Averaging filter

Simple averaging can be used as a filter. The filter can be represented as 

N is the number of historical values included in the average and is the tuning constant defined by the engineer. The filter can also be written as 

This filter offers little advantage over the standard exponential filter. Rather than a lag, it introduces a ramp function where the duration of the ramp is given by N.ts. This would be visible if the input were a step change. But when superimposed on the process lag the result, with N adjusted to give equivalent noise reduction, is virtually indistinguishable from the exponential filter - as shown in Figme 5.18. 

Given that the averaging filter is unlikely to be standard feature of the DCS and that its impact on process dynamics is not quite so easy to predict, it offers little advantage. 

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V = average filtering velocity (cm/s) t = operating time between cleaning cycles (s). 

To illustrate behaviors of different filters, consider a moving average filter that averages over 11 terms. Such a filter has the frequency response shown in Fig. 8. Note that this filter has a relatively low gain of 0.55 at the break-point frequency of 0.05 cycles per minute. So in the range of... 

Individial filter cake compositions vary widely. As conversion increases, sulfur and ash increase while oxygen and hydrogen and possibly nitrogen concentrations in the filter cakes decrease. The average filter cake yield is 30 weight percent of the as-fed coal. The sulfur in the filter cake averaged 49 percent of the sulfur in the coal feed and is made up of the sulfur remaining after partial pyrite decomposition and sulfate sulfur. 

The net (average) filter capacity is determined by the amount of slurry processed during the total cycle time, not just the filter time, and represents the average flow rate (Q) ... 

An example is the relatively simple moving average filter. In case of a digitized signal, the values of a fixed (odd) number of data points (a window) are added and divided by the number of points. The result is a new value of the center point. Then the window shifts one point and the procedure, which can be considered as a convolution of the sipal with a rectangular pulse function, repeats. Of course, other functions like a triangle, an exponential and a Gaussian, can be used. 

Filter out any fast ripple of period Aw/2 in V(z), due to interference with internal reverberations in the lens (Fig. 8.5(b)). This may be achieved most simply by convolving with a rectangular function of length Aw/2. This is known as a moving average filter it is equivalent to a sine filter in the Fourier domain, but is computationally somewhat more efficient. Because of its period the ripple removed at this stage is sometimes called water ripple. 

Averaging is a least-squares process that reduces the effects of noise, if the noise is zero-mean and fairly random [10], and the moving-average filter removes high-frequency noise well. It is less successful at removing low-frequency noise, since these nonzero-mean variations are less likely to be affected by the averaging. It also... 

FIGURE 10.13 FIR signal processing with a simple moving-average filter. 

FIGURE 10.14 Time-domain processing of noisy data with a ten-point, moving-average filter. The moving-average-filtered data are indicated as a solid line. The true signal is shown as a dotted line. 

FIGURE 10.15 Transfer functions for FIR filters shown as a function of window size. Transfer functions for simple, moving-average filters with windows of 5 (...), 10 (-), and... 

Selection of points to use in a three point moving average filter... 

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