A sinusoidal signal is a signal (Onde) of which the amplitude, observed at a precise place, is a sinusoidal function of time.

• the function sine is a function which makes it possible to calculate the sine of an angle starting from the value of this angle.

• a sinusoid is the form which this function takes (see Figure 1).

Examples

The amplitude of the signal can correspond to a Pression (its), to a displacement (cord which vibrate), to a quantity of electron S in displacement (Electric current) or to an electromagnetic wave.

The importance of the sinusoidal signals is still increased by the fact that any periodic size can all in all break up sinusoidal terms using the decomposition into Fourier series.

Characteristics of a sinusoidal signal

A sinusoidal signal is characterized by its maximum amplitude and its Fréquence. It can be put in the form:

$g\; (T)\; =\; \backslash \; hat\; G.\; \backslash \; sin\; (\backslash \; Omega\; T\; +\; \backslash \; varphi)\; \backslash ,$,

with:

$g\; (T)\; =\; \backslash \; hat\; G\; \backslash ,$: Amplitude of the size, also called peak value.

$\backslash \; Omega\; \backslash ,$: pulsation of the size in rad/s

$(\backslash \; Omega\; T\; +\; \backslash \; varphi)\; \backslash ,$ instantaneous phase in radians

$\backslash \; varphi\; \backslash ,$ phase at the origin in radian (often fixed by the experimenter)

When one compares two of the same signals frequency, it is necessary to indicate how long they are shifted. One speaks then about Déphasage.

                                                       

• One says that the signals are “in phase” if they are superimposed.

• the figure 2a represents signals out of phase of 90°.
• the figure 2b represents signals in “opposition of phase”: out of phase of 180°.

Dephasing results by a simple rule from 3 from the temporal shift separating the two signals. Indeed, 0° (or 0 radian) corresponds to 0 second of dephasing and 360° (or 2 π radians) corresponds to one period shifted signals (T), they are then again in phase. If one calls τ the temporal shift between the signals, one can write:

in degrees: $\backslash \; Delta\; \backslash \; varphi\; =\; \backslash \; frac\; \{360\; \backslash \; cdot\; \backslash \; tau\}\; \{T\}$

in radians: $\backslash \; Delta\; \backslash \; varphi\; =\; \backslash \; frac\; \{2\; \backslash \; pi\; \backslash \; cdot\; \backslash \; tau\}\; \{T\}$

Arithmetic operations with the sinusoidal sizes

In order to carry out the operations of addition or subtraction of sinusoidal sizes, one uses the Représentation of Fresnel or the Transformation complexes

See too

sinusoidal

Related articles

• Phase
• Dephasing
• Bernard Forest de Bélidor

Simple: Sine wave

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