44kSPS is a reasonable sample rate for an audio processor. 1kSPS is most definitely not going to work except
on a bass synth output band limited to about 300Hz with a really good brick-wall filter, which is just
crazy.
Do the decimation in software for low-pass filtering, a FIR low-pass followed by decimation can be
optimized to only apply the FIR once per output sample, not once per input sample.
However you then need to oversample and low-pass filter again to reconstruct the output samples.
It may well be simpler to work at 44kSPS/38.5kSPS throughout.
The circuit given in that instructible is wrong BTW. No surprise of course.