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Gaussian Filters

Gaussian filters have the most gradual passband roll-off and the lowest group delay of the filter types.  The step response of the Gaussian filter NEVER overshoots the steady-state value.   As the name infers, the Gaussian filter is derived from the same basic equations used to derive  Gaussian Distribution. The most significant characteristic of the Gaussian filter is that the step response contains no overshoot.

FilterSolutions normalizes the Gaussian filter such that the prototype high frequency attenuation matches the Butterworth filter. The passband attenuation of the Gaussian filter increases with the order of the filter when this normalization is applied. However, FilterSolutions allows the user the option of selecting the desired passband attenuation (in dB).

Gaussian Transitional Filters

It is occasionally desirable to transition from a Gaussian frequency response to a steeper roll-off response at a user-defined attenuation point.   FilterSolutions  can create 3, 6, 9, 12, and 15 dB Transitional filters. Passband attenuation is always set to -3.01 dB for Gaussian Transitional Filters.

Below are examples of Gaussian, and Gaussian Transitional, low-pass frequency responses and a Gaussian low-pass step response.