Decomposition in terms of cosine waves. Unique. Demonstrate decomposition of saw-tooth and square waves. Wavelets. Periodic.
The previous page explained that practical Fourier analysis of time series generally involves application of the Discrete Fourier Transform (or more often the Fast Fourier Transform) to finite segments of data, sampled discretely in time. Thus the true signal might be continuous y(t), -∞ < t < ∞, but in practice we operate on another signal, y(iΔt) = yi, i = 0…N-1. This distinction is obviously vital in practice: only finite, discretely sampled data can be dealt with numerically.
| Last changed | Chris Rennie |