Originally Posted by warrior-kid
Mr Monkey has an analogue synth and he wishes to share with the whole country his creations. The synth does two things: emit a white noise in the C4-C5 band and abruptly change the level by 10dB with the raise front of 20 microseconds.
Design a recording and reproduction system capable of the following best or second best goals.
1. Reproduce the step functions with steps equivalent to immediate output change within 20 microseconds.
2. Reproduce the step, but have the raise front somewhat longer while avoiding oscillations.
Analysing the spectrum of the input signal in intervals of 10 milliseconds for 512 samples, Mr Monkey sees that the spectra have normally zero power outside C4-C5. However, if an interval includes a step, one needs at least a 50KHz harmonic to reproduce the signal. We can see that during this 10 milliseconds interval, there is power in the ultrasonic region proportional to the magnitude of the output jump. In the next interval, this power disappears.
I have questions for Mark and the respected members of the forum.
1. Do you generally agree that this setup is not unreasonable?
2. How will your typical ADC treat such signal?
3. If the sharp step signal is still there before the decimation, what effect will that decimation have on a 20 microseconds step?
4. If decimation was done only to the HD music format, would the fronts be sharper?
5. If pt 5 is true, will the DAC have a chance to pass this step as close to the recording as possible?
This is good example, as it reveals some interesting points. It is certainly not unreasonable, so there's question 1.
First, lets consider the "20 microsecond change in signal amplitude". The white noise, extending up to C5, would have its highest frequency content at just above 500Hz (am I right about C5? I'm not at all a musician). A 500Hz sine wave would rise from 0 to maximum in 1000 microseconds, so a 20 microsecond rise would be no different than a 200 microsecond rise if the signal were near zero when the rise started (the signal is rising slower than your ramp). If the signal was near its peak, then the rise would add a linear slope at the leading edge of the wave. We will consider that latter case, as the former case really has no unusual effect.
"2. How will your typical ADC treat such signal?"
A 20 microsecond rise would correspond to one quarter cycle of a 12.5kHz sine wave. That is pretty much how a 48kHz ADC might interpret it - as a sine wave. A 96kHz ADC would see it as more linear, and a 192kHz ADC as still more linear, if it weren't for the analog anti-alias filter in front of the ADC. If that input filter is limited to 20kHz, all sample rates would see the signal looking the same - somewhat sinusoidal.
"3. If the sharp step signal is still there before the decimation, what effect will that decimation have on a 20 microseconds step?"
Which decimation? ADCs over-sample (typically around 12mHz) and there is decimation occurring inside the ADC. But I will assume you mean the decimation that takes place for the purpose of down-converting the sample-rate.
If, due to the analog anti-alias filter, that step looks more like a sine wave in the digital domain, then the decimation would have no effect. A 192kHz sample stream decimated down to 48kHz should look identical to a stream that was originally sampled at 48kHz. However, if the 192kHz stream was captured with cut-off frequency in the anti-alias filter near 96kHz, then your ramp would look more linear in the 192kHz stream (contain higher-frequency content), and decimating down to 48kHz would make your ramp more sinusoidal by removing that content.
"4. If decimation was done only to the HD music format, would the fronts be sharper?"
I don't know what you mean by "HD music format". Do you mean the music from HD-tracks as opposed to Mr Monkey's creation? It would be the same effect.
Any content below the "new" Nyquist frequency should be unaffected by decimation. Any content above the new Nyquist frequency would be removed by decimation. Assuming Mr Monkey's linear-ramp contains content above the new Nyquist frequency, that content would be remove, rendering it more sinusoidal, or softer.
"5. If pt 5 is true, will the DAC have a chance to pass this step as close to the recording as possible?"
Do you mean "If pt 4 is true"? If so, then:
The DAC should output all content that was in the original recording that was below all Nyquist frequencies involved. Any content above the lowest Nyquist frequency will have been removed. That means that Mr Monkey's linear slope would look less linear than it would if all
parts of the signal chain operated at a higher frequency. That slope might look less linear on an oscilloscope, but my understanding is that it wouldn't sound
any different, as it is content above 24kHz that makes it more linear.