# 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 0.93600.9360 1.2168 4 0.92780.9192 1.69950.5560 5 0.80750.71530.8131 0.99730.2053 6 0.70190.66670.4479 0.43221.29312.1363 7 0.61550.54860.29050.6291 0.77031/51542.1486 8 0.54410.51750.43280.1978 0.33580.99621.61002.0703 9 0.49610.45680.35920.14890.5065 0.61921.21451.74292.1003 10 0.45350.43520.38860.29080.1136 0.27940.82891.34481.78372.0599
 Gaussian to 12 dB Order (N) Re Part (-σ) Im Part (±jω) 2 0.8590 0.6981 3 0.69690.8257 1.1318 4 0.74480.6037 0.51331.4983 5 0.67750.54120.7056 0.94011.8256 6 0.65190.61670.4893 0.43741.29632.0982 7 0.61900.58160.45980.6283 0.83381.64552.3994 8 0.57910.56650.53030.4148 0.38571.15051.89142.5780 9 0.56880.55450.51790.40800.5728 0.75951.50892.23292.9028 10 0.52490.51930.50510.47110.3708 0.34871.04291.72642.38502.9940

Data taken from Analog Devices app note.