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Gaussian Lowpass 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.