Hi,
I am trying to "jump" trough an audio wave (in other words cut
it and splice it together - scrambling the content) and
create transitions that avoid strong phase-discontinuities.
Right now I take the spectra (rect. windows around the destination
and departure point with zero-padding), calculate the phase differences
and build a fir allpass:
exp((angle(X) - angle(Y)) * i)
I apply a kaiser window to the result of the expression above and
use that as the filter to align the phases of the transition point.
It works, but I think I could find a more refined method.
The main problem is that the allpass filter will spread energy into
the zeropadded (zeropadded in the 2 original time windoews) region.
Typically the filtered wave shows a slight decrease in power locally
around the transition point, if the cut signal is treated to be
zero in front of the cut point.
Let me try to express one idea to improve the finding of
the filter (hope the web-interface doesn't destroy ascii indentation):
Two signals x and y
x[n-k] x[n]
y[n]
Now I want to find a filter that minimizes the phase differences
in X and Y being STFT frames of x[n...k] and y[n...k]
if the signal is linearly convolved with the filter kernel
starting at x[n-k].
To put it differently:
I am looking for the filter with an imp-response
s[n] that minimizes the phase differences at time in x[n] and y[n]
It looks similar to typical linear prediction problems,
but unlike LPC and co. which match magnitude characterestics
(spectral envelopes..) I want to match the phase information.
Find the linear combination of samples x[n..n-k]
that to express one idea to improve the finding of
the filter (hope the web-interface doesn't destroy ascii indentation):
Two signals x and y
x[n-k] x[n]
y[n]
Now I want to find a filter that minimizes the phase differences
in X and Y being STFT frames of x[n...k] and y[n...k]
if the signal is linearly convolved with the filter kernel
starting at x[n-k].
To put it differently:
I am looking for the filter with an imp-response
s[n] that minimizes the phase differences at time in x[n] and y[n]
It looks similar to typical linear prediction problems,
but unlike LPC and co. which match magnitude characterestics
(spectral envelopes..) I want to match the phase information.
If I set up a toeplitz matrix with all the samples in region
x[n-k].. x[n+k] , what could be the scheme to find
coefficients (the fir filter, with the restriction to be allpass)
that minimizes the phase diffs between STFT frames
FFT(x[m]) and FFT(y[m]) with m = n..k ?
Any thoughts, on that. Sorry, in case the problem
is stated in a confusing manner. I know people here like
well formulated problems, but if I would know how to formulate
the right equations for it, I could probably solve it.
cheers,
Bjoern
_____________________________________
Do you know a company who employs DSP engineers?
Is it already listed at http://dsprelated.com/employers.php ?
fir allpass filters for phase-alignment
Started by ●December 11, 2008
Reply by ●December 11, 20082008-12-11
Your message is all about process. What exactly are you trying to accomplish as the result of that process? What are the problems? Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com banton wrote:> Hi, > > I am trying to "jump" trough an audio wave (in other words cut > it and splice it together - scrambling the content) and > create transitions that avoid strong phase-discontinuities. > Right now I take the spectra (rect. windows around the destination > and departure point with zero-padding), calculate the phase differences > and build a fir allpass: > > exp((angle(X) - angle(Y)) * i) > > I apply a kaiser window to the result of the expression above and > use that as the filter to align the phases of the transition point. > It works, but I think I could find a more refined method. > The main problem is that the allpass filter will spread energy into > the zeropadded (zeropadded in the 2 original time windoews) region. > Typically the filtered wave shows a slight decrease in power locally > around the transition point, if the cut signal is treated to be > zero in front of the cut point. > > Let me try to express one idea to improve the finding of > the filter (hope the web-interface doesn't destroy ascii indentation): > Two signals x and y > > x[n-k] x[n] > y[n] > > Now I want to find a filter that minimizes the phase differences > in X and Y being STFT frames of x[n...k] and y[n...k] > if the signal is linearly convolved with the filter kernel > starting at x[n-k]. > To put it differently: > I am looking for the filter with an imp-response > s[n] that minimizes the phase differences at time in x[n] and y[n] > It looks similar to typical linear prediction problems, > but unlike LPC and co. which match magnitude characterestics > (spectral envelopes..) I want to match the phase information. > Find the linear combination of samples x[n..n-k] > that to express one idea to improve the finding of > the filter (hope the web-interface doesn't destroy ascii indentation): > Two signals x and y > > x[n-k] x[n] > y[n] > > Now I want to find a filter that minimizes the phase