But an 'ideal square wave' only exists in people's imagination, not in the world of physical signals. A real-world square wave will have a finite rise time and hence finite slew rate. Putting a real world 22kHz squarewave into a real world amplifier will probably induce fairly horrendous slewing distortion and maybe overshoot. These secondary effects might have audible consequences.
Did he explain why the practice would deviate so far from the theory? For myself I've yet to see a reasonable explanation that it does.
Let's be grateful that they didn't pay attention to what appears to be religious nonsense
Its not just the first generation of CD players that uses 44k1 sample rate.
Practice deviates so far from theory since the ideal LPF does not exist, and can not exist. The ideal LPF would have a flat amplitude response to the cutoff, zero output above the cutoff frequency, and a linear phase response. If you derive the transfer function for such a filter, you will see that it responds in negative time. That means that the output of the ideal filter appears before the signal that caused it arrived at the input. Physically impossible.
Given that ideal LPFs do not exist, you need a sampling frequency well above the Nyquist minimum if you are to avoid serious aliasing (frequencies above half the sampling rate fold over into the baseband frequency range). Faster sampling allows real LPFs with their less than infinite skirt selectivity to reduce these unwanted frequencies to a level that keeps aliasing below design specs.
Agreed - acausal filters cannot exist as far as we know. So far, so good
Well above the minimum? And this word 'well' means in practice 5X?
Depends on how much aliasing you can tolerate in the design. 5X was the figure the lecturer at Purdue mentioned.
Not in and of itself it doesn't. We also have a choice with regard to the complexity of the anti-aliasing filter.
Not much after that, at a time i was taking a graduate level statistics course on sampling theory (a course i did well in), after reading Sony's CD white paper, my comment was that they would need to increase the sampling rate by at least 4 times to approach analog, and 8 would be needed to be sure,
More recently, when making inquiries here about a digital oscilliscope add-on to an iPad, i was told that (something like) 5-10x the maximum freq was needed before it the scope would be useful.
It is actually amazing to me, that 16/44 can be made to work as well as it does.
dave
I'd be very interested to hear of your reasoning. Analog tape running at 30ips was it you were comparing it with?
Not comparing it with anything.
Reasoning parallels Miles' above, but more thinking of the ADC end. The theory requires NO signal above the Nyquist. ANY signal going into the ADC above the Nyquist gets embedded into the signal and nothing at the DAC end is going to remove that spatter. At the time it made me think of the big Monty Python boot coming out of the sky...
davr
Reasoning parallels Miles' above, but more thinking of the ADC end. The theory requires NO signal above the Nyquist. ANY signal going into the ADC above the Nyquist gets embedded into the signal and nothing at the DAC end is going to remove that spatter. At the time it made me think of the big Monty Python boot coming out of the sky...
davr
Agreed - acausal filters cannot exist as far as we know. So far, so good
Well above the minimum? And this word 'well' means in practice 5X?
If it's anything like "much greater than", I would have to believe that it means "at least 10X", as usual, unless it means "far enough above to actually work, unlike the theoretical value".
Where in the world did you get "5X"?
From your story about your Purdue prof. In that you said he said (paraphrasing) '2X is what the theory says but in practice you'd better have 10X'.
So if 2X is the minimum requirement then 5X the minimum corresponds to your prof's 10X. I took it he was arguing for 10X the 20kHz i.e. 200kHz as a minimum sample rate.
Yepp, exactly.
but *consecutive* min phase / CMP is a different animal.
There is *always* group delay with electronic circuits- even with a single transistor...
Think of it !
Besides, there are also thermal effects that may act "as if" in the context of CMP behaviour / ASAR patterns - no one has explored in detail by now
Instead, audio people seem to rather prefer discussing those parts of filter theory they not really understand and assert it for all those effects at the boarderline of audibility they may have come across
Michael
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Agreed - acausal filters cannot exist as far as we know. So far, so good
I can certainly create an anti causal filter if you don't constrain me to do it in realtime. If you give me a finite stream of samples and tell me "take your time, filter these," I can certainly make a filter that runs forwards or backwards on the stream to produce an output.
One way to make FIR brickwall approximations is precisely this, with a specified maximum delay. You tell me how much delay I can have and I'll make a truncated approximation to the impulse response of a brickwall filter employing a number of samples equal to the amount of delay I'm allotted (in other words, I'll write down a transfer function for a truncated, delayed sinc and use that as my filter). If you play around with such a beast, e.g., in MATLAB, you will see quickly that what you've done is taken an anti-causal filter and added just enough delay to make it causal.
There's nothing special about causality unless you want to listen to your music right now. If you'd started playing your CD ten hours ago, I'd be able to give you a more or less brickwall filtered version of it now
Absent such constraint, I'd teach myself to do it thanks all the same
But we were talking about anti-aliasing filters and those do work in real-time because they're normally being sent real-world signals from mics and the like.But the context wasn't listening, it was recording. And yeah recording does need to take place right now or the moment is lost
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