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Properties of periodic signals table
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Properties of periodic signals table
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Table shows properties of common periodic signals (sine, square, triangle etc.) such as absolute mean value, effective value or shape factor.

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Periodic signals

Type of signalGraphAbsolute mean valueRoot Mean Square (RMS)Waveform factorCrest factorTotal Harmonic Distortion h1Total Harmonic Distortion h2
Constant signal (DC)Show source11Show source11Show source11Show source11Show source−-Show source−-
SineShow source2π≈0,637\frac{2}{\pi}\approx 0,637Show source12≈0,707\frac{1}{\sqrt{2}}\approx 0,707Show sourceπ22≈1,11\frac{\pi}{2\sqrt{2}}\approx 1,11Show source2≈1,414\sqrt{2}\approx 1,414Show source00Show source00
Sine (full-wave rectification)Show source2π≈0,637\frac{2}{\pi}\approx 0,637Show source12≈0,707\frac{1}{\sqrt{2}}\approx 0,707Show sourceπ22≈1,11\frac{\pi}{2\sqrt{2}}\approx 1,11Show source2≈1,414\sqrt{2}\approx 1,414Show source≈0,225\approx 0,225Show source≈0,219\approx 0,219
Sine (half-wave rectification)Show source1π≈0,318\frac{1}{\pi}\approx 0,318Show source12=0,5\frac{1}{2} = 0,5Show sourceπ2≈1,571\frac{\pi}{2}\approx 1,571Show source22Show source≈0,441\approx 0,441Show source≈0,404\approx 0,404
Triangle symmetricShow source12=0,5\frac{1}{2} = 0,5Show source13≈0,577\frac{1}{\sqrt{3}}\approx 0,577Show source23≈1,155\frac{2}{\sqrt{3}}\approx 1,155Show source3≈1,732\sqrt{3}\approx 1,732Show sourceπ496−1≈0,121\sqrt{\frac{\pi^4}{96}-1}\approx 0,121Show source1−96π4≈0,120\sqrt{1-\frac{96}{\pi^4}}\approx 0,120
Square symmetric (50% fill)Show source11Show source11Show source11Show source11Show sourceπ28−1≈0,483\sqrt{\frac{\pi^2}{8}-1}\approx 0,483Show source1−8π2≈0,435\sqrt{1-\frac{8}{\pi^2}}\approx 0,435
SawtoothShow source12=0,5\frac{1}{2} = 0,5Show source13≈0,577\frac{1}{\sqrt{3}}\approx 0,577Show source23≈1,155\frac{2}{\sqrt{3}}\approx 1,155Show source3≈1,732\sqrt{3}\approx 1,732Show sourceπ26−1≈0,803\sqrt{\frac{\pi^2}{6}-1}\approx 0,803Show source1−6π2≈0,626\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=1T∫0T∣x(t)∣dtARV = \frac{1}{T}\int\limits_0^T{|x(t)|dt}
    where:
    • T - signal period (e.g. 2π2\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=1T∫0T x2(t)dtRMS = \sqrt{\frac{1}{T}\int\limits_{0}^{T}\,x^{2}(t)dt}
    where:
    • T - signal period (e.g. 2π2\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:
    kf=RMSARVk_f = \frac{RMS}{ARV}
    where:
    • RMSRMS - root mean value (effective value),
    • AVRAVR - mean absolute value.
  • Crest factor - peak (maximum) value to RMS ratio:
    kc=XmaxRMSk_c = \frac{X_{max}}{RMS}
    where:
    • XmaxX_{max} - maximum signal value (peak value),
    • RMSRMS - root mean square (effective value).
  • Total Harmonic Distortion (THD) - a factor determining how much the signal deviates from the sinusoidal signal, defined as:
    h1=∑n=2∞Xn2X1h_{1}=\frac{\sqrt{\sum\limits_{n=2}^{\infty}X_{n}^{2}}}{X_{1}}
    or
    h2=∑n=2∞Xn2∑n=1∞Xn2h_{2}=\frac{\sqrt{\sum\limits_{n=2}^{\infty}X_{n}^{2}}}{\sqrt{\sum\limits_{n=1}^{\infty}X_{n}^{2}}}
    where:
    • X1X_1 - effective value (RMS) of base component,
    • XnX_n - effective value (RMS) of n-th harmonic.

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