I gave a good example with AM radio, which you didn't address. The encryption example was not an analogy to digital, it was a question about whether you considered something repacked but containing the same material as "exactly equivalent"—your emphasis with italics.mystran wrote: ↑Mon Mar 25, 2024 10:38 amEncryption is a poor example, as there is additional secret information (the key) in the mix. A better example would be lossless compression: even though the files (in the sense of byte streams) are not the same, the "signal" (ie. the logical file stored) is still the same.earlevel wrote: ↑Mon Mar 25, 2024 8:28 am I don't understand how you think they are "exactly equivalent". Is it a language issue? You emphasize exact equivalence twice. Do you consider an encrypted file as exactly equivalent to the original file? It's not. The encrypted file contains the information of the original file, but is not equivalent to it. For one thing, the original file doesn't contain the information of the encrypted file, which must be true if they are equivalent. If A = B, then B = A.
Does a file become something else because you put it inside a zip? No. Does it become something else when you download it over the internet (so it's split and encapsulated into TCP or UDP packets)? No. For all intents and purposes it is the same file... unless you are concerned by the implementation of the codec or the networking protocol.
In a discussion about the meaning of the sampled data, you said the samples and the continuous signal were "exactly equivalent". Twice in the same post. In a discussion about digital signal processing. Now you're saying they are the same once the digital data is encoded, and that's all we care about. Of course it's not all we care about, we do digital signal processing, this is forum about DSP.And.. that's the point I'm trying to make: if we are not concerned about the actual dirty details of converting between digital and analog domain, but rather we are only interested in the band-limited signal that we can (theoretically) convert back and forth in a lossless fashion, then we can treat the signals as being equivalent.
Sorry, there's no way to undo what you've said, if you won't admit that it as wrong. This just looks like spin.
There are no mathematical difficulties if the samples represent. Which you've told me is this thread, is incorrect. I gave you the take from Crochiere and Rabiner, which you didn't address, but by extension think they are wrong. You seem to be trying to change from telling my my understanding of sampling theory is fundamentally wrong to treating it as if we were having a philosophical discussion and you're just expressing your view on life.While we can't store every possible time-instant of a continuous signal in finite memory, we can (theoretically in the limit and given exact arithmetics) obtain the value of the band-limited signal at any arbitrary point in time from only the Nyquist samples. There is no mathematical difficulties here, only practical ones.
Sorry, I'm not trying to badger you on this. But you've said I'm wrong and won't give any mathematical reason.
Not a good analogy. You can look at a displayed picture. You can't look at the numbers in the file and see the picture. But audio is far different on top of that, the eye is fine with discrete data.Ofcourse in practice we can't do this perfectly, so it would be closer to the situation with a lossy codec. If we store a picture as a JPEG or a movie as an MPEG, then certainly there is some generation loss in practice... but from the logical point of view it's still the same picture or the same movie, just slightly degraded due to (what I previously called) "implementation details."
This all started with me making statement that you said were fundamentally wrong. Now you're saying it's philosophy or something. And you're contrasting that with "pure mathematics", but you don't present any math. You disagree with my math but don't tell me how. I present you similar mathematics from a text book, you don't address it.ps. Also.. for the most part when I say "discrete-time" or "band-limited continuous-time" I am not concerned about actual "digital" or "analog" signals, but rather two signals that exist in the realm of pure mathematics. We can defined a bijection between the two domains and declare said bijection as an equivalence relation. All I'm trying to say is that whether or not this is helpful or counter-productive depends on the situation.
PS—Let me retract the "wrong" part. At least, skimming the old part of the thread, probably Z1202 was closer to saying that. You've questioned the usefulness of telling it like it is (it's PCM, it's a pulse modulation—no, not viewpoint, it's what made the samples), for some reason, preferring a philosophical "the samples are the signal, they are one and the same" zen thing. But this is a discussion about sample rate conversion. Understand that the samples are impulses, and the frequency domain implications (sidebands) is of utmost usefulness in designing oversampling systems (and also non-linear processing). Viewing it as just the signal is not helpful in the context of this thread.