Sinusoid

The sinusoid (adjective sinusoidal ) is a sinusoidal function derived from the sine function by scaling of amplitude and frequency and phase shifting is formed. It forms the basis of the representation in the frequency domain .

definition

The sinusoid is defined by ${\ displaystyle x}$

{\ displaystyle x \ left (t \ right): = A \ sin {\ bigl (} \ omega t + \ varphi {\ bigr)} + ​​C}

,

in which

${\ displaystyle A}$ the scaling of the amplitude ,
${\ displaystyle \ omega}$ the scaling of the angular frequency
${\ displaystyle \ varphi}$ the phase shift and
${\ displaystyle C}$ the absolute term

is. In electrical engineering , the absolute term is the constant component over time .

cosine

Since one function of the form is also a sinusoid, the other trigonometric functions are not. ${\ displaystyle \ cos \ left (t \ right) = \ sin \ left (t + {\ tfrac {\ pi} {2}} \ right)}$ ${\ displaystyle x \ left (t \ right) = A \ cos \ left (\ omega t + \ varphi \ right) + C}$

Web links

Sinusoid . In: Michiel Hazewinkel (Ed.): Encyclopaedia of Mathematics . Springer-Verlag , Berlin 2002, ISBN 978-1-55608-010-4 (English, online ).