Gaussian Lowpass Filter Poles
(to 6 dB & to 12 dB)

Click here for the Analog Devices document containing the graph.

A Gaussian filter is a filter whose impulse response is a Gaussian function. Gaussian filters are designed to give no overshoot to a step function input while minimizing the rise and fall time. This behavior is closely connected to the fact that the Gaussian filter has the minimum possible group delay. Mathematically, a Gaussian filter modifies the input signal by convolution with a Gaussian function; this transformation is also known as the Weierstrass transform. - Wikipedia

See the online filter calculators and plotters here.

Here are the lowpass prototype poles for a Gaussian filter to 6 dB and to 12 dB. Lowpass prototype inductor and capacitor values are here.

Gaussian to 6 dB
Order (N)	Re Part (-σ)	Im Part (±jω)
3	0.9360 0.9360	1.2168
4	0.9278 0.9192	1.6995 0.5560
5	0.8075 0.7153 0.8131	0.9973 0.2053
6	0.7019 0.6667 0.4479	0.4322 1.2931 2.1363
7	0.6155 0.5486 0.2905 0.6291	0.7703 1/5154 2.1486
8	0.5441 0.5175 0.4328 0.1978	0.3358 0.9962 1.6100 2.0703
9	0.4961 0.4568 0.3592 0.1489 0.5065	0.6192 1.2145 1.7429 2.1003
10	0.4535 0.4352 0.3886 0.2908 0.1136	0.2794 0.8289 1.3448 1.7837 2.0599

Gaussian to 12 dB
Order (N)	Re Part (-σ)	Im Part (±jω)
2	0.8590	0.6981
3	0.6969 0.8257	1.1318
4	0.7448 0.6037	0.5133 1.4983
5	0.6775 0.5412 0.7056	0.9401 1.8256
6	0.6519 0.6167 0.4893	0.4374 1.2963 2.0982
7	0.6190 0.5816 0.4598 0.6283	0.8338 1.6455 2.3994
8	0.5791 0.5665 0.5303 0.4148	0.3857 1.1505 1.8914 2.5780
9	0.5688 0.5545 0.5179 0.4080 0.5728	0.7595 1.5089 2.2329 2.9028
10	0.5249 0.5193 0.5051 0.4711 0.3708	0.3487 1.0429 1.7264 2.3850 2.9940

Data taken from Analog Devices app note.

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