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Periodic signals

Type of signal	Graph	Absolute mean value	Root Mean Square (RMS)	Waveform factor	Crest factor	Total Harmonic Distortion h₁	Total Harmonic Distortion h₂
Constant signal (DC)		$1$	$1$	$1$	$1$	$-$	$-$
Sine		$\frac{2}{\pi}\approx 0,637$	$\frac{1}{\sqrt{2}}\approx 0,707$	$\frac{\pi}{2\sqrt{2}}\approx 1,11$	$\sqrt{2}\approx 1,414$	$0$	$0$
Sine (full-wave rectification)		$\frac{2}{\pi}\approx 0,637$	$\frac{1}{\sqrt{2}}\approx 0,707$	$\frac{\pi}{2\sqrt{2}}\approx 1,11$	$\sqrt{2}\approx 1,414$	$\approx 0,225$	$\approx 0,219$
Sine (half-wave rectification)		$\frac{1}{\pi}\approx 0,318$	$\frac{1}{2} = 0,5$	$\frac{\pi}{2}\approx 1,571$	$2$	$\approx 0,441$	$\approx 0,404$
Triangle symmetric		$\frac{1}{2} = 0,5$	$\frac{1}{\sqrt{3}}\approx 0,577$	$\frac{2}{\sqrt{3}}\approx 1,155$	$\sqrt{3}\approx 1,732$	$\sqrt{\frac{\pi^4}{96}-1}\approx 0,121$	$\sqrt{1-\frac{96}{\pi^4}}\approx 0,120$
Square symmetric (50% fill)		$1$	$1$	$1$	$1$	$\sqrt{\frac{\pi^2}{8}-1}\approx 0,483$	$\sqrt{1-\frac{8}{\pi^2}}\approx 0,435$
Sawtooth		$\frac{1}{2} = 0,5$	$\frac{1}{\sqrt{3}}\approx 0,577$	$\frac{2}{\sqrt{3}}\approx 1,155$	$\sqrt{3}\approx 1,732$	$\sqrt{\frac{\pi^2}{6}-1}\approx 0,803$	$\sqrt{1-\frac{6}{\pi^2}}\approx 0,626$

What is the meaning of each calculator field ?

Type of signal - the name of the signal, usually comes from the mathematical function that describes the signal (sinusoidal, square etc.).
Graph - graphical representation of the signal in the form of a graph, the graph is normalized to one and shows one period.
Absolute mean value - average value of the signal without sign (absolute value):

$ARV = \frac{1}{T}\int\limits_0^T{|x(t)|dt}$
where:
- T - signal period (e.g. $2\pi$ for sine signal),
- t - time,
- x(t) - signal value in time t.
Root Mean Square (RMS) - The effective value of the alternating current is the value of the direct current, which in the course of time equal to the period of alternating current will cause the same thermal effect as the given AC signal (alternating current). It's statistical value defined as:

$RMS = \sqrt{\frac{1}{T}\int\limits_{0}^{T}\,x^{2}(t)dt}$
where:
- T - signal period (e.g. $2\pi$ for sine signal),
- t - time,
- x(t) - signal value in time t.
Waveform factor - the ratio of the rms value to the mean of the absolute value:

$k_f = \frac{RMS}{ARV}$
where:
- $RMS$ - root mean value (effective value),
- $AVR$ - mean absolute value.
Crest factor - peak (maximum) value to RMS ratio:

$k_c = \frac{X_{max}}{RMS}$
where:
- $X_{max}$ - maximum signal value (peak value),
- $RMS$ - root mean square (effective value).
Total Harmonic Distortion (THD) - a factor determining how much the signal deviates from the sinusoidal signal, defined as:

$h_{1}=\frac{\sqrt{\sum\limits_{n=2}^{\infty}X_{n}^{2}}}{X_{1}}$
or

$h_{2}=\frac{\sqrt{\sum\limits_{n=2}^{\infty}X_{n}^{2}}}{\sqrt{\sum\limits_{n=1}^{\infty}X_{n}^{2}}}$
where:
- $X_1$ - effective value (RMS) of base component,
- $X_n$ - effective value (RMS) of n-th harmonic.

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Tags:

periodic_signals · signal_properties · sine_signal_properties · squre_signal_properties · triangle_signal_properties · sawtooth_signal_properties

Tags to Polish version:

sygnaly_okresowe · wlasciwosci_sygnalu_sinusoidalnego · wlasciwosci_sygnalu_piloksztaltnego · wlasciwosci_sygnalu_trojkatnego · wlasciwosci_sygnalu_prostokatnego

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