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I have researched about PDM Data and I have seen this sentences on wikipedia:

In section of Digital-to-analog conversion

  • "The process of decoding a PDM signal into an analog one is simple: one only has to pass the PDM signal through a low-pass filter. This works because the function of a low-pass filter is essentially to average the signal" *

Then, I have tried this situation with MEMS Microphone which microphone has PDM Data output and I have seen low pass filter(RC filter) has able to converting PDM Data to analog data clearly.

So, my main interest is about this 2 terms; "average the signal" and "low pass filter".

That are the questions:

  • How can the low pass filter do that?

  • What is the theory of behind the low pass filter can average of signal? Can you explain this situation with mathematically through RC Low Pass Filter?

  • Can we say this "Low pass filters filtering almost (not clearly) all harmonics except Fourier first coefficient?(Note that ı assume fourier first coefficient corresponds average of signals.)

Note thats:

*Wikipedia link is below

https://en.wikipedia.org/wiki/Pulse-density_modulation

*Yes, ı have research about this questions on the website but ı haven't found clearly answer...

and thank you for your interest...

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    \$\begingroup\$ If a car engine didn't have a heavy crankshaft then, as it rotated through one revolution, it would be pulsing in rotational speed throughout that cycle. Clearly this is not what we want so, we use a heavy flywheel on the crankshaft and it acts like a capacitor and, the force from the pistons (variable throughout the cycle) is like a pulsing current through a resistor. Hence why an RC averages. \$\endgroup\$
    – Andy aka
    Jan 13, 2021 at 9:39

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What is the theory of behind the low pass filter can average of signal? Can you explain this situation with mathematically through RC Low Pass Filter?

A low-pass filter lets through signal at 0 Hz (otherwise it wouldn't be called a low-pass).

The 0 Hz of any signal is its average.

How can the low pass filter do that?

It lets through low frequencies – that has the above-mentioned averaging effect. That means that at the output of a low-pass filter of sufficiently low cut-off frequency you don't notice the on/off of the PDM – you just see the average weighted over the whole impulse response duration of that filter.

If you want more details, you'll need to understand how frequency response and impulse response relate – but that's really the central thing in every "systems and signals" textbook, so I don't think I could contribute anything to that by writing it in an answer.

Can we say this "Low pass filters filtering almost (not clearly) all harmonics except Fourier first coefficient?

No. "first Fourier coefficient" assumes that there's countably many Fourier coefficients, i.e. a discrete Fourier Series. Only periodic signals have such, your signal is not periodic, hence there's no "first Fourier coefficient"; your PDM signal has a continuous spectrum.

I'm not sure this is the case, but my guess is really you only need a refresher on what a (continuous) Fourier transform is.

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    \$\begingroup\$ Yeah, ı need to work on fourier.But thank you about you said that "ou'll need to understand how frequency response and impulse response relate". I will research about that... \$\endgroup\$
    – KaruF
    Jan 14, 2021 at 9:25

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