[deleted]
Fourier Transform existed, but I never had intuitive understanding until now
11–20 of 24 posts
Re: Fourier Transform existed, but I never had intuitive understanding until now
#12Earlier quoted context omitted.
I think the writing was poor, but also there are some things that are just wrong. Like most of the time people sample at 10x Nyquist. That would be a huge waste of processing given that it doesn't give you any more information about the signal than just Nyquist.
Almost by definition, it does give you more information about the signal than sampling at the Nyquist frequency though? If you have any noise at all, oversampling will be very helpful to improve the signal to noise ratio.
for band limited signals the snr is not increased by oversampling
Re: Fourier Transform existed, but I never had intuitive understanding until now
#13Earlier quoted context omitted.
I think the writing was poor, but also there are some things that are just wrong. Like most of the time people sample at 10x Nyquist. That would be a huge waste of processing given that it doesn't give you any more information about the signal than just Nyquist.
Almost by definition, it does give you more information about the signal than sampling at the Nyquist frequency though? If you have any noise at all, oversampling will be very helpful to improve the signal to noise ratio.
That's true but sampling beyond your target domain bounds seems pointless, right? If, say, you're sampling audio oversampling will just give you a bunch of frequencies you'd end up throwing away regardless. It's extra work for no benefit if the domain already has well-prescribed bounds.
I guess it could be useful in cases where you don't have bounds to work against.
This comes back to the poor writing, though, as I believe the author meant to indicate that the industry standard for sampling audio is 10x their cited sampling rate of 2000HZ in the text (though this is incorrect, too. Audio is sampled at 44100HZ because the general upper bound on hearing is 22000HZ, so by Nyquist's theorem, sampling at 44100 gives you enough range to avoid aliasing within the 0-22000 band).
Re: Fourier Transform existed, but I never had intuitive understanding until now
#14For those wanting a visual understanding to Fourier transforms, I enjoyed 3blue1brown's video [0] which is a bit more of a continuous approach.
Re: Fourier Transform existed, but I never had intuitive understanding until now
#15Earlier quoted context omitted.
Almost by definition, it does give you more information about the signal than sampling at the Nyquist frequency though? If you have any noise at all, oversampling will be very helpful to improve the signal to noise ratio.
That's true but sampling beyond your target domain bounds seems pointless, right? If, say, you're sampling audio oversampling will just give you a bunch of frequencies you'd end up throwing away regardless. It's extra work for no benefit if the domain already has well-prescribed bounds. I guess it could be useful in cases where you don't have bounds to work against. This comes back to the poor writing, though, as I b…
Here's what I've never understood, isn't Nyquist sampling discrete in time but continuous in amplitude? If the amplitude is instead (as is normal in digital) being sampled discretely (in steps), wouldn't that introduce errors, and wouldn't more samples make up for these errors?
what would Nyquist in amplitude, continuous in time look like? that's sort of a class D amplifier, and even sort of CVSD.
Re: Fourier Transform existed, but I never had intuitive understanding until now
#16For me this produced more confusion than it explained anything.
Yes, This reads more like someones notes to self, than an article written with a general audience in mind.
Re: Fourier Transform existed, but I never had intuitive understanding until now
#17Earlier quoted context omitted.
That's true but sampling beyond your target domain bounds seems pointless, right? If, say, you're sampling audio oversampling will just give you a bunch of frequencies you'd end up throwing away regardless. It's extra work for no benefit if the domain already has well-prescribed bounds. I guess it could be useful in cases where you don't have bounds to work against. This comes back to the poor writing, though, as I b…
Here's what I've never understood, isn't Nyquist sampling discrete in time but continuous in amplitude? If the amplitude is instead (as is normal in digital) being sampled discretely (in steps), wouldn't that introduce errors, and wouldn't more samples make up for these errors? what would Nyquist in amplitude, continuous in time look like? that's sort of a class D amplifier, and even sort of CVSD.
There are Sigma Delta ADCs, which sample quantised to one bit at a higher frequency. They need to do some processing in the analogue domain though. IIRC you need to multiply the sample rate by 4*N to get the equivalent of an N but DAC
Re: Fourier Transform existed, but I never had intuitive understanding until now
#18For anyone wanted an intuitive understanding of Fourier transforms I recommend "Who Is Fourier?: A Mathematical Adventure".
It seems a bit childish, but it actually explains everything perfectly.
Re: Fourier Transform existed, but I never had intuitive understanding until now
#19For those wanting a visual understanding to Fourier transforms, I enjoyed 3blue1brown's video [0] which is a bit more of a continuous approach. [0]: https://www.youtube.com/watch?v=spUNpyF58BY
I like his video too! Thanks for sharing.
Re: Fourier Transform existed, but I never had intuitive understanding until now
#20https://www.dspguide.com/ is a great, general introduction to digital signal processing and includes coverage of the Fourier Transform. I'd recommend checking it out for anyone struggling to grok DSP concepts. This article seems to have the right intent, but I felt the quality of the writing would need to improve for it to become truly useful for learners.
Thank you. I read a lot of papers drive equations from Euler's formula, which helped with result, but I didn't have any intuitive understanding, but when I watched geometric breakdown of it, it suddenly made sense. It's just my attempt to share my excitement. I do agree my writing could definitely be improved.