Hi Landman,
Your question could take a booklet to fully answer, but the simple response is the SAT or autotune as I am used to calling it, simply tries to maintain a constant threshold level. This is accomplished by using a basic high pass filter and adjusts the discharge rate of the filter. The detector signal is sent through the filter and the output from the filter is then added to a constant level signal, set by the threshold control. A high pass filter will generally take an increase in amplitude and make a hump type signal out of it. When the target is removed, this same hump will be generated in the opposite audio level. So, passing a rising signal through a filter will create a shorter increasing audio and on some detectors a wee type signal and when the target is removed, the signal changes to a woo, or quieter signal. On some detectors this simply translates to an increase in audio followed by a decrease in audio level. Now, when you are adjusting the SAT speed, you are basically adjusting how fast the filter responds which translates to how fast the hump type signal returns to the basic threshold level.
Now, keep in mind that any signal from a target would have a certain amplitude if nothing were to influence it. Unfortunately, the ground signal or other signals may add to or subtract from this signal as a coil is passed over the ground. Fortunately, the ground signal is generally a slow response and is dependent upon the sweep speed of your search head. As such, the signal is quite slow. Pass this ground signal through a high pass filter and some to much of this signal is eliminated. Speed up how fast the filter circuitry responds and more of any slow signal is reduced.
On the down side, the target signal, which normally is a much faster response is also reduced some but not as much as the ground signal. The reason is if a high pass filter is used, it allows faster signals through easier than slow ones. So, a target response is reduced but the ground signal is reduced by a greater amount.
As you speed up the SAT, you are further reducing the ground signal, but because the filter speed is increasing, you will also be reducing the target response also. So, there will be some depth loss as the result of using the sat, especially at faster rates.
A detector with a SAT can be easily determined by simply taking a target and passing it over the coil, but stopping the object at the center of the coil. If the signal rises and doesn't change, then no SAT is involved. However, if the signal rises and then decreases back to the normal threshold, there is a SAT involved. Just how fast that signal rises and returns back to the normal threshold will be determined by the SAT adjustment.
This is a basic explanation without going into too much technical detail.
Reg