Theory and implementation of a Gaussian decay low-pass filter

We have developed a method for approximating a Gaussian decay low-pass filter using subthreshold CMOS VLSI circuits. The time constant (or σ) of the delay is adjustable over several orders of magnitude and the DC gain is guaranteed to be unity. Since the design is compact and straightforward, the proposed circuit can be used as a building block that can replace first-order low-pass filters in many situations. Gaussian decay circuits have applications in temporal preprocessing for neural networks, demodulation in communication, and auditory sound localization. We also believe that the Gaussian decay function may be superior to other time-delay elements in adaptive filter implementations