Redirect stdout and stderr to Function

Question

I need help sending the output (stdin and stdout) from system commands to a bash function, while still accepting input from arguments. Something like the example that follow

Answer 1

Thanks to people who posted their responses. I came up with my version which will add timestamp once per message.

#!/bin/bash
CURRENT_PID=$$
PROCESS_NAME=$(basename $0)

LOGFILE=/var/log/backup-monitor.log
function log_message {
  if [ -n "$1" ]; then
      MESSAGE="$1"
      echo -e "$(date -Iseconds)\t$PROCESS_NAME\t$CURRENT_PID\t$MESSAGE" | tee -a $LOGFILE
  else
      MESSAGE=$(tee)
      echo -e "$(date -Iseconds)\t$PROCESS_NAME\t$CURRENT_PID\t$MESSAGE" | tee -a $LOGFILE
  fi
}

log_message "Direct arguments are working!!"

echo "stdin also working" | log_message