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Smoothing windows, IIR filters, and FIR filters are linear because they satisfy the superposition and proportionality principles, as shown in Equation A.

where a and b are constants, x(t) and y(t) are signals, L{•} is a linear filtering operation, and inputs and outputs are related through the convolution operation, as shown by the following two equations:

A nonlinear filter does not satisfy Equation A. Also, you cannot obtain the output signals of a nonlinear filter through the convolution operation because a set of coefficients cannot characterize the impulse response of the filter. Nonlinear filters provide specific filtering characteristics that are difficult to obtain using linear techniques.

The median filter, a nonlinear filter, combines lowpass filter characteristics and high-frequency characteristics. The lowpass filter characteristics allow the median filter to remove high-frequency noise. The high-frequency characteristics allow the median filter to detect edges, which preserves edge information.

Example: Analyzing Noisy Pulse with a Median Filter

The Transition Measurements VI and the Pulse Measurements VI analyze an input sequence for a pulse pattern and determine the best set of pulse parameters that describes the pulse.

Note  You can use the Transition Measurements VI and the Pulse Measurements VI only in the LabVIEW Full and Professional Development Systems.

After these VIs complete modal analysis to determine the baseline and the top of the input sequence, discriminating between noise and signal becomes difficult without more information. Therefore, to accurately determine the pulse parameters, the peak amplitude of the noise portion of the input sequence must be less than or equal to 50% of the expected pulse amplitude. In some practical applications, a 50% pulse-to-noise ratio is difficult to achieve. Achieving the necessary pulse-to-noise ratio requires a preprocessing operation to extract pulse information.

If the pulse is buried in noise whose expected peak amplitude exceeds 50% of the expected pulse amplitude, you can use a lowpass filter to remove some of the unwanted noise. However, the filter also shifts the signal in time and smears the edges of the pulse because the transition edges contain high-frequency information. A median filter can extract the pulse more effectively than a lowpass filter because the median filter removes high-frequency noise while preserving edge information.

The following figure shows the block diagram of a VI that generates and analyzes a noisy pulse.

The VI in the previous figure generates a noisy pulse with an expected peak noise amplitude greater than 100% of the expected pulse amplitude. The signal the VI in the previous figure generates has the following ideal pulse values:

• Amplitude of 5.0 V
• Delay of 64 samples
• Width of 32 samples

The following figure shows the noisy pulse, the filtered pulse, and the estimated pulse parameters returned by the VI in the previous figure.

In the previous figure, you can track the pulse signal produced by the median filter, even though noise obscures the pulse.

You can remove the high-frequency noise with the Median Filter VI to achieve the 50% pulse-to-noise ratio the Transition Measurements VI and the Pulse Measurements VI need to complete the analysis accurately.

Note  You can use the Median Filter VI only in the LabVIEW Full and Professional Development Systems.