Filters And Fourier Analysis

Trigonometric nomenclature for periodic waves

The basics. But note that in a discretized domain, L is the horizontal spatial scale of the domain, and x=n delta x.
Spreadsheet example of discretized waves in periodic domain.

Digital filters

Recursive and nonrecursive filters
An example of a nonrecursive low-pass filter used by meteorologists - the Shapiro filter
Spreadsheet example of 1-2-1 Shapiro filter
Spreadsheet example of 1-8-28-56-186 Shapiro filter. Why is the result almost the same as the original? What has been removed?
The classic Shapiro papers. Paper one. Paper two.
Other nonrecursive common filters. Written by Ken Turkowki of Apple Computer. Notice that in electronic nomenclature, "decimation" represents the weight values, the frequency response is written such that no damping effect has a gain of 0 dB, and damping is represented by negative gain.
Gibbs phenomenon.
The classic Lanczos paper. Written by Claude Duchon. The Lanczos filter can perform lowpass or highpass fitlering, and is designed to reduce Gibbs phenomenon.
Optional material - More on recursive exponential smoothing
Optional material - Univariate time series methods

Running mean (moving average)

Nonrecursive moving average, also known as a running mean. Smooths data, but does not remove any frequencies since all weights are equal. See Kalnay lecture for more details.
Example application - the Oceanic Nino Index (ONI)
Example application - Running mean of global temperatures since 1880

Comparison of moving average, the one-two-one filter, and the Lanczos filter

Fourier (Harmonic) analysis

1) Tidal analysis and prediction
2) Example - Bridgeport, CT
3) Example - San Diego, CA
4) More realistic example - Seattle, WA

Computer language examples

Recorded lectures