Frequency Domain Applications to Data Processing

Filtering a set of (2N + 1) sampled data consists in taking a weighted average of these data. The operation can be compared to that of a linear transducer, characterized by its frequency response. The only filters discussed in this paper are those for which the weights are either symmetric or skew symmetric about the center weight. With these types of filters, it is possible to design low low-pass filters to determine means and trends, low-pass filters to smooth data, sampling filters for frequency analysis, differentiators, integrators, etc. It is shown that least square polynomial fitting and Fourier analysis of sampled data are particular cases of filtering. Power of filtering techniques and precautions to take in their use for data processing are discussed