I have dedicated lines, but why is this happening?

When an air conditioner cycles, there are relay contacts that are actuated. These relays commonly arc when they are actuating, whether opening or closing. The older they get, the more they arc. This arc throws wideband hash into the air and onto the power line. It is similar to a small arc-weld. This is very likely to be the culprit. You probably need better RFI/EMI protection/filtering in your system.

Two things you can check:

The central ac unit may have a problem such as a faulty compressor (overheats?), pull-in contacts, loose wiring on the motor, loose wiring in the circuit (wire nuts, j-boxes, etc), loose fan belt on the blower, or a bad low-voltage transformer. I would bet on the contacts that pull in the blower line voltage.

The work done by the electrician. Each circuit have its own neutral home-run? Sometimes they'll cheat by grabbing the nearest white wire. Big no-no.

All motors cause transients and surges in your house power system. The above can make it worse, in terms of hearing the noise in your gear. If everything checks out ok (including your gear), then you may look into getting a whole-house surge suppressor (TVSS) installed in your main panel. I also agree it ain't a grounding issue and that dedicated circuits are not the cure-all for power problems.

I resolved this problem at the source of noise in my home. I filter the AC blower, AC compressor, microwave oven, all three computers, the refrigerator and every other device that causes me misery.

Expensive you say? Not at all. You can buy good filters for each of the above items for less than one audiophile device.

More importantly these don’t degrade the performance of your sound system. Stopping the noise from entering your stereo is much easier than trying to remove it once it’s already there.

Here is the company I bought my suppressors from:
http://www.elect-spec-transformer.com/about.htm

Some very good points here and one that was overlooked.

As Herman stated, dedicated lines do not mean isolated or filtered lines. Everything in your house ties back into the breaker box, so it would not be unusual for noise to find its' way from one circuit into another. This is not to mention that dedicated lines do nothing to keep out "sludge" that was already present on the lines feeding your house.

As Gs stated, many electricians will "share" the neutral wire with other circuits and this is not a good thing. Since AC is traveling on both the "hot" and the "neutral", having "half" the circuit dedicated with the other half "shared" doesn't make much sense.

Albert stated that filtering other devices in the house will cut down on the amount of "crosstalk" between noisy devices feeding from outside circuits without detriment to you dedicated lines. This too is a very valid valid approach to noise reduction.

Several others mentioned loose connections at the breaker box, ground system, the central air unit itself, etc... These too should all be checked out. It is good practice to clean the connection at the ground rod every once in a while and this may be your perfect opportunity to do so. Personally, i would kill the mains of the house before attempting to do this though. You might be surprised how many electronic components "leak" voltage from the device to ground, even when not turned on. You don't want your body acting as the conductor bridging the electrical gap between the ground wire and the ground rod as you separate the two.

The part that was overlooked ( from what i can tell ) is that it's quite possible that one of the components that you recently "upgraded" to may not have proper filtering in the power supply. Can you think back to when you first noticed the compressor / fan problem and if you had just swapped some components or cabling in the system ? It's possible that there's nothing wrong with your central air unit and that the problem itself is a poorly designed component.

The reason that i bring this up is that i went through something similar quite a while back. At the time, i was using several different PLC's in various systems. I swapped a PLC ( Brand A ) into a system where i was previously using a different ( Brand M ) PLC. After doing so, i noticed that i was now hearing the noise generated by the arc of a lightswitch coming through this system whereas i had never heard or noticed it before. Re-installing the Brand M PLC into the system solved the problem. Obviously, not all PLC's are as effective as we would like to think. As such, it would only be logical that some components aren't as well designed / filtered as others too. Does this make sense and is the appearance of the noise and the replacement of a piece of gear more than a coincidence ? Sean
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TWL's answer makes the most sense. I sometimes get a pop from the microwave. It's RF and it somehow gets in my system. Maybe shielding the RF source will work.