We used to classify signals as 1D and 2D etc ie one dimensional and two dimensional. For example a periodic square wave signal is 1D and an image is a 2D signal etc (reference - Signals and systems by Simon Haykin and Barry Van Veen, 2nd edition , page 2). But the same periodic square wave signal can be decomposed using fourier series to infinite sinusoids with different frequencies. In the linear algebra terms these infinite orthogonal sinusoids forms the basis and the the dimension of a periodic square wave is infinite. So actually which is the actual dimension or what is dimension?