Least Squares Digital Differentiators (LSDD) The 2-D Subclass

In this paper, we present results of our investigation of the 2-D LSDD subclass of digital differentiation filters. We discuss methods of their generation from least-squares normal equations, and examine their properties in the space and frequency domains. In addition to ease of generation and implementation via convolution, the filters are shown to have many desirable properties. They are low pass linear phase, stable filters with narrow transition band attenuating rapidly at high frequencies. More important is that the filters are separable implying considerable computational time saving and except for an integer scalingfactor, their coefficients are all integers thus reducing the risk of cumulative round-off errors. The filters may be generated for any order derivative with arbitrary length to suite any desired sampling frequency. Unlike ordinary full-band DD that typically amplify high frequency noise, the low-pass nature of LSDD renders them noise suppressant with very low noise amplification factor. Moreover, the filters are actually multitasking, performing data smoothing and differentiation simultaneously. Their only drawback is that they are not maximally linear near the DC frequency.