This is a special case of wireless audio transmission.
If one were to implement wireless sub-woofer for 20Hz to 250Hz band, by digitising a line level signal then what would be the requirements for
The wireless system should not be different from wired in terms of quality.
Thanks,
WonderfulIOT
16 bit is good enough for audio. For a 250Hz bandwidth 1kSPS or more is good, be sure to antialias
with a hard cutoff filter or you'll just have higher audio frequencies overlain on the bass. This is not
easy for audio as 80dB stopband attenuation or so is needed (pass band 0 .. 250Hz, stopband from 500Hz...)
Sound travels at 340m/s so each ms of delay is about 1 foot of speaker offset.
Your PWM must be ultrasonic or you'll hear it. For 16 bit resolution that means either
two 8 bit PWM's scaled 1:256 by resistors, or noise-shaping.
Alternatively reconstruct the full audio bandwidth before sending the signal through a class D
amp?
- The minimum ADC bit resolution
- The minimum DAC bit resolution,
CDs are 16-bit. That's good enough for anything* and you could probably get-by with less. But personally, I wouldn't go less than 16-bits.
would 16 bit PWM via digital GPIO of micro controller work?
16-bits is fine, but you need a higher sample rate with PWM (compared to normal PCM). I don't know how much higher but maybe 5 - 10 times the normal PCM sample rate. From what I recall, some class-D amplifiers (which is a kind of PWM) run at 200kHz or more (for full-range ~20kHz audio). If the clock is in the audible range (less than ~20kHz) there's a chance of insufficient filtering and you might hear the clock.** Personally, I wouldn't use PWM... I'd use a real DAC.
- Minimum sampling frequency
For the actual PCM audio data you need at least twice the signal frequency (500 Hz in your case). Simplified... You need at least one sample for the positive-half of the wave and one sample for the negative-half. For example, audio CDs have a sample rate of 44,100 Hz to cover the full 20 - 20,000Hz audio range and allow for some (real-world imperfect) filtering.
- Max end to end delay that can be tolerated
Normally you start to hear a delay/echo somewhere over 20 milliseconds. At 50ms you'll normally clearly-hear the delay/echo but with bass you might get-by with a longer delay.
Just to give you an idea... Sound travels at about 1 foot per second. So, 20ms is about the same delay you'd get by moving the woofer 20 feet away. You might hear the sound coming from a different direction but you won't hear a delay/echo at 20 feet.
** A couple of notes about filtering - You MUST filter-out signals above the Nyquist limit (half the sample rate) and that has to be done with an "analog" filter BEFORE the signal is digitized. If any signal above the Nyquist limit "leaks through", you'll get aliasing (false frequencies). If you are using a subwoofer-output, of course that's already done for you.
The DAC-output should also be filtered. The filtering "smooths" the waveform and filters-out the sample clock. This is super-important if the sample clock runs at an audible frequency (less than ~20kHz) and with PWM because with PWM you get a full-voltage clock and you shouldn't feed that into your amp. PWM that's not properly filtered could burn-up your amp. (With a regular DAC and a 44.1kHz sample rate, you can get-by without filtering because you can't hear it and it will be filtered by the amplifier or if it gets-through the amplifier it will be filtered the mechanical-physical limitations of the speakers.)
I think the best approach is to sample with an I2S ADC at 48kSPS, digitally filter to 250Hz bandwidth,
multi-stage decimate to 1kSPS, transmit, then multi-stage upsample back to 48kSPS.
That's not going to happen without some proper DSP clout, but that's how its best done.
If you can afford the bandwidth why not transmit the audio full bandwidth, no need for high performance
anti-aliasing filters then, just use the subwoofer driver amp for that.
Looks like wireless sub is more complicated then wireless fullrange 
Anyways thanks everyone, I need to figure out quite a few things to get to the design phase.