Pipe only STDERR through a filter

Is there any way, in bash, to pipe STDERR through a filter before unifying it with STDOUT? That is, I want

STDOUT ────────────────┐
                       ├─────> terminal/file/whatever
STDERR ── [ filter ] ──┘

rather than

STDOUT ────┐
           ├────[ filter ]───> terminal/file/whatever
STDERR ────┘

Here's an example, modeled after how to swap file descriptors in bash . The output of a.out is the following, without the 'STDXXX: ' prefix.

STDERR: stderr output
STDOUT: more regular

./a.out 3>&1 1>&2 2>&3 3>&- | sed 's/e/E/g'
more regular
stdErr output

Quoting from the above link:

1. First save stdout as &3 (&1 is duped into 3)
2. Next send stdout to stderr (&2 is duped into 1)
3. Send stderr to &3 (stdout) (&3 is duped into 2)
4. close &3 (&- is duped into 3)

TL;DR:

$ cmd 2> >(stderr-filter >&2)

Example:

% cat /non-existant 2> >(tr o X >&2)
cat: /nXn-existant: NX such file Xr directXry
%

This will work in both bash and zsh. Bash is pretty much ubiquitous these days, however, if you really do need a (really gnarly) solution for POSIX sh, then see here.

Explanation

By far, the easiest way to do this is to redirect STDERR via process substitution:

Process substitution allows a process’s input or output to be referred to using a filename. It takes the form of

>(list)

The process list is run asynchronously, and its input or output appears as a filename.

So what you get with process substituion is a filename.

Just like you could do:

$ cmd 2> filename

you can do

$ cmd 2> >(filter >&2)

The >&2 redirect's filter's STDOUT back to the original STDERR.

A naive use of process substitution seems to allow filtering of stderr separately from stdout:

:; ( echo out ; echo err >&2 ) 2> >( sed s/^/e:/ >&2 )
out
e:err

Note that stderr comes out on stderr and stdout on stdout, which we can see by wrapping the whole thing in another subshell and redirecting to files o and e

( ( echo out ; echo err >&2 ) 2> >( sed s/^/e:/ >&2 ) ) 1>o 2>e