Here are some sources would fit your problem,

Also, ANSYS  FLUENT  tutorial in the chapter of 'solvers'  has some information about simulation in PISO under different circumstances. 

Timlelt, what is CFD BFD? Anyway, you can use an extended Kalman filter to estimate the magnitude and frequency in real time. There are a number of papers. The estimation error strongly depends on the measurement noise. If SNR is low, then the estimation noise can be large. The estimate variance Var_est lower bound can be found as Var_in/N, where N is the number of samples on 1/4 of period T of a harmonic signal and Var_in is the variance of the measurement noise.

Have you ever considered WAVLET TRANSFORM?

Dear Timlelt Hakima, Start thinking that how we analyze transients. There are many techniques to deal with such kind of situations.

Time varying frequencies are hard to track in low SNR regime. Are you already filtering the extra noise if u know roughly what is the frequency range of ur signal?

Hi,

Thanks a lot for your answers,

@Peter Husar : My signal is an acoustic signal sampled at 44100 Hz so the number of DATA to be analyzed become important very rapidly and the time cost of the time frequency distribution become very huge. I went to implement a real time algorithm.

@Yuriy Shmaliy : CFD (central finite difference ) and BFD (backward finite difference ).

I think that the EKF ( extended Kalman filter) is the more adapted for my signal. Please would you give some reference paper of this method.

I have an acoustic Doppler effect as a signal and I want to extract the instantaneous frequency and use it for future processing, my problems are :

1- I have a huge Data

2- the estimation must be real time.

3- Signal to noise ratio is very low.

Hakima

Timlelt, I do not have a proper paper in hands, but you can find it in the Internet. Hope you are aware of the state space. So, the 1st state should be your mono (harmonic) signal. The 2nd state is the magnitude. The 3rd state is the frequency. This is a clue. In papers, you may find more sophisticated models. If you have a measurement of the 1st state, you may then apply the EKF straightforwardly.

@ Yuriy Shmaliy:

Do you recommend a kind of IEEE-1057-like algorithm with a sliding analysis window where each iteration in your Kalman filter corresponds to a time-shift of the analysis window?

@ Timlelt Hakima:

You have already opened a thread on this subject:

https://www.researchgate.net/post/MATLAB_code_for_instantaneous_frequency

What results did you get with the algorithms featured there?

What do you name "low SNR"? -10dB? 0dB?

Regards,

Nico

Sorry, Nico, I do not know what is the IEEE-1057 algorithm.

IEEE-1057 is a sine wave fit algorithm with a unknown parameter vector:

http://www.ee.kth.se/php/modules/publications/reports/2000/IR-S3-SB-0009.pdf

If you apply it on a sliding window, you get a time-dependent state space. I find your idea of EKF and state space quite similar and perhaps easier to implement.

Regards,

Nico

Hi,

Nicolas : thanks a lot for your suggestion, exact I asked the same question before. I implemented the LMS and RLS methods ( the main idea of these methods is to update the coefficient of p order filter by using the gradient descent for each iteration and estimate the frequency by taking the peak of the filtered signal's FFT ). the obtained results are good but still sensitive to the noise.

@ Yuriy Shmaliy your idea is more interesting, I implemented the EKF with a state vector (phase, first derivative of the phase (frequency) , and the second derivative of the phase ) I can estimate all these parameters at the same time and for each new data (real time) but as you have mentioned before the estimation variance become important for low SNR, some of my experimental signals have an SNR (-10 to 0 dB).

Is there a possibility to improve the filter's estimation?

Regards

Kim

Timlelt, if you know the noise statistics exactly, then the EKF may be a good choice. Otherwise, try the counterpart of the EKF - the iterative EFIR filter (Kalman-like) which ignores the noise statistics [Suboptimal FIR filtering of nonlinear models in additive white Gaussian noise, IEEE Trans. Signal Process., 60(10), 5519–5527, 2012]. Note that if the nonlinearity is large and noise is large (as in your case), both filters may diverge. Seems that your state model is linear and observation is nonlinear. Is not it?

Hi Nico and sorry that I´ve missed your question...

I took a look at this report and have two comments: 1) The least squares (Gauss´s approach) implemented in (6) is associated with FIR filtering, whereas the Kalman filter is IIR. 2) The counterpart of the Kalman filter associated with (6) is the unbiased FIR filter. The difference between the Gauss and unbiased FIR estimators is that the FIR one uses both the state and observation equations, whereas the Gauss´s approach relies only on measurements. The unbiased FIR and Kalman are thus more universal. They produce very closely related estimates. But, the unbiased FIR filter does not require the noise statistics (!!!). Both have extended versions for nonlinear problems.

Timlelt, instantaneous frequency may be estimated directly in time domain.

By using Parseval Theorem we can obtain a corresponding equation to compute the average instantaneous frequency directly in the time domain. Take a look at equation 17 and the steps of the algorithm for direct computation of the average instantaneous frequency, in the paper:

https://www.researchgate.net/publication/259678988_High-resolution_time_frequency_analysis_using_Wigner-Ville_distribution_and_the_maximum_entropy_method_application_for_gas_and_hydrates_identification?

https://www.researchgate.net/publication/259496853_Instantaneous_frequency_and_Wigner-Ville_distribution_using_the_maximum_entropy_method_Application_for_gas_and_hydrates_identification?ev=prf_pub

Conference Paper High-resolution time frequency analysis using Wigner-Ville D...

Conference Paper Instantaneous frequency and Wigner-Ville distribution using ...

Here are some sources would fit your problem,

Also, ANSYS  FLUENT  tutorial in the chapter of 'solvers'  has some information about simulation in PISO under different circumstances. 

Here are some sources would fit your problem,

Also, ANSYS  FLUENT  tutorial in the chapter of 'solvers'  has some information about simulation in PISO under different circumstances.