Set iTerm2 title to current buffer in vim

.vimrc

" Set the title of the Terminal to the currently open file
function! SetTerminalTitle()
    let titleString = expand('%:t')
    if len(titleString) > 0
        let &titlestring = expand('%:t')
        " this is the format iTerm2 expects when setting the window title
        let args = "\033];".&titlestring."\007"
        let cmd = 'silent !echo -e "'.args.'"'
        execute cmd
        redraw!
    endif
endfunction

autocmd BufEnter * call SetTerminalTitle()

This works, but adds ~1,200 ms to my vim startup time.
I measured with "vim --startuptime vim.log somefile.txt"

Thank you, this saved me a bunch of time tinkering with it myself and made life a little bit easier!