differences > in X and Y being STFT frames of x[n...k] and y[n...k] > if the signal is linearly convolved with the filter kernel > starting at x[n-k]. > To put it differently: > I am looking for the filter with an imp-response > s[n] that minimizes the phase differences at time in x[n] and y[n] > It looks similar to typical linear prediction problems, > but unlike LPC and co. which match magnitude characterestics > (spectral envelopes..) I want to match the phase information. > If I set up a toeplitz matrix with all the samples in region > x[n-k].. x[n+k] , what could be the scheme to find > coefficients (the fir filter, with the restriction to be allpass) > that minimizes the phase diffs between STFT frames > FFT(x[m]) and FFT(y[m]) with m = n..k ? > > Any thoughts, on that. Sorry, in case the problem > is stated in a confusing manner. I know people here like > well formulated problems, but if I would know how to formulate > the right equations for it, I could probably solve it. > > cheers, > Bjoern
Reply by ●December 11, 20082008-12-11
Valdimir Vassilevsky wrote:> >Your message is all about process. What exactly are you trying to >accomplish as the result of that process? What are the problems?It's a sound synthesis process. It's about concatenating wave-segments and aligning the phases at the transitions from one segment to the next. For this process I want to find a way to create filter kernels on the fly that will shift phases in order to maximize the correlation between the two waves at the transition point. So its about filtering audio signals in order to align phase values at cuts (or jumps from one position in the original wave to another). I am doint that because of the audible consequences of applying "phase-aligning filters" to concatenated audio segments. However I'll try again to state what I am looking for as exact as I can. I am looking for a way to solve the following problem: Given two signals x and y, find allpass response h (of a given size) so that convolving h with y will minimize the sum of the phase differences (modular in 2*pi) between X = FFT(x[n] ... x[n+k]) and Y = FFT(y[n] ... y[n+k]) where n (the position of FFT frames) and k (the size of the FFT frames) are given. It could look like the answer is trivial: Just create the spectrum H with constant magnitude 1.0 and phase values angle(X) - angle(Y), after multiplication of Y with H the phase values are equal, but this is not the best response, for the problem stated above, since this approach is based on circular convolution of the two frames, while I want to convolve y (the whole signal, not just the given frame) with h. The best solution has to be dependent on the samples in frame X plus samples x[n-m] where m is the length of the response. cheers, Bjoern>banton wrote: >> Hi, >> >> I am trying to "jump" trough an audio wave (in other words cut >> it and splice it together - scrambling the content) and >> create transitions that avoid strong phase-discontinuities. >> Right now I take the spectra (rect. windows around the destination >> and departure point with zero-padding), calculate the phasedifferences>> and build a fir allpass: >> >> exp((angle(X) - angle(Y)) * i) >> >> I apply a kaiser window to the result of the expression above and >> use that as the filter to align the phases of the transition point. >> It works, but I think I could find a more refined method. >> The main problem is that the allpass filter will spread energy into >> the zeropadded (zeropadded in the 2 original time windoews) region. >> Typically the filtered wave shows a slight decrease in power locally >> around the transition point, if the cut signal is treated to be >> zero in front of the cut point. >> >> Let me try to express one idea to improve the finding of >> the filter (hope the web-interface doesn't destroy ascii indentation): >> Two signals x and y >> >> x[n-k] x[n] >> y[n] >> >> Now I want to find a filter that minimizes the phase differences >> in X and Y being STFT frames of x[n...k] and y[n...k] >> if the signal is linearly convolved with the filter kernel >> starting at x[n-k]. >> To put it differently: >> I am looking for the filter with an imp-response >> s[n] that minimizes the phase differences at time in x[n] and y[n] >> It looks similar to typical linear prediction problems, >> but unlike LPC and co. which match magnitude characterestics >> (spectral envelopes..) I want to match the phase information. >> >> If I set up a toeplitz matrix with all the samples in region >> x[n-k].. x[n+k] , what could be the scheme to find >> coefficients (the fir filter, with the restriction to be allpass) >> that minimizes the phase diffs between STFT frames >> FFT(x[m]) and FFT(y[m]) with m = n..k ? >> >> Any thoughts, on that. Sorry, in case the problem >> is stated in a confusing manner. I know people here like >> well formulated problems, but if I would know how to formulate >> the right equations for it, I could probably solve it. >> cheers, >> Bjoern >_____________________________________ Do you know a company who employs DSP engineers? Is it already listed at http://dsprelated.com/employers.php ?
