how do audio high pass and low pass filters work? (what’s the science behind it?)
In: 5
**Digital**
In the digital realm, filters are normally implemented via difference equations. These are the discrete counterpart to differential equations, so the math can get a bit beyond the ELI5 level.
But imagine you have a list of numbers which we’ll call x[n]. These represent the amplitude of your signal, sampled at a regular interval.
Now we send it through a difference equation y[n] = (x[n] + x[n-1])/2. The just says that the value of y at time n will be the average of the current and last value of x at time n.
The impact of doing this is that you ‘smooth’ the original signal x[n]. But ‘smoothing’ the signal is the same as subtracting the high frequency components. Conversely, if you only cared about the high frequency components, you could simply subtract your ‘smoothed’ waveform from the original waveform and all those low frequency components would be subtracted out while the high frequency ones remained.
Note: While Fourier Transforms can be used to mathematically analyze signals, they’re rarely used as part of the filtering algorithm because (a) they’re really slow compared to the difference equation method above and (b) masking off a discrete frequency spectrum before converting it back to a time-varying waveform creates all sorts of ‘artifacts’ due to the varying granularity of the phase analysis (at low frequencies, you have huge jumps between each phase angle you’re testing; at high frequencies, you have small ones; the size of those jumps corresponds to the amount of error that can exist in your math).
**Analog**
Let’s say you have a signal source, a resistor and a capacitor.
As the signal rises, it starts to charge up the capacitor. But the capacitor doesn’t want to charge and impedes changes to its voltage. So it slows down the charging. If you try to change the voltage very fast – as high frequency signals do – then the capacitor will not fully charge by the time the signal drops again. The high frequency components will essentially be ‘trapped’ in the resistor waiting their turn.
In contrast, the low frequency components only try to change the capacitor voltage slowly, so they’re able to locate their voltage in the capacitor rather than the resistor.
If you measure across the resistor, you’ll see all those high frequency components piled up. If you measure across the capacitor, you’ll see all the low frequency components. This effectively ‘filters’ high vs. low.
Note: Actual filter design is considerably more complicated that I outlined above. The above is just the basics.
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