Sentence examples for median filter root from inspiring English sources

Note that this sequence is a median filter root sequence.

Step-and-ramp sequence (median filter root) for k=1,2,…,420; Fig. 1 A simulated 420-point signal.

In addition, it was shown that Hampel filter root sequences nest, with the median filter root set included in all Hampel filter root sets.

The upper right plot presents the results for Segment 1 ("Noise only"), consisting of the median filter root sequence, low-level Gaussian noise, and impulsive noise spikes.

Here again, it is easy to see that this sequence is an implosion sequence for K, but it is not a median filter root sequence.

Finally, it is important to note that, for the filter window width considered here (K=5), the signal sequence shown in Fig. 1 is implosion-free and is not a median filter root sequence.

Thus, the signals of greatest interest in characterizing Hampel filter performance are implosion-free sequences that are not median filter roots.

Since any root sequence for the median filter K is also a root for all Hampel filters K, regardless of threshold, the important implosion sequences are those that are not median filter roots: these sequences are modified by the median filter and also modified in exactly the same way by the Hampel filter, independent of the threshold parameter t.

As with the standard Hampel filter, note that the weighted Hampel filter reduces to the weighted median filter for t=0, and the root sequence nesting condition for these filters for fixed weights follows as before: s≤t implies s ⊂ t.

In this case, it follows by the above result that {x k } is also a root sequence for the median filter K, so we expect no difference in behavior between the median and Hampel filters for this case by the root sequence nesting condition (6).

At the other extreme, if the sinusoidal frequency is low enough, the N-point finite signal sequence will be monotonic, and thus a root sequence for the median filter and all Hampel filters.