spectral band energy detection

>SteveSmith <Steve.Smith1@SpectrumSDI.com> wrote:
>
>>Hi Steve,
>
>>I had the same idea, but after some thought there is a point that I
really
>>don't understand.   
>
>>Say we start with x[n], and run it through a low-pass filter to create
>>xl[n]. We then could form the matching high-pass filter by calculating
>>xh[n] = x[n] - xl[n].   Since x[n] = xl[n] + xh[n], the frequency
responses
>>of the two filters should add to unity, as we would like.  
>
>>The problem is, working through the algebra, the energy in xl[n] plus
the
>>energy in xh[n] doesn't seem to add up to the energy in the original
signal
>>x[n].  What am I missing here?
>
>If the low-pass filter were zero-phase, then the energy would
>be equal.  
>
>However if there is phase shift through the low-pass filter, then you
>are right it does not add up.  To illustrate this, consider the
>case of a frequency at which the lowpass filter has a gain
>of 0.1 and a phase shift of 180 degrees.  
>
>Depending on your application and your signal, if using this approach 
>you may need to use a zero-phase-shift filter, or you may get away 
>with a (simpler) filter that has some phase shift but does
>not give too much of an incorrect result.
>
>Steve
>

Ah yes, the Phase problem.  It seems I forget this every few years and try
to rediscover the wheel.  Thanks!