[Tftb-help] analytic signal and wish list

[Eric Chassande-Mottin]

> Often the message "Be careful: the signal is not analytic!"
> appears even during the demos. What is the reason for this
> warning in tfrqview.m?

this warning is related to what's explained on this page of the tutorial:
http://gdr-isis.org/tftb/tutorial/node44.html

the TFTB computes discrete time and discrete frequency TFRs. this raises 
the question of the sampling of the time-frequency plane and consequently 
of the aliasing of the TFRs. to avoid aliasing terms, several TFRs (for 
instance, the Wigner-Ville distribution) require specific condition on the 
input signal, namely it should be a _half-band signal_ (with Fourier 
spectrum occupying only a width equal to 1/2 expressed in reduced 
frequency unit). if your signal is not half-band, it can be transformed 
into a half-band signal with no loss of information by using its analytic 
version or by resampling it at twice the Nyquist rate.

the TFTB favors the first solution (analytic). the warning just warns you
that the input signal is not analytic and that the TFR you're computing
is possibly (but not necessarily!) affected by aliasing. note that this
warning comes only when needed (i.e., when the chosen TFR has the above
mentioned requirement).

> Does that mean the Hilbert transform of the signal has to be computed 
> before doing the analysis?

it is just a warning. if you know the spectral contents of your signal and 
what you are doing, you can ignore it. it is usually safer to compute the 
TFR with the analytic signal since you can be misled by folded aliasing 
terms.

> This things are missing:
>
> 1) a numerical scale along the colorbar which would give an idea
> of the amplitude attached to a given color
>
> 2) Error bars and et confidence intervals

i agree with the first wish. we'll see how to do that. suggestion and 
patches are welcome.

error bars over TFRs: the second one is much more difficult since error
bars are generally closely related to assumptions on the considered 
signal.

eric.