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

Filter Gaussian to 12 dB (Analog Devices) - RF Cafe

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.


Gaussian to 6 dB, Gaussian to 12 dB Copyright © 2006 The McGraw-Hill CompaniesNote*: 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 Chapter 8 of Analog Device's Design Handbook 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 0.9622

0.9776

1.2214
4 0.7940

0.6304

0.5029

1.5407

5 0.6190

0.3559

0.6650

0.8254

1.5688

6 0.5433

0.4672

0.2204

0.3431

0.9991

1.5067

7 0.4580

0.3649

0.1522

0.4828

0.5932

1.1286

1.4938

8 0.4222

0.3833

0.2878

0.1122

0.2640

0.7716

1.2066

1.4798

9 0.3700

0.3230

0.2309

0.08604

0.3842

0.4704

0.9068

1.2634

1.4740

10 0.3384

0.3164

0.2677

0.1849

0.06706

0.2101

0.6180

0.9852

1.2745

1.4389

Gaussian to 12 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

2.0532

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

2.1468

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

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

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