Reply by ●December 11, 20082008-12-11
On Dec 12, 3:49�am, "banton" <bant...@web.de> wrote:> Hi, > > I am trying to "jump" trough an audio wave (in other words cut > it and splice it together - scrambling the content) and > create transitions that avoid strong phase-discontinuities. > Right now I take the spectra (rect. windows around the destination > and departure point with zero-padding), calculate the phase differences > and build a fir allpass: > > exp((angle(X) - angle(Y)) * i) � > > I apply a kaiser window to the result of the expression above and > use that as the filter to align the phases of the transition point. > It works, but I think I could find a more refined method. > The main problem is that the allpass filter will spread energy into > the zeropadded (zeropadded in the 2 original time windoews) region. > Typically the filtered wave shows a slight decrease in power locally > around the transition point, if the cut signal is treated to be > zero in front of the cut point. > > Let me try to express one idea to improve the finding of > the filter (hope the web-interface doesn't destroy ascii indentation): > Two signals x and y > > x[n-k] x[n] > � � � �y[n] > > Now I want to find a filter that minimizes the phase differences > in �X and Y being STFT frames of x[n...k] and y[n...k] > if the signal is linearly convolved with the filter kernel > starting at x[n-k]. > To put it differently: > I am looking for the filter with an imp-response > s[n] that minimizes the phase differences at time in x[n] and y[n] > It looks similar to typical linear prediction problems, > but unlike LPC and co. which match magnitude characterestics > (spectral envelopes..) I want to match the phase information. > Find the linear combination of samples x[n..n-k] > that �to express one idea to improve the finding of > the filter (hope the web-interface doesn't destroy ascii indentation): > Two signals x and y > > x[n-k] x[n] > � � � �y[n] > > Now I want to find a filter that minimizes the phase differences > in �X and Y being STFT frames of x[n...k] and y[n...k] > if the signal is linearly convolved with the filter kernel > starting at x[n-k]. > To put it differently: > I am looking for the filter with an imp-response > s[n] that minimizes the phase differences at time in x[n] and y[n] > It looks similar to typical linear prediction problems, > but unlike LPC and co. which match magnitude characterestics > (spectral envelopes..) I want to match the phase information. > If I set up a toeplitz matrix with all the samples in region > x[n-k].. x[n+k] �, what could be the scheme to find > coefficients (the fir filter, with the restriction to be allpass) > that minimizes the phase diffs between STFT frames > FFT(x[m]) and FFT(y[m]) with m = n..k ? > > Any thoughts, on that. �Sorry, in case the problem > is stated in a confusing manner. �I know people here like > well formulated problems, but if I would know how to formulate > the right equations for it, I could probably solve it. > > cheers, > Bjoern > > _____________________________________ > Do you know a company who employs DSP engineers? � > Is it already listed athttp://dsprelated.com/employers.php?Unless it's stereo, phase should not matter as to how you hear the sound. Hardy
Reply by ●December 11, 20082008-12-11
> > >> Any thoughts, on that. �Sorry, in case the problem > >> is stated in a confusing manner. �I know people here like > >> well formulated problems, but if I would know how to formulate > >> the right equations for it, I could probably solve it. > >> cheers, > >> Bjoern > >is you goal to be able to splice two segments of sound togther without a CLICK? Mark
Reply by ●December 11, 20082008-12-11
Hardy wrote:> >Unless it's stereo, phase should not matter as to how you hear the >sound.Hardy, I am concatenating segments of audio. simplest example: You take little segments of a sine-wave and concatenate them. Does the phase of the sinusoid at the boundaries between two segments matter? Or equally simple: You loop a sample, does phase at the loop points matter? _____________________________________ Do you know a company who employs DSP engineers? Is it already listed at http://dsprelated.com/employers.php ?
