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## Main Question or Discussion Point

I understand that the Fourier transform maps one function onto another. So it is a mapping from one function space onto another.

My question is, why is it often referred to as a mapping from time domain to the frequency domain? I don't understand why the image of the Fourier transform represents a signal in the frequency domain. I don't see how the word frequency is even related to the Fourier transform.

What I do know is that the complex exponential and the trigonometric Fourier series both form an orthonormal basis for a certain class of functions under the function inner product. But I don't understand how these ideas are tied to the Fourier transform.

Insight is appreciated. Thanks!

BiP

My question is, why is it often referred to as a mapping from time domain to the frequency domain? I don't understand why the image of the Fourier transform represents a signal in the frequency domain. I don't see how the word frequency is even related to the Fourier transform.

What I do know is that the complex exponential and the trigonometric Fourier series both form an orthonormal basis for a certain class of functions under the function inner product. But I don't understand how these ideas are tied to the Fourier transform.

Insight is appreciated. Thanks!

BiP