Effect of Room Correction on Home Theater Performance.

Introduction
Is room correction worth it? Additional processing introduces new artifacts. But it also corrects others caused by room modes and reflections. I think a (somewhat) quantitative look at the numbers will help answer this question.

So what does room correction address?

• Amplitude response over frequency (frequency response) caused by room modes and speaker/system defects
• Transient response caused by room reflections or phase distortion in drive electronics and speakers

And what does it introduce?

• Increased THD
• Possibly lowered SNR

What is unaffected?

• The amplifier is decoupled from the processor so output power and output impedance (think damping factor) should be unaffected
• Channel separation should also be decoupled from the processor

Analysis
A compact disc is capable of about 98dB of SNR and I suppose it's possible for a good studio to meet or exceed theses values as well, so for compact disc and vinyl reproduction there shouldn't be a need for anything better than 100dB (if you want to include some margin).

A good processor has 110dB of SNR and similar for THD. Frequency response for both processors and amplifiers is usually +/-0.1dB 20-20kHz, some amplifiers a little wider. And of course neither the processor nor amplifier are responsible for amplitude or time distortions.

Speakers and rooms are a completely different story however. Speaker distortion is frequently over 1% even for good speakers and some of the best speakers are below 0.1%. This information is hard to come by, so I'm unsure how good or bad most midfi or hifi really are. Rooms can easily cause THD in excess of a few percent caused by vibrations in the wall, etc or even rattles. Of course SNR cannot be increased by passive speakers but room noise is rarely lower than 40-50dB which puts limits to how quiet a room can get.

The elephant in the room however is the error in frequency response caused by rooms. It is rarely better than +/-5dB, almost always +/-10dB and frequently +/-20 to 30dB. Most speakers are +/-3dB although some are much better, around +/-1dB.

That's where room correction comes in. Room correction can take 5-10dB of variation out of your room/speakers. The cost is an increase in THD/SNR. I'm not sure how much but let's say 3dB.

I'll admit I don't have a good grasp on the causes of error in transient response and phase distortion, how to characterize it and how room correction algorithms address it so it will remain largely ignored for the time being.

In theory it is also possible for room correction software to measure deterministic THD, IMD, Noise and crosstalk and introduce cancellation signals. This is particularly true for AVR with integration room correction software. You could easily calibrate out most of not all of the deterministic error introduced by the electronics but I have not seen anything about this in the writings I have encountered.

Ok let's do some math.

Calculations
Frequency response is typically measured in dB so let's do that.

Frequency Response w/o Room Correction
Processor: +/-0.1dB
Amp: +/-0.2dB
Speaker: +/-2dB
Room: +/-20dB
Processing: -/+0dB
Total: +/-22.3dB

Frequency Response w/ Room Correction
Processor: +/-0.1dB
Amp: +/-0.2dB
Speaker: +/-2dB
Room: +/-20dB
Processing: -/+10dB
Total: +/-12.3dB

Let's combine SNR and THD into THD+N and use percent as the unit of measurement. There are quiet a lot of assumptions here. Like THD is independent of frequency. Which it is not. And one channel driven, so no effects of coupling/crosstalk in the electronics.

THD+N w/o Room Correction
Processor: 0.002%
Amp: 0.02%
Speaker: 0.2%
Room: 2.0%
Processing: 0.0%
Total: 2.222%

THD+N w/ Room Correction
Processor: 0.002%
Amp: 0.02%
Speaker: 0.2%
Room: 2.0%
Processing: 2.0%
Total: 4.222%

Summary
The addition of processing double THD+N. But in absolute terms it is still acceptable, albeit it probably a noticeable harshness. You do however improve frequency response of the room by almost a factor of ten.

In the end room correction is a stop gap measure while we wait for the state of the art to perfect. Realistically there may be nothing the average consumer can ever do out acoustic physics. But we can with better design, electronics and possibly even a small amount of integrated room correction address everything else. So I'm generally not a big fan of high THD, I do think this is quite an acceptable trade off.