We know that the Probability density function (PDF) of Noise is usually Gaussian. could anyone explain the special statistical features of periodic signal in time or frequency domain ? When I look at the histogram of periodic signal like voiced, It is difficult to judge its PDF.
You can use Fourier analysis when studying periodic signals. A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines. The computation and study of Fourier series is known as harmonic analysis and is extremely useful as a way to break up an arbitrary periodic function into a set of simple terms that can be plugged in, solved individually, and then recombined to obtain the solution to the original problem or an approximation to it to whatever accuracy is desired.
Hello Amir,
First of all, I saw the image you attached. The first figure (1st row) indicates the signal in time domain, which represents the periodicity (I think the period is approximately 50 or the frequency is 0.02). With this assumption, I also guess that the left figure in 2nd row is the power spectrum. Am I right? In addition, the right figure is the histogram.
Secondly, to analyze your histogram, you can use HOSA (Higher Order Statistical Analysis), using HOSA toolbox, which can be easily added to MATLAB. In fact, HOS can be very useful in the analysis of deterministic (periodic and transient) and stochastic signals. You can extract the higher order moments, named skewness and kurtosis to describe your PDF, quantitatively. Skewness statistic is a measure of symmetry of the distribution. A positive skewness represents right tail, while the negative one shows the left tail in the distribution. Moreover, a normal distribution has a zero skewness due to its symmetry. In addition, kurtosis statistic corresponds to the degree of peakedness of a PDF. Positive kurtosis indicates a peaked distribution, while a negative one shows the flattened distribution. Like skewness, a normal distribution has a zero kurtosis. Moreover, you can use Gaussianity test (glstat command). Additionally, in frequency domain you can utilize ‘harmest’ command to estimate the power spectrum with different methods. You can also use ‘bispeci’ command to estimate the bispectrum, … .
Although this toolbox is very useful, you can also import your data into a statistical software, for example SPSS. This software has the facilities to calculate skewness and kurtosis and also to test for normality (Kolmogorov-Smirnov test) and other well known distributions.
All in all, I suggest to study HOSA toolbox manual by Swami, Mendel and Nikias, specially case study section (page 108), which is about the analysis of a periodic (sunspot) signal in time and frequency domain.
Furthermore, with a short glance to the histogram of your signal, we do see that the distribution is not unimodal. So, another important problem is how to estimate the true PDF of the signal. This is a pattern recognition problem, and there are some choices to answer, for example KNN method. For detailed information, you can study pattern classification book by Duda, Hart and Strok.
Hope this information be useful to you.
Kind regards,
Fariba
Thanks for your best answer. The left figure in 2nd row is the ksdensity (MATLAB command). Actually I read the paper that said the speech PDF is Laplacian and silence part is Gaussian but I could not see laplacian PDF. Could you please help me about it ?
Dear Amir,
In fact, speech signals have high diversity. Thus, it is not surprising to see a kind of speech signal, which does not have a well known distribution (Normal, Uniform, Poisson, Exponential or Laplacian, …). I believe that it is case dependant. Furthermore, data length (number of samples) also affects the estimation of a PDF.
Any way, I'd be glad to analyze your data and extract some features from your signal in time and frequency domain and also analyze your PDF, if you send me your whole data completely in ‘.wma’ or ‘.wav’ format, of course if you want.
In addition, ‘ksdensity’ command in MATLAB, uses Gaussian kernel as default.
My email: [email protected]
Best wishes,
Fariba
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