On the Performance of the Martin Digital Filter for High- and Low-pass Applications

A nonrecursive numerical filter is described in which the weighting sequence is optimized by minimizing the excursion from the ideal rectangular filter in a least squares sense over the entire domain of normalized frequency. Additional corrections to the weights in order to reduce overshoot oscillations (Gibbs phenomenon) and to insure unity gain at zero frequency for the low pass filter are incorporated. The filter is characterized by a zero phase shift for all frequencies (due to a symmetric weighting sequence), a finite memory and stability, and it may readily be transformed to a high pass filter. Equations for the filter weights and the frequency response function are presented, and applications to high and low pass filtering are examined. A discussion of optimization of high pass filter parameters for a rather stringent response requirement is given in an application to the removal of aircraft low frequency oscillations superimposed on remotely sensed ocean surface profiles. Several frequency response functions are displayed, both in normalized frequency space and in period space. A comparison of the performance of the Martin filter with some other commonly used low pass digital filters is provided in an application to oceanographic data.