1957/09/01 by Marvin Blum · 1 voice · 3 citations
Computer Science · #Digital Filter Design and Implementation #Numerical Methods and Algorithms #Sensor Technology and Measurement Systems
paper · doi:10.1109/tit.1957.1057412
openalex publication_date 1957/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
Given a set of equally spaced measurements, it is possible to curve fit a "least squares" polynomial to theNobserved data points and obtain estimates of the past, present, or future values of the data or its derivatives by appropriate manipulations of the curve fit. This curve fitting can be accomplished by a linear weighting of the observed data over an interval(n-1) T. If the data is measured in real time such that a new data point is observed eachTseconds, then the desired output (for example, the smooth or predicted value of the data) can be obtained by sliding these fixed number of weights such that the same weight always multiplies the data which is at a fixed lag with respect to the most recent data. Since these weights are zero for lags greater thann, they may be described as a fix-finite memory linear digital filter. In calculating the desired output for each new sample one requires a machine which can storencoefficients,ndata points and performs n multiplications andn - 1additions in at leastTseconds. The coefficients do not change but the multiplications and additions must be performed eachTseconds as a new data point is measured. For large values ofn, and smallT, this may put a severe requirement on the real time solutions of the computer. This paper presents an alternate technique using recursion formulas to obtaining the same results as thenpoint weighting equation. The method has the advantage of requiring considerably less storage, multiplications and additions whenn ≫ 1and the degree of the curve fitting polynomial(K)is small.