March 31st, 2025.
Time to make a connection between what is seen and heard with just a little math.
if you’ve done the numbers then you’ll realize that a single-pole lowpass filter is mathematically equivocal to an exponential moving average.
And that’s when things start to click, because averaging is simply smoothing out numbers.
Think of the square.
The square is full of harmonics, and has a (pseudo) discontinuity between low points and high points.
The wave looks like a square.
A square wave.
A square wave freq. content.
Think of filters.
We know that when we filter something we are (typically) removing some content.
That’s why it’s called filtering.
So, as we filter the square wave, we round the corners of the square, and the square becomes a sine.
We are removing the frequency content by averaging.
That is we take a frequency rich signal, the square, and remove all of it’s frequencies (with averages) to make the signal dull. *A sine wave is a single frequency.
So put two and two together.
Filtering is averaging, and averaging on a square (could) make a sine.
**Note, this is as a theoretical perfection, and inconsiderate of the roll-off (transition band).