LabVIEW 2013 Adaptive Filter Toolkit Help
Edition Date: June 2013
Part Number: 372357B01
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An adaptive filter is a computational device that iteratively models the relationship between the input and output signals of the filter. An adaptive filter selfadjusts the filter coefficients according to an adaptive algorithm. The following figure shows the diagram of a typical adaptive filter.
where 
x(n) is the input signal to a linear filter at time n 

y(n) is the corresponding output signal 

d(n) is an additional input signal to the adaptive filter 

e(n) is the error signal that denotes the difference between d(n) and y(n) 
In the previous figure, an adaptive algorithm adjusts the coefficients of the linear filter iteratively to minimize the power of e(n). For different applications, you choose the input and output signals x(n), d(n), y(n), and e(n) in different ways.
Differences between Traditional Digital Filters and Adaptive Filters
An adaptive filter differs from a traditional digital filter in the following ways:
 A traditional digital filter has only one input signal x(n) and one output signal y(n). An adaptive filter requires an additional input signal d(n) and returns an additional output signal e(n).
 The filter coefficients of a traditional digital filter do not change over time. The coefficients of an adaptive filter change over time. Therefore, adaptive filters have a selflearning ability that traditional digital filters do not have.
Advantages of Using Adaptive Filters
Compared to traditional digital filters, adaptive filters have the following advantages:
 Adaptive filters can complete some signal processing tasks that traditional digital filters cannot. For example, you can use adaptive filters to remove noise that traditional digital filters cannot remove, such as noise whose power spectrum changes over time.
 Adaptive filters can complete some realtime or online modeling tasks that traditional digital filters cannot. For example, you can use adaptive filters to identify an unknown system in online mode. Typically, adaptive filters are useful when you perform realtime or online signal processing applications. For offline applications, you can use other signal processing tools, such as the Time Frequency Analysis Tools of the LabVIEW Advanced Signal Processing Toolkit.