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

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.

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

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