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# Re: General Question about the Perception of Transients

```Hi Chris,

Cochlear frequency analysis is just a first step of auditory function, and it
considerably differs from complex valued FFT in that, the latter includes an
arbitrarily chosen temporal reference and fourfold redundancy. While FFT yields
a complex spectrum in terms of magnitude and phase, cochlea provides a
real-valued spectrum of alternating amplitudes and subsequent one-way
rectification. The only correct mathematical correlate to cochlear frequency
analysis is real-valued cosine transform within IR+. Notice that the zero of
elapsed time permanently shifts relative to our event-related ordinary time.
That's why spectrograms are so awkward.

ZChris Share <cshare01@xxxxxxxxx> wrote:

> I recently attended a course on the mathematics of the FFT. In the
> course I was told that one of the reasons why the FFT is so useful as an
> audio analysis tool is because it is similar to how the human hearing
> mechanism works (i.e. that the human hearing mechanism acts, to a
> certain degree, like a frequency analyser).
>
> I'm interested in the perception of transients, as they play such an
> important role in the perception of music and in hearing generally.

By means of Matlab, I calculated an exemplary transient response to simple
stimuli based on cosine transform in IR+. With respect to joint time-frequency
resolution, the result was about as superior to FFT based analysis as are
cochlear frequency analysis and are, to a lesser extent, tweaked physical
models.

> I was wondering if there are any mathematical models of transient
> perception analogous to the FFT/hearing idea. I've come across research
> into transient analysis, however most of this seems to be from a
> strictly DSP perspective, and does not incorporate perceptual factors
> (or any perceptual model).

Do not underestimate the role of subsequent neurons, in particular onset
choppers. What about cochlear function, DSPs have to mimic the more or less
gradual forgetting-like limitation of the time window's backfront. I simply used
assumed attenuation for that.

> I guess what I'm really asking is, are there any DSP approaches to
> transient analysis that are analogs of the hearing mechanism?

Since the topic is of high commercial interest, there might be some implemented
but unpublished solutions.

> Any help or thoughts on this question would be greatly appreciated.

Physics does not require IR, zero-padded future events, FFT, and linear phase
for analysis of what is generally located within elapsed time. This insight is
anything but welcome in physics because it relates to errors being unseen so
far.

Cheers,
Eckard

```