How to measure spectral flatness in Matlab?

[omidi_sbu]

what is the measure of spectral flatness?
how can i implement it in matlab?

 

[brmadhukar]

spectral flatness

You measure using ripple.

Find the freq response and then the variance.

 

[purnapragna]

spectral flatness matlab

Spectral Flatness Measure is the ratio of the Geometric mean and the Arithmetic mean of the given signal's power spectrum.

Let the given signal be given by \[x[n]\] and let its power spectrum be given by \[S_x(e^{j\omega)}\], then SFM is given by the formula,

\[SFM = \frac{exp\left[\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}\ln \left\{|S_x(e^{j\omega})|\right\}d\omega\right]}{\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}|S_x(e^{j\omega})| d\omega}\]

You can easily see that the numerator term is the GM and the denominator is the AM of the spectrum.

As GM<AM we can say that the maximum value of \[SFM\] can take is \[1\]. If the spectrum is completely flat, then you see that the numerator is \[1\] and also the denominator is \[1\]. Thus \[SFM\] is also one. Thus we say that the above gives the measure of the flatness of the spectrum and hence the name Spectral Flatness Measure