Bispectrum Indirect FFT method

1. Mostly, the bispectrum were computed using the indirect FFT method (I hope I am right) ([bspec, waxis] = bispeci(y, nlag, samp_seg, overlap, flag, wind)). Here, I do not understand what “nlag” specifies. In the toolbox, it is mentioned as “number of cumulant lags to be computed”. Also I do not understand the term “flag” (biased or unbiased). Can you please explain with an example? How to set these parameters? Apart from default window, is there any way to do our analysis with other windows (e.g., hanning)?

Answer 1

[Wayne King]

This function estimates the bispectrum by first estimating the third-order cumulants of the random process, x(t), which is formally

E\{x*(t)x(t+k)x(t+l)\}

The asterisk denotes complex conjugation. k and l are lags.

'biased' (the default) means that the average in the expectation is obtained by dividing by the number of samples 'unbiased' means the average in the expectation is obtained by dividing by the number of samples-1

Look at biased vs. unbiased estimates in statistics and you'll see where that comes from. I would recommend using 'biased' in this case for the same reasons you should use biased in the autocorrelation sequence estimates. This is well documented in the literature.

Without the application of a smoothing window, the bispectrum estimate is an inconsistent estimator of the true bispectrum. The nlags parameter determines how many samples are used in the smoothing window. I would start with approximately 1/4 of your input time series length as a first pass.

[Yuvaraj]

Thank u for ur answer. Now i understand clearly. Apart from applying default window (eg.Parzen window), is it possible to any other window (e.g., hanning). I have tried like this:([bspec, waxis] = bispeci(y, 128, 512, 50, biased, hanning(64) )); Is this is the correct way to calculate bispectrum using hanning window?

Look forward for our reply..!!!