Desired signal o If such a thing is available why bother with the filter? o It is usually possible to obtain a signal that is sufficient for the purpose of controlling the adaptation process. o Examples will be given in the context of ‘adaptive filtering Data based:do not assume knowledge of the stochastic parameters But is based on a very similar idea. 2020-01-18 6
2020-01-18 6 Desired signal ? If such a thing is available why bother with the filter? It is usually possible to obtain a signal that is sufficient for the purpose of controlling the adaptation process. Examples will be given in the context of ‘adaptive filtering’ Data based: do not assume knowledge of the stochastic parameters But is based on a very similar idea
A priori design o Wiener Filter Dates back to the work of Wiener in 1942 and Kolmogorov in 1939. o‘A priori'design ● Based on a priori statistical information. Be optimal when the statistics of the signals at hand truly match the a priori information on which the filter design was based. When such a priori information is not available, it is not possible to design a wiener filter. 2020-01-18 7
2020-01-18 7 A priori design Wiener Filter Dates back to the work of Wiener in 1942 and Kolmogorov in 1939. ‘A priori’ design Based on a priori statistical information. Be optimal when the statistics of the signals at hand truly match the a priori information on which the filter design was based. When such a priori information is not available, it is not possible to design a Wiener filter
(3)Adaptive filter:self-designing o A priori information is not available o The signal and/or noise characteristics are nonstationary. Statistical parameters vary with time 0 Although the Wiener theory still applies,it is difficult to apply it in practice o An alternative method is to use an adaptive filter .Data based,Self-designing 2020-01-18 8
2020-01-18 8 (3) Adaptive filter: self-designing A priori information is not available The signal and/or noise characteristics are nonstationary. Statistical parameters vary with time Although the Wiener theory still applies, it is difficult to apply it in practice An alternative method is to use an adaptive filter Data based, Self-designing
Prototype adaptive filtering scheme filter input adaptive filter parameters filter filter output error desired signal 2020-01-18 9
2020-01-18 9 Prototype adaptive filtering scheme
Adaptation algorithm o Monitor the environment and vary the filter transfer function accordingly. o Starts from a set of initial conditions,that may correspond to complete ignorance about the environment o Find the optimum filter design based on the actual signals received ● Stationary:the filter is expected to converge to the Wiener filter. Nonstationary:the filter is expected to track time variations and vary its filter coefficients accordingly. 2020-01-18 10
2020-01-18 10 Adaptation algorithm Monitor the environment and vary the filter transfer function accordingly. Starts from a set of initial conditions, that may correspond to complete ignorance about the environment Find the optimum filter design based on the actual signals received Stationary: the filter is expected to converge to the Wiener filter. Nonstationary: the filter is expected to track time variations and vary its filter coefficients accordingly