>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 effects? Otherwise I don't see what you're trying to get at. Nobody is going to take up homework assignments from you, so I suggest that you simply try to state your thoughts directly. >I will not answer to this thread further, unless directly asked to, >because I think I've made my point clear enough. It seems somewhat bad form to exit a thread you started after your second post, but regardless, it remains unclear what your point is supposed to be. Also, I'd appreciate it if you'd refrain from casting aspersions on the educations and intellects of others (even though it's not clear who you are insulting, exactly). That's not a pleasant, constructive way to interact, and the music dsp list has an admirable history of being a welcoming, productive place. E On Mon, Jun 8, 2015 at 6:06 AM, Theo Verelst <theo...@theover.org> 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/FourierTransformExponentialFunction.html . > Some people language is so full of mistakes an misinterpretations, I > suggest a good university undergrad might solve that to understand the > difference of endless hinein interpretations, and decent, usable theory. So > that's a big njet on that stream of incoherent attempts to lay claim on > certain long and well known theoretics that range from 19th century > mathematics, physics, to in slightly different form, electronics. > > Also, it's not fair to change the direction of the question. I understand > as a practical working software employee, there's a sort of conservative > thought about one's credibility, but these theories aren't saying that the > course that this place an many other modernistic DSP tracks took is a > particularly good track to solve the problems at hand. > > A simple example of *my* point, not going into a quantification of the the > rather basic errors I've tried to bring to the attention (even though that > is an interesting exercise), how about we make a digital filter, let's say > applied to a pretty decent input signal (for instance a number of added > sine waves, possibly, if that satisfies some people more, including a step > function at t=0) that simply approximates a first order high-cut filter. We > could take a FIR or IIR implementation, and we could chose a shelving > filter (so at "inf" frequency, there's still signal) or an approximation of > a first order low pass in electronics (which at infinite frequency lets no > signal though). > > 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 ? > > (Part of the answer is you have to contemplate on the full problem, so > that preferably we would get (minus a signal shift we can ignore) the > *exact* input signal. This might include an huge matrix inversion problem, > as one of the possible solutions. Just taking "the opposite" filter leads > to an understanding of why I do not like any digital processing unless the > sampling frequency is pretty high, and a lot of signal and DSP precautions > are taken, and a lot of signal integrity issues are involved in the big > picture). > > I will not answer to this thread further, unless directly asked to, > because I think I've made my point clear enough. > > T. > > -- > dupswapdrop -- the music-dsp mailing list and website: > subscription info, FAQ, source code archive, list archive, book reviews, > dsp links > http://music.columbia.edu/cmc/music-dsp > http://music.columbia.edu/mailman/listinfo/music-dsp > -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
