3. Baseband and passband signals Flashcards
Energy of a signal formula
Integral of magnitude of signal function squared
Power of a signal formula
Given by the time average of energy, computed over a large interval T.
i.e. 1/T times the energy integral, with with bounds of T/2
Energy of a sinusoid Acos(2pift + theta)
(A^2)/2
What is a conjugate symmetric signal
A signal where if the real part is an even function, and imaginary part is an odd function
What is the use of the in-phase and quadrature-phase component signals in terms of modulation?
A passband signal can be modulated separately using a sine and cosine signal.
Formula of a modulated signal in terms of in-phase and quadrature components?
U(t) = Ui(t)cos(2pifct) - Uq(t)sin(2pifct)
Why are the in-phase and quadrature signals useful in regards to up-conversion and down-conversion?
Since these signals are orthogonal, they can be modulated and demodulated without any loss of information via up-conversion and down-conversion.
What is required at the receiver for down conversion?
Receiver must use coherent demodulation, multiply by 2cos(wt) for Ui(t) and 2sin(wt) for Uq(t), then use a LPF
What are the three representations of a passband signal (hint in terms of Ui(t) and Uq(t))?
Rectangular coordinates: I and Q
Polar coordinates: envelope + phase U~(t) = e(t)e^(jtheta(t))
Complex number: complex envelope U~(t) = Ui(t) + jUq(t)
How can the time domain expression for a passband signal be obtained from its complex expression?
U(t) = Re {U~(t)e^(jwt + theta(t))}
What is the formula of the Hilbert transform?
U^(t) = 1/pi x int(over infinity) {u(tau)/t-tau}dtau
U^(f)=-jsgn(f)U(f)
What is the Hilbert transform of G^(t)?
G(-t)
What is the pre-envelope used for?
Used to remove negative frequencies (U+(t)) or positive frequencies (U-(t))
