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

Click here for the Analog Devices (Fig. 10) 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.

Note*: The values given in the two tables below have been edited to agree with those in Table XI and Table XII in "AN-649: Using the Analog Devices Active Filter Design Tool." Even it contains an extraneous number in the 3rd-order Gaussian to 12 dB table. The values given in for both the Gaussian to 6 dB and Gaussian to 12 dB appear to be wrong (they are what I originally used). Always be sure to verify critical references.

 Gaussian to 6 dB Order (N) Re Part (-σ) Im Part (±jω) 3 0.96220.9776 1.2214 4 0.79400.6304 0.50291.5407 5 0.61900.35590.6650 0.82541.5688 6 0.54330.46720.2204 0.34310.99911.5067 7 0.45800.36490.15220.4828 0.59321.12861.4938 8 0.42220.38330.28780.1122 0.26400.77161.20661.4798 9 0.37000.32300.23090.086040.3842 0.47040.90681.26341.4740 10 0.33840.31640.26770.18490.06706 0.21010.61800.98521.27451.4389
 Gaussian to 12 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 0.99732.0532 6 0.70190.66670.4479 0.43221.29312.1363 7 0.61550.54860.29050.6291 0.77031.51542.1468 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

* Thanks to RF Cafe visitor Tim C. for pointing out the errors.