This article is from the Car Audio FAQ, by Ian D. Bjorhovde (email@example.com) with numerous contributions by others.
This kind of problem is often caused by transients in the signal
processor as it powers down finding their way into the signal path,
which the amplifier then transmits to the speakers.
Usually this can be solved by adding a little turn-off delay to the
processor. This allows the processor to stay powered on for a short
time after the amplifiers have powered down, thus preventing the pop.
Many components sold today (such as crossovers, equalizers, etc) have
delays built-in. Read your manual to see if it is possible to set this
delay on your piece of equipment or be sure to look for this feature
during your next car audio purchase.
If your processor does not have this feature, you can build your own
delay circuit with a diode and a capacitor. Add a 1N4004 diode in
series with the processor's turn-on lead, striped side towards the EQ.
Then add a capacitor in parallel, the (+) side of the cap connects to
the striped (processor) side of the diode, the (-) side of the cap goes
to ground (not the radio or EQ chassis - connect to the car chassis).
Experimenting with the cap value will give you the right amount of delay
before the EQ shuts off. You don't want it too long, just long enough to
make sure the amp is off before the EQ powers down. 220 - 1000 uF is
about right, and make sure the cap is a polarized electrolytic, 16V or
higher. Also keep in mind that the diode will introduce a 0.7V drop on
the remote wire, which can cause the processor to power down before the
rest of the system.