Hi,
Playing with analog and digital processing, I came to the conclusion I'd
like to contemplate about certain digital signal processing
considerations, I'm sure have been in the minds of pioneering people
quite a while ago, concerning let's say how accurate theoretically and
practically all
"Perfect" sinusoids/square waves/etc. only exist as mathematical
abstractions. A good starting point would be to get a feel for what, say,
the "square wave" coming out of an analog synthesizer actually looks like -
the noise floor, the distribution of harmonics, frequency jitter,
under/overshoot, e
Also a good starting place for beginners are the xiph show-and-tell videos
(probably been posted here before, but whatever):
https://xiph.org/video/vid2.shtml
E
On Wed, Jun 3, 2015 at 3:05 PM, Ethan Duni wrote:
> "Perfect" sinusoids/square waves/etc. only exist as mathematical
> abstractions.
Theo,
Any continuous function bandlimited to frequencies < fs/2 is completely
determined by its samples.
That’s the essence of the sampling theorem, which answers all your questions.
Stefan
> On 03 Jun 2015, at 22:47 , Theo Verelst wrote:
>
> Hi,
>
> Playing with analog and digital processi
Well, bandlimited to a bandwidth < fs/2 (but the distinction isn't
useful for audio), and given perfect reconstruction circuitry. But as
far as I can gather, Theo's concern is "what happens when, as is
inevitable in practice, the reconstruction circuitry is imperfect?"
And that is an interesting qu
Hi,
I was asking a very similar question about one year ago on this list in
the context of the BLEP theory. The point is that the samping theorem is
incomplete compared to how we would like to (and do) use it in the
signal processing. The sampling theorem applies only to the class
signals whi
Not sure I understand this sentence. As far as I know the FT is defined as an
integral between -inf and +inf, so I am not quite
sure how it cannot capture infinite-lenght sinusoidal signals. Maybe you meant
something else? (I am not being difficult, just
trying to understand what you are trying t
If you try to take the Fourier transform integral of a exp(j*omega_0*t),
it will not converge in the sense, how an improper integral's
convergence is usually understood. You will need to employ something
like Cauchy principal value or Cesaro convergence to make it converge to
zero at omega!=ome
IIRC, the discussion back then covered some topics like distortions created
with polynomial functions, etc.
Although DC isn’t a real problem in practical applications, there are many
cases, which are hard to predict, if they cause aliasing. A good example is FM,
which spectra can be predicted u
The direct impact on the application can be e.g. using BLEPs (of 0th and
higher orders) to antialias a sine hard sync or an exp-scale-modulated
or self-modulated sawtooth (which produces exp segments), which seems to
work but is lacking a firm theoretical foundation. In fact so does even
the ba
Clearly, there's very little knowledge around the basic mathematical
proofs underpinning a decent undergrad engineering course. Prisms
understand fine what the Fourier transform is, and isn't. Maybe there's
an interest in this:
http://mathworld.wolfram.com/FourierTransformExponentialFunction.ht
On 08-Jun-15 15:06, Theo Verelst wrote:
Clearly, there's very little knowledge around the basic mathematical
proofs underpinning a decent undergrad engineering course. Prisms
understand fine what the Fourier transform is, and isn't. Maybe there's
an interest in this:
http://mathworld.wolfram.com/
On 2015-06-08, vadim.zavalishin wrote:
The sampling theorem applies only to the class signals which do have
Fourier transform, separating this class further into bandlimited and
non-bandlimited. However, it doesn't say anything about the signals
which do not have Fourier transform.
Correct.
>If you try to take the Fourier transform integral of a exp(j*omega_0*t),
it will not
>converge in the sense, how an improper integral's convergence is usually
understood.
>You will need to employ something like Cauchy principal value or Cesaro
convergence
>to make it converge to zero at omega!=ome
>Now the assignment is as follows: can we, given the output signal
>coming from our filter which was fed the input signal, and the filter
>coefficients, compute the input signal ?
Invertible digital filters are invertible, up to numerical precision. Are
you wanting to talk about finite word length
On 2015-06-08, Ethan Duni wrote:
But both of these are overkill for day-to-day engineering practice.
Especially so, because you can treat the distributional framework as a
black box. It has a certain number of rules. If you follow the rules,
you'll land with a nice calculus which fully encom
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