Evaluation of the sensitivity coefficient of an eigenvalue

Coefficient quantization effects on pole locations for state model digital filters

“…( [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and, assuming that 6x(o) = o, (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) where n-1 ( . ) are the errors due to the input, product, and coefficient quantizations, respectively.…”

“…AlthoUgh this development allows the three types of errors to be expressed distinctly in (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19), (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) and (1-21}, it should be kept in mind that the effect of coefficient quantizations, shown in (1-21}, couples into those of input quantization in (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)…”

“…From (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) - it is seen that ~y 3 (n) is directly proportional to the magnitude of the input, while ~y 1 (n) and ~y 2 (n) are independent of it. This means that the signal-to-noise ratio for the error due to coefficient quantizations is fixed for a given network, while those for the input and product quantizations can be improved by increasing the input level.…”

“…Thus, searching for a better network realization entails minimizing the effects of coefficient and product quantizations. 13 The error due to input quantization, as shown in (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) is often referred to as .. quantization noise 11 • It is inherent in any A/D conversian process and has been studied in great depth [33] [34].…”

“…The error due to product quantizations, as shown in (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20), is similar to the input quantization error in that it also involves quantization of the data. However, this form of error is different in that the data is already in digital form and the quantization, in the form of either rounding or truncation, takes place within the filter, not just at the input.…”