Reply by ●December 11, 20082008-12-11
Mark wrote:>> >> Any thoughts, on that. =A0Sorry, in case the problem >> >> is stated in a confusing manner. =A0I know people here like >> >> well formulated problems, but if I would know how to formulate >> >> the right equations for it, I could probably solve it. >> >> cheers, >> >> Bjoern >> >> > >is you goal to be able to splice two segments of sound togther without >a CLICK? >Let's say it's related to that, but I am dealing also with segments of very short size, so in that case phase discontinuities will result in sharper timbres, rather than clicks. But please, if somebody is now going to tell me, I should simply use crossfades, that is not the point! Look at it that way: If you want to loop or cut periodic sound material, you simply make sure that both points, are in phase (same position in terms of time modolu funamental period). If you have non-periodic content, e.g. two sinusoids in a non rational frequency relation, you can shift them against each other to achieve a smooth transition - both sinusoids will be in phase. That's why I apply frequency dependent phase shifts (allpass filters) to the concatenated segments, in order to make transitions more smooth. _____________________________________ Do you know a company who employs DSP engineers? Is it already listed at http://dsprelated.com/employers.php ?
Reply by ●December 11, 20082008-12-11
banton wrote:> Hi, > > I am trying to "jump" trough an audio wave (in other words cut > it and splice it together - scrambling the content) and > create transitions that avoid strong phase-discontinuities. > Right now I take the spectra (rect. windows around the destination > and departure point with zero-padding), calculate the phase > differences and build a fir allpass: > > exp((angle(X) - angle(Y)) * i) > > I apply a kaiser window to the result of the expression above and > use that as the filter to align the phases of the transition point. > It works, but I think I could find a more refined method. > The main problem is that the allpass filter will spread energy into > the zeropadded (zeropadded in the 2 original time windoews) region. > Typically the filtered wave shows a slight decrease in power locally > around the transition point, if the cut signal is treated to be > zero in front of the cut point. > > Let me try to express one idea to improve the finding of > the filter (hope the web-interface doesn't destroy ascii indentation): > Two signals x and y > > x[n-k] x[n] > y[n] > > Now I want to find a filter that minimizes the phase differences > in X and Y being STFT frames of x[n...k] and y[n...k] > if the signal is linearly convolved with the filter kernel > starting at x[n-k]. > To put it differently: > I am looking for the filter with an imp-response > s[n] that minimizes the phase differences at time in x[n] and y[n] > It looks similar to typical linear prediction problems, > but unlike LPC and co. which match magnitude characterestics > (spectral envelopes..) I want to match the phase information. > Find the linear combination of samples x[n..n-k] > that to express one idea to improve the finding of > the filter (hope the web-interface doesn't destroy ascii indentation): > Two signals x and y > > x[n-k] x[n] > y[n] > > Now I want to find a filter that minimizes the phase differences > in X and Y being STFT frames of x[n...k] and y[n...k] > if the signal is linearly convolved with the filter kernel > starting at x[n-k]. > To put it differently: > I am looking for the filter with an imp-response > s[n] that minimizes the phase differences at time in x[n] and y[n] > It looks similar to typical linear prediction problems, > but unlike LPC and co. which match magnitude characterestics > (spectral envelopes..) I want to match the phase information. > If I set up a toeplitz matrix with all the samples in region > x[n-k].. x[n+k] , what could be the scheme to find > coefficients (the fir filter, with the restriction to be allpass) > that minimizes the phase diffs between STFT frames > FFT(x[m]) and FFT(y[m]) with m = n..k ? > > Any thoughts, on that. Sorry, in case the problem > is stated in a confusing manner. I know people here like > well formulated problems, but if I would know how to formulate > the right equations for it, I could probably solve it. > > cheers, > BjoernThe thing that concerns me about this is that you probably can't accomplish what you want with a very short filter. That means that there will be all sorts of temporal spreading involved in the output. It seems to me that tweaking