Re: psychoacoustically driven temporal approximation

[Steve Beet <stevebeet@xxxxxxxxx>]

Alberto,

Although a strict application of Fourier analysis does rather contradict the idea of localising a particular frequency component to a particular time, there are other analysis methods which can do something similar to what you are asking about.

Obviously, wavelet transforms have finite support, and so can locate different components within a finite time interval, and because each wavelet responds more to some Fourier frequencies than others, you could say that each wavelet is representative of a particular frequency.

My own personal favourite approach is based on the "analytic signal", from which you can calculate an instantaneous frequency and an instantaneous amplitude. If you manipulate these values appropriately, you can simultaneously get a pretty good tradeoff between time and "frequency" resolution.

In some ways this is similar to the Teager energy operator, which gives an idea of the source energy at each instant, where the energy of a stationary source is proportional to the square of the source frequency. That's to say that if you know the instantaneous amplitude, then you can use the Teager energy to find the "frequency" at each sample.

These references are a bit long in the tooth now, but may be of interest:

"Teager Energy and the Ambiguity Function". R. Hamila, J. Astola, F. Alaya Cheikh, M. Gabbouj, and M. Renfors. IEEE Trans Sig Proc, vol 47(1), January 1999, pp 260-262.

"The time and frequency resolution of an auditory representation of speech". S. W. Beet and I. R. Gransden. In "Visual Representations of Speech Signals", eds.: M. P. Cooke, S. W. Beet and M. D. Crawford, pp 175-179. John Wiley and Sons, Ltd., 1993.

"Computationally efficient methods for calculating instantaneous frequency for auditory analysis". I. R. Gransden and S. W. Beet. Proc Eurospeech ’93, Berlin, September 1993, pp 385-388.

Steve



On Wed, 5 Mar 2014 08:05:59 -0800
"Richard F. Lyon" <dicklyon@xxxxxxx> wrote:

> Alberto, the question is not clear.  When you say "in the time domain" do
> you mean you are looking for alternatives to the widely used perceptual
> audio coders that use filterbanks?
> 
> If "a spectral-weighted temporal approximation method" is what you want,
> don't try to "connect frequency components to specific samples in the time
> domain".  Frequency components are not a relevant concept in the time
> domain.
> 
> Possibly what you want is something like LPC whitening with residual
> coding.  See for example:
> Singhal, Sharad. "High quality audio coding using multipulse LPC." *ICASSP*,
> 1990.
> 
> Dick
> 
> 
> 
> On Tue, Mar 4, 2014 at 3:05 AM, JesterN Alberto Novello
> <jestern77@xxxxxxxx>wrote:
> 
> > Hi all,
> > i'm trying to find a way to approximate the sample values of an audio
> > waveform in time domain.
> > I want a method that takes care of approximating perceptually-relevant
> > audio bands better than others.
> > Basically a spectral-weighted temporal approximation method.
> > In my head it's not clear how to connect frequency components to specific
> > samples in the time domain.
> > Any DSP wizard out there with a good idea/papers ?
> > Best regards
> > Alberto
> >
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