Equivalent low-pass signal = complex envelope of band-pass Signal

The equivalent low-pass signal of a band-pass signal refers to the frequency shift of the Equivalent Time-domain signal in the positive frequency domain. (Band-pass signal, first eliminate the negative frequency part, in order to ensure the power remains unchanged, equivalent to the positive frequency part of the power * 2, and then move the positive frequency part to the baseband. This baseband signal corresponds to a complex envelope .)

 

 

A band-pass SignalEnvelopeIt is actually itsEquivalent low-pass Signal.
Band-pass signal S (t), center frequency f0, perform a Hilbert transformation, and get s '(t ).
Resolution signal: s' (t) = S (t) + js' (t); (Equivalent Time-domain signal in positive frequency domain)
The resolution signal can be expressed as s' (t) = S' ''(t) exp (J * 2 * pI * f0 * t)

Then s ''is a complex signal called S's complex envelope
S ''(t) can also be expressed as s ''' (t) exp (J * theta );
S ''' is the real letter, called the envelope of S, and theta is the phase of S.

 

When S is a real-value band-pass signal, because of the Hilbert transformation, s ''is usually a complex signal.

 

 

PS:

It is often said that the output signal of the same phase branch of the orthogonal inverter is regarded as a complex signal consisting of the real and orthogonal branch output signals.Zero Intermediate Frequency Signal. Zero-intermediate frequency is a technology in which the obtained signal is used. Perform orthogonal downconversion on the received signal to obtain the zero-intermediate frequency signal.