Bash script variable manipulation, how to remove characters?

I've wrote a script to convert a .mp3 into .spx, but the output of files are <filename>.mp3.spx, and I would prefer to get <filename>.spx, but I'm at a total loss of how to do it. (I'm aiming to convert around 2000 files)

I've looked a several bash scripting guides and can't figure out a way to do it. Here's the script

#!/bin/sh

for file in *.mp3

do madplay -q -m -R 16000 --output=raw:- $file | speexenc --16bit -w - ${file}.spx

done

Now I now I could run a separate command after to rename with regular expressions, but I was wondering if I could just change "${file}.spx" to something that would name the output how I wanted it, that would be great. If you tell me a little bit about how it works and why, that would be the greatest.