Welch's estimate of the Spectral Kurtosis

The spectral kurtosis decomposes the kurtosis of a signal as function of frequency

The spectral kurtosis (SK) is a fourth-order statistical tool which can indicate the presence of transients and their locations in the frequency domain by "decomposing" the kurtosis of a signal as function of frequency. As such, it helpfully supplements the classical power spectral density.
The matlab function SK_W.m provides the Welch's estimate of the SK.
The following example illustrates its usage for the detection of transients with theoretical spectral content in band [.15 .19]:
load x % synthetic signal provided in the pack
Nw = 2^8;
Nfft = 2*Nw;
Noverlap = round(3/4*Nw);
[SK,M4,M2,f] = SK_W(x,Nfft,Noverlap,Nw);

figure,newplot;
subplot(211),plot(f(1:Nfft/2),M2(1:Nfft/2)),grid on,
xlabel('normalized frequency'),xlim([f(1) f(Nfft/2)]),ylim([0 .1]),title('Power spectrum')
subplot(212),plot(f(1:Nfft/2),SK(1:Nfft/2)),grid on
xlabel('normalized frequency'),xlim([f(1) f(Nfft/2)]),title('Spectral Kurtosis')

As demonstrated in Ref. [2], the square root of the spectral kurtosis is related to the optimal filter (in the mean-square sense) that extracts the transients of interest. This is achieved as follows:

b = fftshift(real(ifft(SK)));
xf = fftfilt(b,x);

figure,newplot;
subplot(211),plot(x,'k'),title('Original signal')
subplot(212),plot(xf,'k'),title('Filtered signal with square root of spectral kurtosis')

References:
[1] J. Antoni, The spectral kurtosis: a useful tool for characterising nonstationary signals, Mechanical Systems and Signal Processing, Volume 20, Issue 2, 2006, pp.282-307.
[2] J. Antoni, R. B. Randall, The spectral kurtosis: application to the vibratory surveillance and diagnostics of rotating machines, Mechanical Systems and Signal Processing, Volume 20, Issue 2, 2006, pp.308-331.