the splice is a better idea. I've done some of this in generating continous loops from short samples. One artifact of generating loops from short samples is that the output will have a discrete spectrum associated with the length of the sample. Is that tolerable? If not, you have a serious problem. While that's not exactly what you describe, it may suggest a type of difficulty. If the waveform is a general one then let's split it into two types: 1) periodic 2) aperiodic - For a periodic waveform, a splicing approach would be to have a FIR filter with a single nonzero coefficient. Here I'm assuming that the sample rate is very high or that we're talking about an analog delay line as the FIR filter. All you have to do is set the delay to an appropriate value and there will be no splice transient - the delay (or the skipped part of the record) is an integer number of periods. - For an aperiodic waveform there is *no* theoretical solution. But, as has been observed here many times (I credit Jerry with this idea) one can come arbitrarily close as the delay time is increased. Example: The signal is the sum of a 1 Hz sinusoid and a PI Hz sinusoid. It is not periodic because the two constituent frequencies aren't rationally related. But, the longer you're willing to wait, the closer they *appear* to be periodic - at some point the difference is lost in the noise. How does this apply to your application? I'm not sure what you're trying to accomplish overall. What I will observe is that the approach of using a "filter" has long time implications while the approach of using a pure "delay line" has no long time implications. A delay line is a *perfect* all pass and the phase matching is as good as you can accomplish as above (... I think). The challenge seems to be to find an appropriate delay. What if you did a short-term correlation between the signals to find a likely splice point? Then, don't filter at all - just splice the raw signals (which is an implementation of the delay line approach). In fact, that's implied by your all-pass I hope this helps. Fred
Reply by ●December 11, 20082008-12-11
Fred wrote:>banton wrote: >> Hi, >> >> I am trying to "jump" trough an audio wave (in other words cut >> it and splice it together - scrambling the content) and >> create transitions that avoid strong phase-discontinuities. >> Right now I take the spectra (rect. windows around the destination >> and departure point with zero-padding), calculate the phase >> differences and build a fir allpass:(snip)>> Let me try to express one idea to improve the finding of >> the filter (hope the web-interface doesn't destroy ascii indentation): >> Two signals x and y >> >> x[n-k] x[n] >> y[n] >> >> Now I want to find a filter that minimizes the phase differences >> in X and Y being STFT frames of x[n...k] and y[n...k] >> if the signal is linearly convolved with the filter kernel >> starting at x[n-k].(snip)>> It looks similar to typical linear prediction problems, >> but unlike LPC and co. which match magnitude characterestics >> (spectral envelopes..) I want to match the phase information. >> If I set up a toeplitz matrix with all the samples in region >> x[n-k].. x[n+k] , what could be the scheme to find >> coefficients (the fir filter, with the restriction to be allpass) >> that minimizes the phase diffs between STFT frames >> FFT(x[m]) and FFT(y[m]) with m = n..k ? > >The thing that concerns me about this is that you probably can'taccomplish>what you want with a very short filter. That means that there will beall>sorts of temporal spreading involved in the output.Yes, you get the problem exactly right. But as I say I am trying to _minimize_ the phase differences, not to make them exactly equal. Temporal spreading is a major issue, and of course longer filters would make them even worse.>It seems to me that tweaking the splice is a better idea. I've done someof>this in generating continous loops from short samples. > >One artifact of generating loops from short samples is that the outputwill>have a discrete spectrum associated with the length of the sample. Isthat>tolerable? If not, you have a serious problem. While that's not exactly>what you describe, it may suggest a type of difficulty.I understand what you describe, and it's definitely not tolerable for my purpose. Basically is is exactly what I want to avoid (The influence of segment length on the periodicity of the output material).