Dear ResearchGate community,
I am currently working on a MATLAB project involving Multisynchrosqueezing and S Transform for the analysis of signals, particularly focusing on the Ricker waveform at 30 Hz. However, I am encountering a puzzling issue where the observed frequency in the time-frequency representation (TFR) does not match the expected frequency, showing values around 26 or 27 Hz.
Why is there a discrepancy between the expected and observed frequencies in the time-frequency representation?
What factors could contribute to this frequency displacement, especially when analyzing spiky signals like the Ricker waveform?
Are there alternative methods or modifications that could enhance the accuracy of time-frequency representation and reconstruction for spiky signals?
There are several reasons why there may be a discrepancy between the expected and observed frequencies in the time-frequency representation. These include:
- Noise: Noise is always present in real-world signals, and it can cause the observed frequencies to differ from the expected frequencies.
- Interference: Interference from other signals can also cause the observed frequencies to differ from the expected frequencies.
- Non-stationarity: Many real-world signals are not stationary, meaning that their frequency content changes over time. This can cause the observed frequencies to differ from the expected frequencies.
- Model error: The time-frequency representation model itself may be inaccurate, which can also cause the observed frequencies to differ from the expected frequencies.
In general, the discrepancy between the expected and observed frequencies in the time-frequency representation is an indication that there is some underlying structure or process that is not captured by the model. This can be a valuable clue for understanding the signal.
Here are some specific examples of discrepancies between expected and observed frequencies in the time-frequency representation:
- In a musical signal, the observed frequency of a note may be slightly different from the expected frequency due to vibrato or other effects.
- In a speech signal, the observed frequency of a phoneme may be different from the expected frequency due to coarticulation or other effects.
- In an image, the observed frequencies of edges and other features may be different from the expected frequencies due to noise or other artifacts.
The discrepancy between expected and observed frequencies can be quantified using a variety of measures, such as the mean square error (MSE) or the signal-to-noise ratio (SNR). These measures can be used to evaluate the performance of the time-frequency representation model.
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