John,
A "high pass filter" when operating in its passband has a response proportional to the rate of change (slope) of the incoming signal. In other words, it is a differentiator and "calculates" the derivative of the incoming signal. All practical high pass filters "roll off" at some upper frequency, above which they are not differentiators. In typical metal detector practice, the rolloff frequency of a high pass filter is usually in the range of 6 to 20 Hz.
Differentiators (call them high pass filters if you like) are used in metal detectors to boost the target signals (which are predominantly in the 4-12 Hz range) relative to the signals from ground minerals, which are predominantly in the 1-3 Hz range.
Differentiate the signal once, and you have "autotune" or "SAT". Most gold prospecting machines do it this way. The response you hear to a metal target is a "zip" sound.
Differentiate it again, and you have "second derivative" or so-called "two-filter" response. This arrangement happens to be particularly well suited to discriminators. It is economical to manufacture and has good response characteristics. The sound is typically "bip".
Differentiate it a third time to further improve separation of target signal from ground interference, and you get a signal that's too confusing to listen to. But the signal can be sampled and used to operate a visual or tone ID system or a discrimination blanking system. In most such cases the signal you actually hear will be a second derivative signal.
A high pass filter with a rolloff has infinite bandwidth, and therefore infinite noise unless another rolloff (i.e., a low pass filter) is provided. In a typical op amp circuit-based inverting differentiator, the first rolloff (of the high pass filter) is done with a resistor in series with the input, and the low pass filter is done with a capacitor in the feedback network. The low pass filters are usually designed to roll off in the range of 8 to 30 Hz. Although the combination of a high pass and low pass filter comprises a very low-Q (nonresonant) bandpass filter, the underlying thinking and analysis is based on the concept of differentiation.
The underlying concept of the so-called "four-filter" machines is narrowband high-Q (resonant)bandpass filtering, although they may include high pass and low pass filters as well. The designation "four-filter" started with a particular model back in the early 1980's, and since that time has been applied to all bandpass-type designs regardless of the number of filters. When they were first introduced in the mid-1970's, the center frequency was usually around 12 Hz and the bandwidth was usually a lot less than that. If swept at just the right speed, "4-filter" machines give separation of target and ground signals slightly better than that which can be achieved by differentiation. Because their narrow bandwidth is associated with a long response time, the "four-filter" machines usually have rather smeared response and poor target separation. Some of the more recent "four filter" designs have broadened the bandwidth and lowered the center frequency to get quicker response and less dependence on sweep speed. These newer designs are usually more sensitive as well, because they "see" the big chunk of target signal that lies outside the passband of the earlier narrowband systems.
Since they first introduced their "motion discriminators" in the early 1980's, most of the Fisher, Tesoro, and Garrett machines have been second derivative types. Most of White's "motion discriminators" have been of the bandpass type, although their "Classic" series is second derivative type. I don't know enough about Minelab or the modern Bounty Hunter to comment with any confidence on what kind of motion discrimination systems they use. C-Scope in England used to do second derivative, but I'm not familiar with what they're doing these days.
As far as I know, all "real" gold prospecting machines offer first derivative all-metals operation. The recent White's GMT provides a type of second derivative operation as well. I'm under the impression that the new Fisher Gold Strike also provides second derivative operation. Some pulse induction machines use first derivative operation, primarily to eliminate drift but also to reduce residual ground noise.
--Dave Johnson
