The LM386 amplifier's inputs are an internally biased differential pair, with common mode input range extending to the indicated ground, Vee, or actually 0.4 Volts below ground.
In order to not disturb this internal biasing, the input signal must be capacitively coupled (or perfectly ground-referenced) - a capacitor in series on the input line is needed.
Next, for a voltage gain of 200, the input signal peak to peak needs to be under 1/200 of the output voltage range of the amp. While I could not find this specified in a quick scan of the datasheet, if we assume 7 volts output voltage range with a 9 Volt supply, the input signal needs to be under 35 mV peak to peak, to avoid clipping the signal. Clipping would result in mild to severe distortion of the output - though this does not explain the complete lack of signal you find on output.
If the incoming signal is higher than this 35 mV P-P, a potentiometer as an attenuator on the input is suggested.
Once these fixes are done, please revert with results, so the answer can be added to if needed.
I thought I'd sum up my comments in an answer - maybe it'll be of some use to somebody.
- Using white noise will make it harder to remove the modulation signal rather than easier. In the case of a normal PWM signal, you need a low pass and you are done. When using white noise to do the modulation you will cause noise in the same frequency range as the signal you are trying to create. This cannot easily be removed.
- The noise left in your generated signal will be about 14dB below the level of the white noise that you used as a modulator signal. Assuming true white noise up to 1MHz as in your example, then the amount of noise left is a simple proportion. 44100Hz/1MHz gives 4.41 percent or about -14dB.
- I verified my estimate above by generating a white noise signal with a 1MHz sampling rate then filtering and resampling down to 44100Hz. The resulting signal was indeed 14dB below the original white noise signal.
- Interestingly enough, 14dB is also about the dynamic range of the 5Bit sampling at 1MHz mentioned in the question. So, you don't really gain anything in the signal to noise department. You trade scratchy 5Bit quantized audio that is at least quiet when there's no signal to get a signal that is quantized at a much higher bit depth but has a constant white noise at -14dB - even when there's no actual signal present.
So, the idea does and doesn't work.
As you expected, you can use noise modulation to get a better bit depth and have less quantization error by spreading the modulation signal over the entire bandwidth.
That comes at the cost of not being able to remove the modulation noise from the generated output signal so that you end up with the same signal to noise ratio.
All you've done is to change the cause of the poor signal to noise ratio.
Best Answer
The audio signal that contains a spectrum of multiple frequencies is still just an audio signal that can be sampled by and ADC and recreated by a DAC. Providing the sampling rate used is higher than twice the highest audio frequency then all is good. A DAC that uses PWM techniques is no different. In any one cycle of the PWM waveform, the ratio of mark-to-space must accurately "represent" the instantaneous analogue signal and a single PWM cycle must be shorter in time than half the period of the highest audio signal: -
The above is a simple representation of 3 DC levels using PWM. Clearly if the PWM frequency is "high" those three levels can be regarded as part of a complex AC waveform. Hopefully you can see that controlling the PWM mark-space ratio accurately is really fundamental to obtaining low audio distortion.
Traditionally no, but it's getting better.
Controlling PWM ratio accuracy is quite difficult to get really good hi-fi quality and with class D amplifiers power supply rejection is still a pretty difficult challenge. See the embedded picture above - if the 5V power rail doubled then the gain also doubles - now imagine that instead of it simply doubling, you had a load of crappy noise on that rail - this would directly modulate your audio signal and create some very noticeable effects.