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Correct me if I misunderstood, but if I understand correctly, you are proposing the following approach:
Given a time domain signal assumed to comprise of a quasi-period glottal pulse train, estimate the onset time and spectrum of each glotal pulse (i.e. a vector of pulse spectra and pulse onset times). [Note: by quasi-periodic we mean a signal with slowly varying fundamental period, and small amplitude local period-to-period variability.] Estimate E_0: First, to bootstrap the estimator assume that the signal is locally periodic. Form a fundamental frequency analysis and, under a perfect periodicity assumption, estimate the onset time (or some centroid) and pulse spectrum for each glottal pulse. Resynthesize a time domain pulse train using E_0. Compute a time domain residual. (Somehow) extract an error vector comprising pulse spectra error and pulse time error for each pulse in the estimate. Then you ask: > Although I have proposed this algorithm, I am yet to implement it. The main challenge is how the > optimization taking into account the heuristics should be performed. The simplest idea would be to > optimize each row of the matrix individually using any appropriate technique (e.g. gradient > descent, Simultaneous Perturbation Stochastic Approximation). Then repeat this many times. > However this would presumably be very inefficient. Besides, we should ideally be optimizing > globally or at least using regions larger than a single sample. Another issue is that optimization > procedure may change the deltas to minimize the heuristics, instead of distributing the residual in > the way that minimizes the heuristics' cost. These all seem like reasonable questions, but to me, ultimately boil down to "what is the best way to construct an estimator for this problem?". I am not an estimation theorist, but I suggest approaching it experimentally: don't worry about efficiency yet, code up some approaches using standard tools and see whether you can get *anything* to work. Regarding global vs local estimation: This boils down to how much of the input signal to use to calculate the residual, which components of the estimation vector to adjust, and how to weight them. Given that humans need to breath, I think you don't need to optimise globally. You could consider a sliding window of "active" pulses. The maximal temporal extent you would need to consider must comprise a segment where at least two pulses overlap at all times. If you can find gaps you can segment the input. The minimal temporal extent must be at least as long as a pulse duration (i.e. take into account all available information about that pulse). Glottal pulses are causal impulse responses with finite temporal extent. You should be able to derive an upper bound on their duration, either a static upper bound based on what we know about vocal tract resonance, or an adaptive bound based on your pulse spectra estimates. The estimator should, for any time segment, consider all pulses that make a non-zero contribution to the signal (possibly weighted). So you might want to estimate at least a few overlapping pulses simultaneously. This could be done as a moving-horizon estimate where you estimate pulse parameters sequentially: i.e. once the window moves past a pulse onset, that pulses estimate is frozen, and you could subtract its time domain representation from the estimator's input signal. Maybe you could estimate one pulse at a time and assume all previous pulse estimates are perfect. These kind of considerations are standard in moving-horizon estimation. Ross. On 5/08/2026 5:14 am, QueueSevenM wrote: > On 2026-08-04 08: 53, robert bristow-johnson wrote: Maybe you should > post this in the Signal Processing Stack Exchange or some place where we > can read the LaTeX math. Or render it into a .pdf file and post a link > to it? -- r b-j . _ . _ . _ . > ZjQcmQRYFpfptBannerStart > This Message Is From an External Sender > This message came from outside your organization. > ZjQcmQRYFpfptBannerEnd > > On 2026-08-04 08:53, robert bristow-johnson wrote: > >> Maybe you should post this in the Signal Processing Stack Exchange or >> some place where we can read the LaTeX math. Or render it into a .pdf >> file and post a link to it? -- r b-j . _ . _ . _ . _ rbj@ >> audioimagination. com "Imagination is more important >> ZjQcmQRYFpfptBannerStart >> This Message Is From an External Sender >> This message came from outside your organization. >> ZjQcmQRYFpfptBannerEnd >> Maybe you should post this in the Signal Processing Stack Exchange or some place where we can read the LaTeX math. >> >> Or render it into a .pdf file and post a link to it? >> >> >> -- >> >> r b-j . _ . _ . _ . _ [email protected] >> >> "Imagination is more important than knowledge." >> >> . >> . >> . > > > Or render it into a .pdf file and post a link to it? > > That's a good idea. I've attached a pdf version. > > > Maybe you should post this in the Signal Processing Stack Exchange or > some place where we can read the LaTeX math. > > It's not really a question, so I don't think they'd accept it. Maybe you > could say just the part optimization could be made into a question, but > I think it would too open-ended. I believe Stack Exchange requires > questions to not be open-ended. >
