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The development of a digital filter using sampled data theory techniques and having a desired frequency response characteristic is described. Specifically, design of a digital notch filter is accomplished through formulation of a regression equation for application to sampled input and output values from the filter. After first expressing the desired transfer function in the continous domain, the equation is developed using sampled data theory relationships. Although the techniques are applied to a specific type of filter, they are general in nature. The problem considered involves attenuation of a particular frequency and those in its immediate vicinity while leaving other even slightly distant frequencies relatively unattenuated. An additional requirement calls for tracking and attenuating an input whose frequency is time-variable. In particular, a linearly (with respect to time) variable frequency is considered and discussed. Testing and evaluation were performed through simulation on a general purpose digital computer. Results obtaied are described.