>If the waveform is a general one then let's split it into two types: >1) periodic >2) aperiodic > >- For a periodic waveform, a splicing approach would be to have a FIRfilter>with a single nonzero coefficient. Here I'm assuming that the samplerate>is very high or that we're talking about an analog delay line as the FIR>filter. All you have to do is set the delay to an appropriate value and>there will be no splice transient - the delay (or the skipped part of the>record) is an integer number of periods.That's simple, and you don't even need a very high sampling rate, if you use fractional delay filters (e.g use lagrange to generate the kernel)>- For an aperiodic waveform there is *no* theoretical solution. But, ashas>been observed here many times (I credit Jerry with this idea) one cancome>arbitrarily close as the delay time is increased. Example: The signalis>the sum of a 1 Hz sinusoid and a PI Hz sinusoid. It is not periodicbecause>the two constituent frequencies aren't rationally related. But, thelonger>you're willing to wait, the closer they *appear* to be periodic - at some>point the difference is lost in the noise.This is also clear to me and I have done some sound synthesis things related to what you describe.>How does this apply to your application? I'm not sure what you're tryingto>accomplish overall. What I will observe is that the approach of using a>"filter" has long time implications while the approach of using a pure >"delay line" has no long time implications. A delay line is a *perfect*all>pass and the phase matching is as good as you can accomplish as above(... I>think). > >The challenge seems to be to find an appropriate delay. What if you dida>short-term correlation between the signals to find a likely splice point?I am allready doing that to localize the splice points. The allpass filtering comes afterwards to do phase correction.>Then, don't filter at all - just splice the raw signals (which is an >implementation of the delay line approach). In fact, that's implied byyour>all-pass > >I hope this helps.Thanks Fred, All the things you mention are closely related to synthesis methods that I am using and in fact I have played around with all of this ideas. The keypoint is that I am now looking for a way to shift the internal phase relations of the material around to create improved matches. It smears out some signal contents in time and shifts components out of their original phase relation. But limited by the size of the applied allpass filter; so as long as the filter is small, say 256 .. 512 samples, not a problem for me. The filters, simply created by measuring the phase differences in 2 frames around the transition point _do_ allready significantly improve the correlation of the two signals. But I am certain that I can improve the way, I create the filters. Maybe, it helps if I relate the method to phase-vocoding. A phase-vocoder estimates sinusoidal bins and as long as those are distant enough to be identified in the spectrum, the phase-vocoder doesn't care if components have rational frequency relations or not (in other words: if the signal is periodic). In the resynthesis the phases of the components are continuous. So you can for example time-stretch an inharmonic sound. This comes with the expense of blurred spectra and other artefacts through the difficulty to estimate the time-varying sinusoids from fourier frames. What I am doing works in the time domoin and there clearly is a relation to WSOLA and similar techniques. However, I do not aim at timescale modification, but rather at "jumping around" in the wave, but you can see the relation since, time-domain timescalers jump around as well, just in a very specific manner. Even though it is not my original goal (which is simply to synthesise interesting sounds with experimental methods), I'll pretend from now on that the goal of what I am doing is to time-stretch chords. First I identify points which show correlate. Then I compare the phase differences at two selected points and create a phase-aligning filter which is applied to the next segment. And so on.. for every jump (or cut or segment boundary, however you call it) a new filter is created to achieve approximate phase continuity. Needless to say, it creates its own kind of artefacts; but different ones than the pvoc or SOLA based stuff. Sorry, for the long post, but every reply idicated that people are puzzled why I want to find a method to create allpass fir filters that will align-phase values of 2 signals around a given time-point. gr. Bjoern _____________________________________ Do you know a company who employs DSP engineers? Is it already listed at http://dsprelated.com/employers.php ?
