Kvadratuurikomponenttiin

Kvadratuurikomponenttiin refers to a concept in signal processing, particularly in the context of analytic signals. It represents the component of a signal that is 90 degrees out of phase with the original signal. When a signal $x(t)$ is transformed into its analytic signal $z(t)$, the analytic signal is typically expressed as $z(t) = x(t) + i \hat{x}(t)$, where $i$ is the imaginary unit and $\hat{x}(t)$ is the Hilbert transform of $x(t)$. In this representation, $x(t)$ is considered the in-phase component, and $\hat{x}(t)$ is the quadrature component.

The Hilbert transform shifts the phase of each frequency component of the original signal by $-\pi/2$ (or $+ \pi/2$ depending on convention). This transformation is crucial for many signal analysis techniques. The analytic signal itself is a complex-valued signal that provides a convenient way to represent both the amplitude and phase of a real-valued signal. The quadrature component, therefore, carries information about the phase variations of the original signal.

Applications of the quadrature component and the analytic signal are found in areas such as amplitude modulation and demodulation, frequency analysis, and the study of narrow-band signals. It allows for a unified description of signal envelope and instantaneous frequency.