Name
Title | ||
|---|---|---|
An approach to solving linear constant coefficient difference and differential equations |
Abstract | ||
|---|---|---|
The underlying structure inherent in the classical method of undetermined coefficients, which is used to obtain particular solutions to linear constant coefficient (LCC) difference or differential equations, is investigated. A system of equations of the form B=M-1 A is obtained, where B and A are vectors whose elements are the coefficients of the terms in the expressions for the input and solutions, respectively, to the LCC equations. The structure of M that arises for both LCC difference and differential equations, as well as moving-average (FIR) systems, are investigated. It is shown that M is always a lower triangular matrix of order (r-1)×(r+1), where r is the degree of the expressions for the input and solutions. Furthermore, M is characterized by r+1 unique elements, each one defining the diagonal and off-diagonal elements, and is a member of an infinite set of matrices, all of order r+1, which form a group. M can be obtained whenever A and B are given. As a result, if one desires an FIR filter whose output is some linear operation, then the computation of M from A and B imposes a set of necessary and sufficient conditions |
Year | DOI | Venue |
|---|---|---|
1990 | 10.1109/29.52705 | IEEE Trans. Acoustics, Speech, and Signal Processing |
Keywords | Field | DocType |
fir filter,filtering and prediction theory,lower triangular matrix,difference equations,differential equations,moving average fir systems,vectors,linear constant coefficient,differential equation,moving average,interpolation,feedback,polynomials,terrorism,finite impulse response filter,system of equations,linear operator | Diagonal,Differential equation,Mathematical optimization,System of linear equations,Matrix (mathematics),Mathematical analysis,Constant coefficients,Infinite set,Method of undetermined coefficients,Triangular matrix,Mathematics | Journal |
Volume | Issue | ISSN |
38 | 4 | 0096-3518 |
Citations | PageRank | References |
3 | 1.09 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| H. Holtz | 1 | 3 | 1.09 |
| B. J. Campbell | 2 | 4 | 1.52 |