A digital filter can be implemented with a reduced number of components for a transform function having specific characteristics in the regions outside of a center region. The characteristics are that the transform function waveform is periodic with period T and has or can be approximated by at least one envelope, the envelope decaying a multiplier constant for each period T in a direction away from the waveform center. The digital filter has three groups of elements. A center group of components functions in a manner similar to the prior digital filters. A positive time group of components receives the signals from the center, and using a group of delay component, delays the signal by one period T, is reduced by the multiplier constant factor, and after having the current signal from the center group applied thereto, is once again applied to the positive time group delay components. Each positive time group delay component has coefficient multiplier component which multiplies the signal in the associated delay component by a cumulative coefficient prior to applying the signal to the output line. The negative time group of components can include a group of delay components and coefficient multiplier components which function in the prior art manner. In the alternative, the negative time group of components can include a series of delay component which applies the signal transmitted therethrough to the center group of components and to the a negative time group of component similar in structure and function to the positive time group of components.