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

The table below lists prototype element values for the normalized lowpass function, which assumes a cutoff frequency of 1 rad/sec and source and load impedances of 1 Ω. Either an input capacitor (top reference line in table) or an input inductor (bottom line in table) can be used.

Convert values to other cutoff frequencies, impedances, and to highpass, bandpass or bandstop using the equations here.

• Filter denormalization of formulas can be found here.
• Online filter calculators and plotters can be found here.
• Bessel filter complex poles can be found here.

Capacitor Input

Inductor Input

Order	C1	L2	C3	L4	C5	L6	C7	L8	C9	L10
1	2.000
2	0.576	2.148
3	0.3374	0.9705	2.2034
4	0.2334	0.6725	1.0815	2.2404
5	0.1743	0.5072	0.804	1.111	2.2582
6	0.1365	0.4002	0.6392	0.8538	1.1126	2.2645
7	0.1106	0.3259	0.5249	0.702	0.869	1.1052	2.2659
8	0.0919	0.2719	0.4409	0.5936	0.7303	0.8695	1.0956	2.2656
9	0.078	0.2313	0.377	0.5108	0.6306	0.7407	0.8639	1.0863	2.2649
10	0.0672	0.1998	0.327	0.4454	0.5528	0.6493	0.742	0.8561	1.0781	2.2641
Order	L1	C2	L3	C4	L5	C6	L7	C8	L9	C10