Room acoustic - Digital correction

Roberto - Mind if I ask a few questions? 
Are the acoustic problems in the time domain - excessive decay times, or asymmetrical decay times between L vs R or Bass vs Mids/Highs, or excessive energy from 1st order reflections?  Or are the issues frequency nulls/peaks or L vs R asymmetries?  I only ask because as far as I know digital correction does not work in the time domain to fix decay times and early reflections, only the frequency domain.  (It can time-align speakers and subs as part of the time domain.).  

Also, have you treated 1st order reflection points first, then added bass trapping to manage bass decay times, then added diffusion or reflections to manage mids/high decay times, and lastly improved frequency response via gentle EQ?  This order helps you avoid chasing your tail and re-doing your EQ after every treatment addition or placement change.

I don't have "Magic Beans" but I own Audiolense that is a great convolution file generator for frequency response smoothness improvement.

Of course, doing everything possible to acoustically treat the room would be essential and a smart choice. Adding digital correction would complete the picture.

Unfortunately, in my case, we find ourselves in an extreme situation: the room is small and shared with other uses besides listening to music. And it's absolutely impossible to introduce panels, acoustic traps, or any other "physical object".

So my curiosity leads me to this more general question: given the current state of technology, can a fully digital acoustic correction system, easily implemented on my (or other) electroacoustic systems, effectively correct the room acoustics and produce better sound? And, at the same time, could it respect the acoustic signature of the devices I own?

My system: ATC SCM50 ASL speakers, ATC CA2 preamplifier, Chord Hugo TT2+MScaler DAC, Auralic Aries S1 streamer, Roon server on pc, NAS, Audioquest Niagara 1200

My system primarily suffers from asymmetrical speaker placement, which introduces peaks and valleys at frequencies below 300 Hz. Moreover, since the room small (around 20 m2), room modes are prevailing, and the asymmetrical speaker placement further complicates the situation., 

Thanks for the additional info Roberto69.
Here's my thoughts:

> DECAY TIME: Given you are in a small room, it's likely all T30 decay times are pretty low and any difference between the average bass T30 and that of mids/highs is not significant enough in absolute values of milliseconds. So, let's park this one.
> EARLY REFLECTIONS:  your asymmetrical speaker setup is likely casting asymmetrical 1st order reflections that you may be able to absorb using furniture at the sidewall locations.  Ideally, both chairs or couches should be the same at each sidewall's 1st reflection points but you may also need to hang a tapestry or some such thing to extend upward beyond the head rest level of a chair.  The asymmetry of L vs R 1st order reflections in the critical band of 700 to about 2.5kHz will impact imaging moreso than other frequency bands above or below it. Without measurements it's a crap shoot at best using furniture to try and establish early reflection symmetry.
> FREQUENCY RESPONSE:  your smart beans software is likely generating a Finite Impulse Response (FIR) convolution file to smoothen frequency response and improve L vs R symmetry and should be able to deal with your room mode peaks and nulls.  Nulls are usually handled by cutting all other frequencies down to the null's value so it in effect disappears and then raising everything together some amount of decibels.  I've found that the approach can reduce dynamics somewhat or sometimes.  Nothing's perfect - pick your poison.

Improving the frequency response smoothness (including a house curve bass tilt upwards so it's louder than say >150Hz) when coupled with good decay time  values should improve tonal balance.  Imaging will be improved once lateral sidewall 1st reflections from the closest and farthest speaker are handled with furnishings (e.g. cloth not leather chair/sofa/couch/love seat and identical one for the other sidewall and absorbent tapestry/artwork etc above the chair head rest).  Hope this is some help . . .