Hi, i have a big problem, i need to calculate Instantaneous frequency
(IF) using fft (Fast Fourier Transform) and STFT (Short Time Fourier
Transform). I have a discrete sinusoidal signal:
n=1:1024;
omega=0.2;
X=exp(j*omega*n);
To calculate clear signal IF using fft i should find max(fft(X)) and
that would be the IF. the quetsion is, would be the IF=0.2? Becouse
this is a discrete signal what should be the IF value and how to
obtain it? For the STFT calculation I have the window width of 0.25.
Should the IF obtaind using fft and STFT be the same? Should I
calculate the IF using STFT like max(max(SPEC(X))/1024. (SPEC is
spectrogram SPEC=(abs(STFT).^2);
So please, could you show me how to calculate the true IF using fft
and STFT on the clear signal X. So i could in the same way calculate
the IF from the noised signal X and to estimate that the obtained IF
value. that value should be close to the IF value from the clean
signal.
Thank you very much
calculating Instantaneous frequency (IF) using fft
Started by ●March 2, 2008
Reply by ●March 3, 20082008-03-03
I think that you have a bit of confusion.
First of all:
if omega = 2*pi*fo where fo is the frequency of the sinusoidal signal,
what you call n is in effect time t. (the argument of a function must be a
number)
For simplicity, you can transform your exponential like
exp(j*2*pi*fo) = cos(2*pi*fo) + j sin(2*pi*fo)
Now you can analyze the signal in traditional way.
Respect all the constrain of the FFT (dt -> FMAX; 1/T -. df) to obtain a
right result.
Probably you don't need also to respect a FFT with analytical amplitude: you
are looking
only for max so you do not have problem of normalization.
If you are interesting look at
http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectIdV54&objectType=file
About the STFT I cannot help you
Good luck
Bye
On Sat, Mar 1, 2008 at 4:17 PM, marko_jnk wrote:
> Hi, i have a big problem, i need to calculate Instantaneous frequency
> (IF) using fft (Fast Fourier Transform) and STFT (Short Time Fourier
> Transform). I have a discrete sinusoidal signal:
> n=1:1024;
> omega=0.2;
> X=exp(j*omega*n);
>
> To calculate clear signal IF using fft i should find max(fft(X)) and
> that would be the IF. the quetsion is, would be the IF=0.2? Becouse
> this is a discrete signal what should be the IF value and how to
> obtain it? For the STFT calculation I have the window width of 0.25.
> Should the IF obtaind using fft and STFT be the same? Should I
> calculate the IF using STFT like max(max(SPEC(X))/1024. (SPEC is
> spectrogram SPEC=(abs(STFT).^2);
>
> So please, could you show me how to calculate the true IF using fft
> and STFT on the clear signal X. So i could in the same way calculate
> the IF from the noised signal X and to estimate that the obtained IF
> value. that value should be close to the IF value from the clean
> signal.
>
> Thank you very much
>
>
>
First of all:
if omega = 2*pi*fo where fo is the frequency of the sinusoidal signal,
what you call n is in effect time t. (the argument of a function must be a
number)
For simplicity, you can transform your exponential like
exp(j*2*pi*fo) = cos(2*pi*fo) + j sin(2*pi*fo)
Now you can analyze the signal in traditional way.
Respect all the constrain of the FFT (dt -> FMAX; 1/T -. df) to obtain a
right result.
Probably you don't need also to respect a FFT with analytical amplitude: you
are looking
only for max so you do not have problem of normalization.
If you are interesting look at
http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectIdV54&objectType=file
About the STFT I cannot help you
Good luck
Bye
On Sat, Mar 1, 2008 at 4:17 PM, marko_jnk wrote:
> Hi, i have a big problem, i need to calculate Instantaneous frequency
> (IF) using fft (Fast Fourier Transform) and STFT (Short Time Fourier
> Transform). I have a discrete sinusoidal signal:
> n=1:1024;
> omega=0.2;
> X=exp(j*omega*n);
>
> To calculate clear signal IF using fft i should find max(fft(X)) and
> that would be the IF. the quetsion is, would be the IF=0.2? Becouse
> this is a discrete signal what should be the IF value and how to
> obtain it? For the STFT calculation I have the window width of 0.25.
> Should the IF obtaind using fft and STFT be the same? Should I
> calculate the IF using STFT like max(max(SPEC(X))/1024. (SPEC is
> spectrogram SPEC=(abs(STFT).^2);
>
> So please, could you show me how to calculate the true IF using fft
> and STFT on the clear signal X. So i could in the same way calculate
> the IF from the noised signal X and to estimate that the obtained IF
> value. that value should be close to the IF value from the clean
> signal.
>
> Thank you very much
>
>
>
Reply by ●March 4, 20082008-03-04
I have the problem of calculating the likelihood ratio
test. How can i calculate the treshold?
Consider the following hypothesis-testing problem.
There are K independent observations.
HI : ri is Gaussian, N(0, sigmal), i = 1, 2, . . . ,
K,
HO: ri is Gaussian, N(0, sigma0), i = 1, 2, . . . , K,
where sigma1>sigma0.
1. Compute the likelihood ratio.
2.What is the threshold for the minimax criterion when
CM = CF and Coo = Cl1 = O?
when i calculale Pr|H1(R|H1)/Pr|H0(R|H0) should it be
Likelihood ratio test? what value is treshold? is that
value 'ni'? and how to calculate value 'gama'? i read
in theory about ni, ln(ni) and gama.
I need this explanation because i have to solve the
next problem:
In the matlab file example10.mat is given 100
realisations of the random process r. It is given that
K, sigma0=1 and sigma1=2. i have to analyse cases:
a) when CM1, and C00=0
b) when CM=1, CF, C00=0
so i need to find minimax test.
in the attachment I am sending you the problem.
I think this is not very hard for people who knows but
for me.. thank you for your time. If my question is
too confuse please note me and i will try to be more precise.
test. How can i calculate the treshold?
Consider the following hypothesis-testing problem.
There are K independent observations.
HI : ri is Gaussian, N(0, sigmal), i = 1, 2, . . . ,
K,
HO: ri is Gaussian, N(0, sigma0), i = 1, 2, . . . , K,
where sigma1>sigma0.
1. Compute the likelihood ratio.
2.What is the threshold for the minimax criterion when
CM = CF and Coo = Cl1 = O?
when i calculale Pr|H1(R|H1)/Pr|H0(R|H0) should it be
Likelihood ratio test? what value is treshold? is that
value 'ni'? and how to calculate value 'gama'? i read
in theory about ni, ln(ni) and gama.
I need this explanation because i have to solve the
next problem:
In the matlab file example10.mat is given 100
realisations of the random process r. It is given that
K, sigma0=1 and sigma1=2. i have to analyse cases:
a) when CM1, and C00=0
b) when CM=1, CF, C00=0
so i need to find minimax test.
in the attachment I am sending you the problem.
I think this is not very hard for people who knows but
for me.. thank you for your time. If my question is
too confuse please note me and i will try to be more precise.