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Problem with just installing conventional car audio coax or similar speakers is that these seldom if ever have proper crossovers. Yes, some have more than a simple capacitor on the tweeter but I'm not sure if any have a properly engineered crossover. Any cone breakup or other issues resulting in variations in frequency response need to be eliminated. Peaks in the mid-bass driver response even if well above the pass band of its crossover will cause harshness unless it is notch filtered out. This is not easily accomplished with analog passive crossovers.
Having a big high power 2-ch amplifier to drive your door speakers might seem impressive due to the high power numbers but this is not a very good approach. A better approach would be to use more channels of amplification even if each channel is less power. Instead of driving your coax door speakers with the 2-ch amp, drive them with a 4-ch amp so that the tweeters can have their own channel. Not only does this give you the ability to equalize the mid-bass and tweeter independently but if you are driving to high levels, you might only clip the mid-bass amp, and not the tweeter amp. If you have both on one amplifier channel and you clip the mid-bass, you are also clipping the tweeter. Also, at the crossover frequency a passive crossover is wasting 50% of the amplifiers power whereas any crossover prior to the amplifier doesn’t waste any power.
There is a low cost solution for both the active crossover and equalization. MiniDSP offers a variety of products but the one I have found very useful for car audio is the 2x4
When equalizing your system, you should use the individual channel EQ to equalize individual drivers with near field measurements. For a mid-bass driver set the HP filter only, leave the LP filter bypassed. For example if you plan to use this driver from 100 Hz to 2000 Hz, set only the 100 Hz crossover so that the driver is operating full range above 100 Hz. Then use the channel EQ to eliminate any peaks in the response. Make the response as flat as possible using combinations of low-shelf, high-shelf, and peak filters. Be aware that deep notches in the response are likely caused by cancelations and cannot be equalized with gain boost… or at least should not be. Use negative gain peak filters to eliminate peaks in the response but do not use positive gain to attempt to eliminate sharp narrow dips in the response. You can use shelf filters to eliminate gradual drops in output with increasing frequency. If your mid-bass is gradually rolling off above 2000 Hz by a few dB/octave then you should use a shelf to fix this.
Once you have made the frequency response as flat as possible then apply the LP filter at 2000 Hz. The filter will now behave closer to the planned cut off and roll off rate than it would have if the response were not flat.
After the individual drivers are equalized, use the input EQ to make global changes in the response. The input will apply to all the drivers and this is the best way to flaten out the overall response in the listening area correcting for room response.