How do I know if I need a sub woofer?

For all the reasons listed above.  It makes everything better when done right.  I bought two and it took my system to the next llevel, improving soundstage depth and width as well as imaging.  Of course it also filled in below where my stand mounts cut off.  I would not build another system without them.  

**Maybe you haven’t heard a truly good system that delivers excellent imaging and soundstage without the aid of subwoofers.

Well yes I’ve heard plenty of those systems...

Okay, you had. Then I am not concerned that you might be as ignorant as you were on the other subject like the cable impedance issue. So let me ask you if the soundstage is already ’excellent,’ why do you need an additional subwoofer to artificially expand it. What you experienced is likely the reverberation added by the subs, going beyond what the actual music content presents. Remember, my bullet #2 in the original statement already covers my requirement for soundstage.  Don’t just quote the bullet #1.

My system renders a soundstage wider than my speakers, which are set 11 ft apart, and deep enough that at times I feel like I could walk into it when such music content is in the recording. The height also resembles the actual performer’s presence. What more could one reasonably want from subs?

So let me ask you if the soundstage is already ’excellent,’ why do you need an additional subwoofer to artificially expand it. What you experienced is likely the reverberation added by the subs, going beyond what the actual music content presents.
 

@lanx0003  The sub is reproducing frequencies and information not previously presented by the speakers because they can’t.  That’s not artificial, it’s just uncovering more of the recorded information that’s already there.  If you think that’s artificial then you go ahead and believe that. 
 

What more could one reasonably want from subs?

Did you not read the review of the Wilson sub?  That’s what good subs properly set up can provide and perfectly coincides with what I’ve heard, and that’s in a system that likely makes yours look like a toy in comparison.  If you wanna just go on convincing yourself that your system is perfect and subs would provide no benefit and are artificially enhancing sound then live happily ever after in denial, but as I and many others here have heard for ourselves you’re not even aware of what you’re missing.  Ignorance is bliss.

@sounds_real_audio “l am happy with the sound”

No need for a sub. “(l)….Have an incredible fleshed out sound”

You said it yourself. “So why would l need a subwoofer?”

So in this case, there appears to be really no need to waste any more time offering further advice in this discussion.

Next question …. 

@soix  Ignorance is bliss.

Speak for yourself, Mr.  Stick with your crappy streamer and DAC, and keep convincing yourself that you managed to blend in subs seamlessly. Do you even own a $9,000 Wilson sub? I suggest you stop recommending outdated gears or things you’ve neither owned nor auditioned for a meaningful period of time.