Howtosignalprocessing
- How are complex numbers related to sinusoidal signals?
- What is complex sinusoid?
- How do you calculate sinusoidal signal?
- What defines a sinusoid?
How are complex numbers related to sinusoidal signals?
Complex numbers are important in signal processing because we often want, or find it useful, to break a signal down into a bunch of component sinusoids at different frequencies (more on this later, when we get to the DFT and FFT). Each component sinusoid has a magnitude and a phase (see above description of sinusoids).
What is complex sinusoid?
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.
How do you calculate sinusoidal signal?
We imagine a sinusoidal signal y=Y sin ωt, i.e. amplitude Y and angular frequency ω, as being produced by a radial line of length Y rotating with a constant angular velocity ω (Figure 11.2), taking the vertical projection y of the line at any instant of time to represent the value of the sinusoidal signal.
What defines a sinusoid?
A sinusoid is a signal that has a form of a sine wave. The shape of the supply voltage for power distribution is known as a sinusoid as it resembles a sine or cosine waveshape.
