Package window

This package contains a function to create a vector containing a window (also called a taper, lag window, or apodization function). The choices currently available are:

• Rectangular
• Hann
• Welch
• Bartlett
• Parzen
• Papoulis
• Hamming
• Kaiser
• Creighton.

Using window functions is well documented in many places. Their principal purpose is to reduce the bias in power spectrum estimation. For example, if a sinusoidal signal is present, it will give rise to a spike in a power spectrum. If such a signal is present exactly at the frequency of a particular bin, the spike will have some height. If a signal at the same amplitude but slighly different frequency is present, and the frequency is not exactly the same as one of the bins, then the spike will be broader and lower. Without windowing, this effect introduces bias into spectral estimates.

If the signal is first multiplied by the window function, the relative difference between the two resulting power spectra will be less evident. The signal which would have given a single-bin spike will now be spread over several bins. The signal that would have been spread over several bins will now be somewhat more peaked. In short, the two power spectra will appear more similar (apart from the difference in frequency of the two signals). Hence the spectra is less biased.

Definitions of most of the window functions above may be found in Numerical Recipes [1] equations 13.4.13-13.4.15. Definitions of the remaining windows can be found in Spectral analysis for physical applications [2] Section 6.11. Definition of the Kaiser window can be found in Discrete-time Signal Processing by Oppenheim and Schafer, p.474. The Creighton window function is based on a fairly standard $C_\infty$ test function used in distribution theory, e.g. Green's Functions and Boundary Value Problems [4], by Stakgold.