Minimum phase transfer functions providing a compromise between phase and amplitude approximation

1977 ◽  
Vol 24 (12) ◽  
pp. 718-724 ◽  
Author(s):  
B. Rakovich ◽  
M. Popovich ◽  
B. Drakulich
1952 ◽  
Vol 40 (12) ◽  
pp. 1717-1723 ◽  
Author(s):  
P. Ordijng ◽  
F. Hopkins ◽  
H. Krauss ◽  
E. Sparrow

1991 ◽  
Vol 113 (2) ◽  
pp. 313-315 ◽  
Author(s):  
S. Jayasuriya ◽  
M. A. Franchek

Presented in this note is a class of stable, minimum phase transfer functions whose impulse response is non-negative. A simple sufficiency criterion based on the relative locations of the poles and zeros characterizes the class. When the transfer function is in a factored form the sign of its impulse response may either be obtained by inspection or is inconclusive. A need for identifying such transfer functions was recently established by Jayasuriya (1989) who showed that a controller designed on the basis of maximizing a step input disturbance will reject a persistent disturbance bounded by the size of the maximized step if and only if the closed-loop system’s impulse response is of one sign.


1995 ◽  
Vol 12 (6) ◽  
pp. 1191-1210 ◽  
Author(s):  
Duane G. Albrecht

AbstractThe responses of simple cells (recorded from within the striate visual cortex) were measured as a function of the contrast and the frequency of sine-wave grating patterns in order to explore the effect of contrast on the spatial and temporal phase transfer functions and on the spatiotemporal receptive field. In general, as the contrast increased, the phase of the response advanced by approximately 45 ms (approximately one-quarter of a cycle for frequencies near 5 Hz), although the exact value varied from cell to cell. The dynamics of this phase-advance were similar to the dynamics of the amplitude: the amplitude and the phase increased in an accelerating fashion at lower contrasts and then saturated at higher contrasts. Further, the gain for both the amplitude and the phase appeared to be governed by the magnitude of the contrast rather than the magnitude of the response. For the spatial phase transfer function, variations in contrast had little or no systematic effect; all of the phase responses clustered around a single straight line, with a common slope and intercept. This implies that the phase-advance was not due to a change in the spatial properties of the neuron; it also implies that the phase-advance was not systematically related to the magnitude of the response amplitude. On the other hand, for the temporal phase transfer function, the phase responses fell on five straight lines, related to the five steps in contrast. As the contrast increased, the phase responses advanced such that both the slope and the intercept were affected. This implies that the phase-advance was a result of contrast-induced changes in both the response latency and the shape/symmetry of the temporal receptive field.


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