their properties. One of the fundamental concepts I've come across is the use of sines and cosines as an orthogonal basis for representing any functions. This is evident in Fourier series expansions, where any function can be represented as a sum of sines and cosines of different frequencies.

However, this leads me to a question: Are sines and cosines the

*only*orthogonal basis for periodic functions that can generate the entire function space? Specifically, can we consider other periodic functions, like square pulses or triangular waves of various frequencies, as potential candidates for an orthogonal basis?Would love to hear insights and if there are any relevant literature or studies that have explored this topic further.

Thank you in advance!