Question about the impulse response of a lead-lag compensator

Hi,
I am studying an equalizer which uses a lead-lag compensator after a high frequency attenuated distortion. At first, it seems quite simple: The equalizer emphasizes high frequency gain to make the total response flat at the high frequency part. When I try to get the total impulse response, I find that the impulse response of the lead-lag filter (nominator:[2.5e10, 1], denominator:[1.0e10, 1]) has a negative response. This is the first time I have a negative impulse response in contrast to the normal positive impulse response. I guess that it is because the high frequency pass feature.

The further problem is that the total impulse response of the low pass channel and the equalizer is still a negative impulse response. On the other hand, I do not see the equalized result has inversed the signal in the Simulink simulation model. How to explain the contradictory?

Please help me if you have the answer. Thanks.

On Tue, 20 May 2014 05:06:02 -0700, fl wrote:

> Hi,
> I am studying an equalizer which uses a lead-lag compensator after a
> high frequency attenuated distortion. At first, it seems quite simple:
> The equalizer emphasizes high frequency gain to make the total response
> flat at the high frequency part. When I try to get the total impulse
> response, I find that the impulse response of the lead-lag filter
> (nominator:[2.5e10, 1], denominator:[1.0e10, 1]) has a negative
> response. This is the first time I have a negative impulse response in
> contrast to the normal positive impulse response. I guess that it is
> because the high frequency pass feature.

Yes.  Anything high-pass will have that tendency.  The extreme case is a 
1st-order DC blocking filter, which has a positive-going impulse, then a 
negative-going exponential decay with area equal to the impulse.

> The further problem is that the total impulse response of the low pass
> channel and the equalizer is still a negative impulse response. On the
> other hand, I do not see the equalized result has inversed the signal in
> the Simulink simulation model. How to explain the contradictory?
> 
> Please help me if you have the answer. Thanks.

Probably what's going on is that the equalization is either not complete 
or not exact, so the high-pass filter is "showing through".  Then the 
nature of the signal is such that it does not have a lot of content in 
the higher frequencies.

The incomplete equalization is what makes for the negative-going bit in 
the impulse response.  The signal's shape coupled with the final channel 
response is what makes for no negative-going elements in the resulting 
output signal.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com