Quote:
Originally Posted by peeder  False! For one thing, I understand most of these systems actually use a 25 bit mantissa. But you are confusing dynamic range and level/headroom. In the floating point realm, you can alter level without loss of dynamic range. YOU CANNOT DO SO IN FIXED POINT. Nossir, you cannot. 
Do I need to piece it apart as to why? |
No you don't, because you are entirely missing my point.
In the *particular case at hand*, namely normalizing a low signal, there is no difference (other than potential roundoff error down 144dB). The reason is that the source signal is already dynamic-range-limited--it's *quiet* after all. Suppose the peaks are at -24dbFS. This means that the top four bits are zero, and there are (in theory with perfect converters) 20 bits of dynamic range. Boosting this signal by any amount that does not clip (which isn't going to happen with normalizing) only moves those 20 bits higher in the word, either explicitly (in the case of fixed point) or implicitly (by changing the exponent in the case of floating point.)
The point is that all 20 bits are preserved in either case, and there is no practical cost (nor, granted, any practical benefit) in having normalized the signal.
I understand perfectly well that floats preserve significant bits over a much wider range of scaling, but that wider range is not at issue here.
You're right about the 25th bit, though once again it has no practical effect.