I understood the mathematical meanings of the skewness and kurtosis. But when we calculate these quantities for a signal (say an electrical voltage signal), what physical meaning do they convey?
For e.g. I understood mean as the DC component of the signal.
If the mean of the data is made 0, and then if we find the value of variance it is similar to the energy of the signal, the standard deviation is equivalent to the RMS value.
Then what about skewness and kurtosis, what do they physically signify?
Best Answer
Those words which are used to describe statistical distributions - how they differ from the Gaussian bell curve - are not common when one wants to describe with words how a pulse looks in an oscilloscope. That's because elecric circuits can have even much more complex forms of voltages vs. time, there's no "normal pulse form".
If you have a noise signal and you are not interested in its exact voltage vs. time form, but how the voltage values are statistically distributed you, of course, can have originally a Gaussian distribution, but some nonlinear - say diode or transistor - circuit can distort the signal so that the distribution curve has skew. The nolinearity simply multiplies the voltage with a number which depends in a regular way on the voltage.
An example:
In an audio amplifier the negative side of the push-pull output stage has become quiet. It doesn't prevent the positive side working. A Gaussian noise input signal comes out so that all negative values are clipped to zero. Quite a bad skew!
Kurtosis can as well be caused by nonlinearity or there's a fault or interfering signal which occurs as not so usual values time after time so that the distibution pattern becomes wider or narrower than what belongs to the expected noise.
Examples of kurtosis:
An audio system outputs Gaussian noise because there's no actual signal, but the non-ideal components add some Gaussian noise. Then there's some strong interfering sparking device nearby which causes randomly strong sharp peaks to the audio circuit. Every spark creates a loud snap to the output. It stretches the tails of the distribution.
A bad connection which occurs randomly can lift near zero values more common than what belongs to the noise. But as well it can cause the same as an interfering impulse noise. The effect of a bad connection depends radically on its place in the circuit.
Statistical analysis is a cornerstone of the math behind successful communication system designs. Noise distribution analysis is not a common fault searching method because deterministic test signals generally are available. Noise distribution analysis can be useful to find what causes the noise which in electronics is generally something unwanted or how to prevent the noise causing too much communication errors.