Reply by ●December 11, 20082008-12-11
On Dec 11, 12:58�pm, HardySpicer <gyansor...@gmail.com> wrote:> On Dec 12, 3:49�am, "banton" <bant...@web.de> wrote: > > > > > > > Hi, > > > I am trying to "jump" trough an audio wave (in other words cut > > it and splice it together - scrambling the content) and > > create transitions that avoid strong phase-discontinuities. > > Right now I take the spectra (rect. windows around the destination > > and departure point with zero-padding), calculate the phase differences > > and build a fir allpass: > > > exp((angle(X) - angle(Y)) * i) � > > > I apply a kaiser window to the result of the expression above and > > use that as the filter to align the phases of the transition point. > > It works, but I think I could find a more refined method. > > The main problem is that the allpass filter will spread energy into > > the zeropadded (zeropadded in the 2 original time windoews) region. > > Typically the filtered wave shows a slight decrease in power locally > > around the transition point, if the cut signal is treated to be > > zero in front of the cut point. > > > Let me try to express one idea to improve the finding of > > the filter (hope the web-interface doesn't destroy ascii indentation): > > Two signals x and y > > > x[n-k] x[n] > > � � � �y[n] > > > Now I want to find a filter that minimizes the phase differences > > in �X and Y being STFT frames of x[n...k] and y[n...k] > > if the signal is linearly convolved with the filter kernel > > starting at x[n-k]. > > To put it differently: > > I am looking for the filter with an imp-response > > s[n] that minimizes the phase differences at time in x[n] and y[n] > > It looks similar to typical linear prediction problems, > > but unlike LPC and co. which match magnitude characterestics > > (spectral envelopes..) I want to match the phase information. > > Find the linear combination of samples x[n..n-k] > > that �to express one idea to improve the finding of > > the filter (hope the web-interface doesn't destroy ascii indentation): > > Two signals x and y > > > x[n-k] x[n] > > � � � �y[n] > > > Now I want to find a filter that minimizes the phase differences > > in �X and Y being STFT frames of x[n...k] and y[n...k] > > if the signal is linearly convolved with the filter kernel > > starting at x[n-k]. > > To put it differently: > > I am looking for the filter with an imp-response > > s[n] that minimizes the phase differences at time in x[n] and y[n] > > It looks similar to typical linear prediction problems, > > but unlike LPC and co. which match magnitude characterestics > > (spectral envelopes..) I want to match the phase information. > > If I set up a toeplitz matrix with all the samples in region > > x[n-k].. x[n+k] �, what could be the scheme to find > > coefficients (the fir filter, with the restriction to be allpass) > > that minimizes the phase diffs between STFT frames > > FFT(x[m]) and FFT(y[m]) with m = n..k ? > > > Any thoughts, on that. �Sorry, in case the problem > > is stated in a confusing manner. �I know people here like > > well formulated problems, but if I would know how to formulate > > the right equations for it, I could probably solve it. > > > cheers, > > Bjoern > > > _____________________________________ > > Do you know a company who employs DSP engineers? � > > Is it already listed athttp://dsprelated.com/employers.php? > > Unless it's stereo, phase should not matter as to how you hear the > sound. > > Hardy- Hide quoted text - > > - Show quoted text -People like to say phase does not matter, that the ear is insensitive to phase. Often they unwittingly extend that to saying phase discontinuity or phase variation doesn't matter, as you are doing here.You don't think you can hear phase discontinuities? Dirk Dirk
