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# Smoothing

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# Smoothing

Smoothing

There are four smoothing techniques implemented in Easy HVSR. For each of them is shown below the smoothing criterion.

Konno & Ohmachi

This type of smoothing provides that the amplitudes of frequencies around a center frequency are weighted according to the following formula:

where:

is the center frequency

is the frequency to be weighed

b       is the bandwidth coefficient

The frequency band to be weighed on a logarithmic scale and its amplitude are determined by the percentage of smoothing, that is equal to the percentage of smoothing for the amplitude of the entire band to be smoothed.

Moving average

This type of smoothing provides that is performed the average of the amplitudes of a certain range of frequencies around a center frequency. Amplitude of the surroundings to be smoothed is indicated by the value of the percentage of smoothing, that is equal to the percentage of smoothing for the whole frequency band to be smoothed.

Triangular constant

This type of smoothing provides that the amplitudes of the frequencies in the around of a center frequency are weighted according to a linear trend descending from the center frequency, where the weight assumes unitary value, to the limit frequency of the surroundings, where the weight takes the value zero. The environment has an amplitude equal to the percentage of smoothing for the bandwidth of the entire band to be smoothed.

Triangular proportional

This type of smoothing is the same as the previous one with the difference that the amplitude of the surroundings is proportional with the center frequency, or equal to the percentage of smoothing for the value which,from time to time, assumes the center frequency Fc.