Thread Subject: From instantaneaous frequency to analytical signal

Hello everyone,

I am trying to develop a dictionnary of signals to use it in an application.

To create these signals :
-I draw a Time-Frequency representation in a figure.
-I choose some points in these axes.
-I get a vector with the time and frequency coordinates.
-I interpolate these coordinates.

Now, I want to use these instantaneaous frequencies to create a monocomponent analytical signal.

My problem is that the spectrogram of the signal is not similar to what is drawn in my Time-Frequency representation.

Any ideas?
(It's a small part of a student project so I can ignore it but I think it could be useful for next time)

I am allowed to post code in File exchange if it works !
                          

"Nicolas " <cusseani@ensieta.fr> wrote in message
news:gumn02$ep3$1@fred.mathworks.com...
> Hello everyone,
>
> I am trying to develop a dictionnary of signals to use it in an
> application.
>
> To create these signals :
> -I draw a Time-Frequency representation in a figure.
> -I choose some points in these axes.
> -I get a vector with the time and frequency coordinates.
> -I interpolate these coordinates.
>
> Now, I want to use these instantaneaous frequencies to create a
> monocomponent analytical signal.
>
> My problem is that the spectrogram of the signal is not similar to what is
> drawn in my Time-Frequency representation.
>
> Any ideas?
> (It's a small part of a student project so I can ignore it but I think it
> could be useful for next time)
>
> I am allowed to post code in File exchange if it works !
>

If I understand you right, I do not think you can.

Spectrogram does not contain phase information. So it is one-to-many
mapping, i.e. many analytical signals can generate same spectrogram by
changing the phase of such signals which all having the with same |G(w)|

--Nasser

Yes, you're right. But I thought I could create a signal of the form

for k = 1 : length(t),
    x(k)=a(k).*cos(2*pi*fk*tk);
end
where tk and fk are the coordinates I get when I clicked on a point in my time-frequency plane (Spectrogram).

But when I look at the spectrogram I get in Adobe Audition, I see a lot of straight lines.
Each frequency fk is in the signal for all tk.

It's look like x(t) = a1*cos(2*pi*f1*t)+a2*cos(2*pi*f2*t)+...

Now, I am trying to convoluate each cosine with a window located in time, but I am not really sure it's a good thing for the localization of my instantaneous frequency.

The main idea of my project is:
- 1) to create a signal depending on some time-frequency conditions
- 2) to code-decode the signal with my simulator (already done in Matlab)
- 3) to compare the spectrogram of a signal before and after the simulator.

Perhaps there is an other software than Matlab to do 1 and 3 ?