# Negative Group Delay

by Bill Thrasher

The first rule of filters is that everything is a filter. Two insulated wires twisted together will act as a low-pass (band-pass?) filter. There is resistance, inductance, and capacitance involved in the physical wires, therefore it becomes a filter. It will probably have a very wide pass-band, but it does have a pass-band region and then a stop-band.

Past this first rule, we routinely and purposefully design, construct, and introduce filters into our electronic circuits to separate, divide, pass, eliminate, delay, shift, & to change other aspects of our signals.

A filter, by it’s very nature, is an energy storage, release, and dissipation system. It uses these mechanisms to accomplish the filtering. So much of what we read and study about filters is based upon and/or describes the characteristics and behavior of theoretical filters operating under theoretical conditions.

Lets take the idea of a signal generator connected to a filter and then to a load, with measurement devices attached, and then we turn the test signal on, let it all settle down, and then start to make measurements.

After a sufficient period of this (pseudo) “continuous” operation, we can measure a filter output voltage occurring before (leading) the filter input voltage (which we would call negative phase shift), and which implies acausal operation (effect before cause, output before input).

But this measurement is misleading because it is only a partial truth. The measurement does not take into account what all happened when we first turned the signal on and then waited for it to all settle down. If we were to assume an infinitely long term, steady state signal, which cannot actually exist in this universe, then we would again get this same misleading partial truth. While this partial truth is informative and interesting, it is not all that we need to know about this filter, and it is most probably not the most important thing that we know about this filter.

What has happened is that this filter has had sufficient time to use it’s stored energy to get the output “synchronized” with the input, in effect, anticipating what the input signal will do based on the (continuous) signal history over the last several cycles, seconds and/or minutes. This apparent acausal behavior is perfectly predictable, and the information generated by the measurement is predictably misleading.

If we could introduce an on-off switch between the signal generator and the filter, and use a random number generator to turn the same signal on and off at random intervals, then we would be able to measure an entirely different set of characteristics and behaviors. When the signal is left on long enough for the filter to settle and get synchronized, we would again find the apparent acausal behavior described above. The measurements would however be very different and would obviously be causal when the signal has just been started or stopped, or when it is restarted just after being stopped. These transient behaviors would probably be much more interesting and informative, and far more indicative of how the filter would behave using real world speech and music signals.   bt