When should I use Low-pass Filter?

Question

I'm trying to find a pitch of a guitar string. Sound is coming in through mic at a sample rate of 44100. I'm using 2048 bites for a buffer size. Considering the Nyquist rate there is no point for using bigger buffer size. After recieving the data, I apply hanning window... and this is the point where I get confused. Should I use Lowpass filter in the time domain or take FFT first? If I would take FFT first, wouldn't it be easier to use just the first half of the samples, disregarding the other half, because I need frequencies in range of 50-1000? After FFT I will use Harmonic Product Spectrum to find fundamental frequency.

Answer 1

It really depends on your pitch detection algorithm, but why would you use a low-pass filter in the first place?

In addition, a guitar usually produces spectral information way beyond 1000Hz. Notes on the high E string easily produce harmonics at 4-5kHz and beyond, and these harmonics are exactly what will make your HPS nice and clear.

Answer 2

What you suggest makes some sense: if you don't need low frequencies you don't need to use long samples. With long samples you gain frequency resolution, which might be useful in some circumstances, but you lose time resolution (in the sense that successive samples are further apart).

A few things that don't make sense:

1) using a low-pass digital filter in the computation prior to the FFT (I'm assuming this is what you mean) just takes extra computation time and doesn't really gain you anything.

2) "Considering the Nyquist rate there is no point for using bigger buffer size": these aren't really related. The Nyquist rate determines the maximum frequency of the FFT, and the buffer size determines the frequency resolution, and therefore also the lowest frequency.

Answer 3

The less data used or the shorter your FFT, the lower the resulting FFT frequency resolution.

Answer 4

From what I read here a guitar ranges from 82.4 (open 6th string) to 659.2 (12th fret on 1st string) and the difference between the lowest 2 notes is about 5Hz.
If possible, I would apply an analog filter after the mic, but before the sampling circuit. Failing that, you would normally apply an FIR filter before shaping everything with the Hanning function. You could also use Decimation to reduce the sample rate, or simply choose a lower sample rate to start with.
Since you are doing an FFT anyway, simply throw away results above 1000 Hz. Sadly, you can't cut back on the number of samples - cutting the sample rate reduces frequency resolution.

2048 samples at 44100 Hz will give the same resolution as 1024 samples at 22050 Hz.
Which the same as 512 samples at 11025 Hz.