Fig.1. Schematic of adaptive filter
In an adaptive system an absolute minimum of a priori information about the incoming signal is necessary. The adaptive filter operates by estimating the statistics of the incoming signal and adjusting its own-response in such a way as to minimize some cost function. This cost function may be derived in a number of ways depending on the intended application but normally it is derived by the use of the secondary signal source or conditioning input shown in Figure 1. This secondary signal input y(n) may be defined as the desired output of the filter, in which case the task of the adaptive algorithm is to adjust the weights in the programmable filter device in such a way as to minimize the difference or error e(n) between the filter output y(n) and the y(n) input. These adaptive filters are frequently used to recover signals from channels whose characteristic is time varying.
All the systems considered in this text are sampled-data (discrete-time) systems. For convenience the explicit time index has thus been omitted from all mathematical expressions.
Task 1. Translate and learn the following word combinations from Text A. Compose sentences with them.
Conventional signal processing systems; extraction of information; incoming signal; matched filter; open-loop fashion; preceding time interval; basic assumption; time-invariant quantity; closed-loop arrangement; conditioning signal; processor weighting parameters; antenna array; spatial processing; interference reduction; sampled-data system.
Task 2. Compose microtexts to the logical Scheme 1 and Scheme 2 (A, B). Try to reproduce them both: orally and in written form.
Task 3. Home assignment. Compose a microtext to the logical Scheme 3. Present it in written form.
Scheme 1.
*quantity – величина
Scheme 2A.
Scheme 2b.
Scheme 3.
Task 4. Finish the following sentences by memory if you can. Use the information from Text A.
Conventional signal processing systems for the extraction of information from an incoming signal such as a matched filter operate in…………………..
Adaptive processors operate with……………………………….………
The incoming signal is filtered in …………………………… to yield an output y(n).
The error is then used …………….. the processor weighting parameters.
Such processors fall into two broad classes of ………………. and ………………….
Adaptive antennas use spatial processing techniques for……………………………..
Adaptive filters use……………………..filter.
Task 5. Give the definitions to the following notions in oral and written forms:
adaptive filters, antenna array, update filter parameters, programmable filter, conditioning signal.
Task 6. Summarize Text A using the following phrases:
The introductory part is concerned with…….
The paragraph (text) is devoted to …..
It is shown that…..
The problem of….. is outlined.
The author stresses the importance of…….
Special attention is paid to…..
Recommendations for………. are presented.
It considers the problems………………
In conclusion the text stresses…………….
Task 7. Find more information about Adaptive Filters using the Internet.
Task 8. Translate the text into English.
Слово «фильтр» происходит из электротехники. В этой области фильтры используются для преобразования электрических сигналов из одной формы в другую. Как правило, они используются, чтобы исключить (отфильтровать) различные частоты в сигнале. Цифровой фильтр представляет собой линейную комбинацию входных данных и выходных. Он заключает в себе многие из операций для обработки сигнала.
Task 9. Grammar Training. Translate the following sentences, mind the “Complex Subject”.
Conventional signal processing systems to be used for the extraction of information from an incoming signal prove to operate in an open-loop fashion.
The same processing function is known to be carried out in present time interval regardless of whether that function produced the correct result in preceding time interval.
Adaptive processors are found to operate with a closed-loop (feedback) arrangement.
Adaptive filters are considered to be concerned with the use of a programmable filter whose frequency response or transfer function is altered or adapted to pass the desired components of the signal without degradation and to attenuate the undesired or interfering signals, or to reduce any distortion on the input signal.
All the systems considered in this text prove to be sampled data (discrete-time) systems.
The incoming signal s(n) is known to be filtered or weighted in a programmable filter to yield an output y(u) which is certain to be compared against a desired, conditioning or training signal y(n) to yield an error signal.
This error is sure to be used to update the processor weighting parameters (usually in a iterative way) such that the error is progressively minimized (i.e. the processor output more closely approximates to the training signal).
The adaptive filter is found to operate by estimating the statistics of the incoming signal and adjusting its own-response in such a way as to minimize some cost function.
This cost function is supposed to be derived in a number of ways depending on the intended application but normally it is derived by the use of the secondary signal source or conditional input
Read Text B and summarize the information about the early development of Adaptive Filters