Digital Filter Design Using Computer Algebra Systems

Abstract

Digital filter design can be performed very efficiently using modern computer tools. The drawback of the numeric-based tools is that they usually generate a tremendous amount of numeric data, and the user might easily lose insight into the phenomenon being investigated. The computer algebra systems successfully overcome some problems encountered in the traditional numeric-only approach. In this paper, we introduce an original approach to algorithm development and digital filter design using a computer algebra system. The main result of the paper is the development of an algorithm for an infinite impulse response (IIR) filter design that, theoretically, is impossible to be implemented using the traditional approach. We present a step-by-step procedure which includes derivations of closed-form expressions for (1) the transfer functions of the implemented digital filter which contains the algebraic loop; (2) the closed-form expression for computing the number of requested iteration steps; and (3) the error function representing the difference of the output sample values of the new filter and that of the conventional filter. We demonstrate how one can use some already-known multiplierless digital filter as a start-up filter to design a new digital filter whose passband edge frequency can be simply moved by using a single parameter. As a result, we obtain a multiplierless IIR filter, which belongs to the family of low-power digital filters where multipliers are replaced with a small number of adders and shifters.

Symbolic Analysis as Universal Tool for Deriving Properties of Non-linear Algorithms – Case study of EM Algorithm

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“…This means that inputted knowledge is visually identical as in textbook. Notice that the last output is a result of the line that follows input In [3], that is actually input In [4], and the displayed output is Out [4].…”

“…The head of the function is the same as for the trinomial distribution, but the difference is in the number of arguments. Instead of any argument with _ we can use any other symbol or number (instead of y2_ we can use 3 x , and instead of p1_ we can use 2 1 p p  ). Replacing arguments with appropriate symbols, and using the command for displaying expression in the traditional form, equation (16) …”

Development of Aeronautical Communication System for Air Traffic Control Using OFDM and Computer Algebra Systems

“…Symbolic processing can help to error-free derive simulation code, and to find typewriting errors if they exist calculating by hand. Next, symbolic processing can be used for finding the processing errors as the closed-form expression for computing the number of required iteration steps; or the error function due to finite word-length [10], [15]. Therefore, symbolic processing can help gain insight into how a system works, which is preferred to experimenting with numeric simulations.…”

Analysis of finite tolerance effect of critical pole on characteristics of selective RC active special Gegenbauer filters

“…Some designs of lowsensitivity RC active filters are considered in literature [19][20][21][22][23]. Helpful literature for filter theory is given in literature [24][25][26][27][28][29][30].…”