| 释义 |
Z-TransformThe  -transform of  is defined by
 | (1) |
 | (2) |
 is the Delta Function, is the sampling period, and  is the Laplace Transform. An alternative definition is
 | (3) |
 | (4) |
 | (5) |
 |  |  | (6) |  | |  | (7) |  | |  | (8) |  | |  | (9) |  | |  | (10) |  | |  | (11) |  | |  | (12) |  | |  | (13) |  | |  | (14) |
Transforms of special functions (Beyer 1987, pp. 426-427) include
 | |  | (15) |  | |  | (16) |  | |  | (17) |  | |  | (18) |  | |  | (19) |  | |  | (20) |  | |  | (21) |  | |  | (22) |  | |  | (23) |  | |  | (24) |
where  is the Heaviside Step Function. In general,
where the  are Eulerian Numbers. Amazingly, the Z-transforms of  are therefore generators for Euler's Triangle.See also Euler's Triangle, Eulerian Number
References
Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 424-428, 1987.Bracewell, R. The Fourier Transform and Its Applications. New York: McGraw-Hill, pp. 257-262, 1965.
|
