On the behavior of cascaded Gaussian impulse response filters

The behavior of the cascade connection of two filters each having a true Gaussian impulse response function is studied in this work. It is particularly shown that the impulse response of the resulting higher-order filter is not a true Gaussian function, as might initially be assumed based on the properties of the Gaussian distribution. To validate our findings, an approximation of the cascade filter transfer function was performed through the employment of a curve-fitting technique, and simulations as well as experimental results (using a Field Programmable Analog Array) are shown to match well with the theory.