I have two signals and want to multiply them, e.g. voltage and current are multiplied to get power. The result (e.g. power) shall be a filtered result, e.g. to see the average.
Is it better to filter (digitally) each signal separately before the multiplication or to filter after the multiplication?
Intuitively, I would have said that filtering before the multiplication is better for three reasons:
- Less numerical problems
- Noise of both signals is added by the multiplication, thus filtering before multiplication improves SNR
- Multiplication generates modulation products and if you filter out a frequency you do not want to see anyway it also does not cause modulation products.
Am I on the right track here or is there something I am overlooking?
Edit 1: To answer the question of typical signal spectra: Think of a laboratory grade measurement device like a multimeter. It acquires two signals which can be any signal shape (in time domain) but are band-limited by the input circuitry to avoid anti-aliasing. Noise is typically white noise with a bit of 1/f noise added. SNR is usually 10's of dB.