Howtosignalprocessing
A sine wave of frequency f with amplitude r and phase θ is equivalently a complex number rcosθ+irsinθ r cos θ + i r sin θ .
- What is a complex sine wave?
- What is the equation for a sine wave?
- Which relation is used for complex sinusoidal notation?
- How sinusoidal voltage are expressed using complex number?
What is a complex sine wave?
1) The real part of a complex sinusoid is a cosine wave and the imag- inary part is a sine wave. 2) A complex sinusoid x(t) = Ae. jΩt+φ can be visualized in the complex. plane as a vector of length A that is rotating at a rate of Ω radians per second and has angle φ relative to the real axis at time t = 0.
What is the equation for a sine wave?
In its most general form, the sine wave can be described using the function y=a*sin(bx), where: a is known as the amplitude of the sine wave. b is known as the periodicity.
Which relation is used for complex sinusoidal notation?
It is true that eiθ = cos θ + i sin θ. Therefore a complex number z = (A,θ) can be written z = A eiθ .
How sinusoidal voltage are expressed using complex number?
A complex number that is used to represent a sinusoidal voltage or current is called a phasor. The magnitude of the phasor is the same as the maximum value of the sinusoidal waveform, and the phase of the phasor is equal to the phase difference between the sinusoidal waveform and a cosine waveform.
