Vector signal representation

Vector (or complex) representation is used in vector signal generators to synthesize passband signals.

Passband signals that have a symmetric spectrum (relatively to the carrier frequency ω₀) can be represented as s(t) = A(t) cos(ω₀t+φ), where A(t) is a slowly changing signal which modulates the carrier.

This approach can be extended to arbitrary signals (spectra of which are not necessary symmetric): s(t) = Re[A(t) e^j&omega₀t]. Here A(t) = I(t) + jQ(t) is a function named complex envelope of the passband signal. z(t)=A(t) e^j&omega₀t is a complex signal which have the same spectrum as the original signal for positive frequencies, but doesn't have negative spectrum components.

Vector signal generator main page.

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Vector signal generator website team, 2008-2009.