Adaptive filter

An adaptive filter in the digital signal processing is a special digital filter which has the property of being able to vary its transfer function in operation independently.

For this purpose, an FIR filter is provided with a generally Einstellnetzwerk that can change the filter coefficients of the transversal filter according to certain rules.

Function

The arriving at the input sequence passes through the adjustable transversal and forms the output sequence. This sequence is compared with the sequence from the filter to be formed, and supplies the error signal. In the ideal case, i.e. when the filter the input sequence exactly as modified by the filtering that is equal, the error sequence 0 is the case of a deviation, the error signal has values ​​other than 0. The control algorithm then tries to minimize the error signal by changing the filter coefficients, so as much as possible to adjust the output sequence of the filter to the reference signal. The common adjustment algorithm is based on a method for minimizing the error squares, the LMS algorithm. Better results are achieved with more sophisticated mathematical recursive method such as the RLS algorithm.

Application for channel equalization

Adaptive filters are used, inter alia, in the signal processing for the adaptive equalization of an input signal. Transmission channels, such as an electric line or wireless channel distorts the transmitted signal. In order to minimize transmission errors on the receiving end, therefore, it may be necessary to compensate for this distortion as much as possible. In this case, the input sequence, the transmitted via a distorting channel data sequence dar. Since the receiver is not known how the channel changed the data sequence before the start of a user data transfer an agreed fixed between transmitter and receiver, and known to transmit so-called training sequence. This training process is sometimes referred not entirely correct synchronization. By means of the training sequence, which is referred to in previous figure and which should also have certain properties such as a spectrally uniform distribution, the adaptive filter on the receiving side can be set so that the error signal becomes minimum. In this case, the filter compensates for the distortions of the transmission channel. Among the most relevant assumption that the channel characteristics distortions do not change very quickly on time, then the thus-set filters can be used for channel equalization.

If, during operation to a slow increase of the error rate at the receiver, due to be änderenden channel transmission characteristics and can be repeatedly switched to training mode and the adaptive filter are adjusted to the changed conditions in the channel. There also remained a method for channel equalization, in which, in operation, a continuous adaptation to the slightly varying channel characteristics can take place without switching.

Other applications of adaptive filters are in the range of echo cancellation and for simulating unknown transfer functions. As a practical example may be mentioned here modems that use more complex modulation adaptive filter for channel equalization and echo canceling.