Real-Time Composite Signal Decomposition.

Cover Real-Time Composite Signal Decomposition.
Real-Time Composite Signal Decomposition.
Skinner, David Preston, 1947-
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The Hanning window produces considerably worse results than the Hamming. Likewise, the Tapering window gives poor results if a major portion of the composite signal lies in the region of tapering; however, if the composite signal lies in the untapered region the results are almost identical to those for the rectangular window.
One additional drawback of these two windows is that they are zero at the endpoints and thus it is impossible to correct the recovered wavelet at these points. It is note
...d that correction for the window when w(nT)«l (that is, near the ends of the record) appears to introduce some distortion.
I nterpretation of results The following theoretical analysis is intended to clarify the conditions under which wavelet extraction is possible after using one of the foregoing windows. Consider (4-7) which is rewritten as L-1 L-1 Y(z) = w(k T)2 x(nT-k T)2~"+aw(n T+k T)^ x(nT-k T-n T)z'" ~7» n n-u n=0 L-1 n L-1 + ^ x(nT-k T)[w(nT)-w(k T)]z""+a^ x(nT-k-T-n T)[w(nT)-w(n T+k T)]z ^ TTq (4-14) The third and fourth terms of equation (4-14) can be considered error terms.


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