Thanks Dave.
I am confident that Hans is quite knowledgeable in that regard, but is trying to understand my use of the term Gibbs envelope within the context of using it as a detector of over-Fs content.
As far as I am aware, the details I am providing on this forum are beyond the teachings we all received back in the day, and possibly up to the present. If it were already out there, I would need some pertinent google searchwords, as I can't think of any.
Had somebody detailed to me that modulation of a 20K using a 4K, filtering the upper sideband, and the resultant output was 18k modulated by 2...that would have stuck in my memory big time. I would have questioned that statement really big time....exactly what Hans is doing now.
jn
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Could you please stop ventilating this kind of misinformation.
If you want to show something come with real facts.
It took 3 pages before it finally became clear that you think that filtering leads to frequency shifts below the filter frequency.
Instead of producing all this text please come with something more substantial to defend your thesis.
For the time being, I don’t support this frequency shift thing.
Hans
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That is quite alright. Your actual posts and plots support it.
As I said, overlay the input and output together on one plot.
Then create an 18k modulated by a 2k, and overlay it directly on the filter output of the 20k modulated by 4.
You are simply using verbage to disagree, while I am using your posted content to show you.
And it is not as simplistic as you say. I am not saying that the mere act of filtering changes frequency. I am saying that the act of filtering a modulated waveform where only the upper sideband is removed because it is over Fs is causing the resultant output to have a different frequency.
Think it through..what do you think is the result of the summation of a 16Khz sine and a 20Khz sine, your second plot?
The trig identity is probably a thousand years old.. the trig equivalence is that a 16 and 20 sine added is equal to an 18 modulated by 2.
As I said, YOUR plots are showing it. I am only explaining your data to you.
jn
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Yes. Hans provided an FFT in/out characterizing the time domain 20k modulated by 4k.
When looking at an FFT which has only 16K and 20K, the summation has to be mathematically exactly what I said, 18K modulated by 2. And, that is exactly what his 20/4 filter output demonstrates.
So Hans, through significant efforts I thank him for, shows exactly what I have been saying. Conceptually, there is still some understanding needed, but the data is there.
What has yet to be mentioned is...if the input data is carried through two entire lobes, what does the FFT of the input look like...
jn
ps. Hans, please try to avoid creating strawman arguments I did not make.. you said "" it finally became clear that you think that filtering leads to frequency shifts below the filter frequency.""..that is not a correct statement of mine, but a mischaracterization of what I actually did say..
I am confident you were not strawmanning me, but it read that way..thanks as always.
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Fourier analysis formulae provide answers for both phase and frequency of harmonics.benb said:
The problem that I see, although it is more like a paradox, in reality, there are no continually repetitive signals like sines, square waves and anything with a fixed waveform. These simply do not exist. A periodic function continues indefinitely until t=∞, which is another way of saying it never stops. If a repetitive waveform stops its behaviour is like a complex pulse.
Sorry John, I'm not seeing anything new. Do you not accept that the time domain "stretching" of the waveform is due to the mechanism KSTR described? ie, the frequency doesn't shift?
Hans, thank you for your efforts in making those tests!
What occured to me is that in all tests so far, either by you or by others, the type of brickwall filter used was always of so called "linear phase" type which by its nature produces pre-ringing. Do you have any means of using other type of filter for this task? It would be interesting to see what kind of "frequency shift" will be visible then.
(I'd love to participate, but unfortunately I have no means to generate raised cosine test files and I can't work with 192k files. My hardware, which affects all my "real world" audio software settings is limited to 96k).
We were here before, they are equivalent it's known as double side-band suppressed carrier. Where are there new frequencies?
Double-sideband suppressed-carrier transmission - Wikipedia
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I am trying to understand how "time domain stretching" doesn't shift frequency.
Close inspection of the output waveform shows the zero crossings are no longer at the time intervals of the input waveform. And, the envelope is also longer.
A simple analysis of the frequency content into the filter, and what comes out is rather trivial. Wrapping one's head around the conversion from 20/4 to 18/2, that will take others some time. I never said it was easy to understand.
jn
Many of the alternatives end up violating Nyquist which would be a confounder for interpretation.
Well first, in Hans' plot.
Examine his FFT's..
The input spectra is 20K modulated by 4, clearly showing 16K, 20k, and 24K, and mainly because it's only one lobe..
Output spectra is 16K and 20K only. The sum of 16k and 20k is equivalent to 18 modded by 2, but you knew that..
jn
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Now that I finally know what’s it all about, you are right, nothing new to discuss so I stop contributing to this very subject of frequency shifting below the brick wall filter frequency.
Hans
Three in two out none of them new, are the 16k and 20k the same amplitude in both cases? If not it isn't exactly 18 by 2. What about the amplitude envelopes?
Which is unfortunate, as you are the one who has provided actual waveforms which entirely prove my point.
And the real work has yet to start. Using an exponential modulation waveform, it will be possible to note exactly where on the slope the gibbs stuff comes out.
I must admit, I am quite shocked you provide input and output waveforms that are absolutely different, but yet you say nothing has changed..😕
I provided the mathematical basis..
jn
So one should be able to do a test using Fs=1ksps and sweeping a tone and as it is nearing the corresponding Fs, one should hear, or maybe measure with a microphone, a frequency shift?
I have no idea if this is so - must admit that intuitively for me it should not happen - but if it does, I'm happy that it is out of my hearing range 🙂
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Aha... but there isn't any sideband for a sinus - right? Why are anything modulated with sidebands? Other distorsion within the system prior to filtering?
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