Technical Notes - Helicopter Electromagnetics

The Hanning Filter

The "Hanning Filter", in the way FAS Toronto uses the word, is an abbreviation of "low pass spatial-domain filter with Hanning Coefficients for the Roll-off". The Hanning coefficients are really just a cosine roll-off; offset and adjusted to give a value of 1 at the middle, and 0 at the ends. The smooth roll-off produces less ringing (Gibbs Phenomenon) than a square cut-off filter. (How these guys get their names attached to such simple things, I don't know!)

The actual coefficients are calculated from:

0.5+0.5*cos(theta)

where theta varies from -180 to 180 degrees over the filter width for a spatial domain low-pass filter. The whole series then has to be weighted to add up to 1.0 so that the output value equals the input for flat data. If you imagine the shape of a cosine curve between -180 and 180, that's the shape of the filter.

We always use an odd number of coefficients, so that the filter will be symmetric about the data point.

Hanning coefficients can also be used to shape a Fourier-domain filter. Instead of just cutting off a band in the frequency domain, the Hanning coefficients are used to "roll-off" or smooth the cut-off shape, which reduces ringing.

Greg Hodges, Chief Geophysicist, 2001