Hello Forum, in AM modulation, a carrier (pure monochromatic signal) is multiplied by the message signal m(t). In angle modulation, the phase or derivative of the phase is modulated according to m(t). In both case we have a real signal. What is the advantage of associating the analytic signal to the real modulated signal? The analytic signal has its imaginary part equal to the Hilbert transform if its real part...Does it have to do with respecting causality? I think the analytic signal should offer an easier way to de-modulated the modulated signal and extract the message m(t). Does it work only in AM or also in PM and FM? Why is it hard to separate the phase and magnitude if we don't use the analytic signal but stick with the real representation of the modulated signal? Any simple example? x(t)= A(t) cos(w*t) is the modulated AM signal.... we just need to detect its envelope to detect m(t).. thanks fisico32
Analytic signal
Started by ●October 30, 2009
Reply by ●October 30, 20092009-10-30
fisico32 wrote:> Hello Forum, > > in AM modulation, a carrier (pure monochromatic signal) is multiplied by > the message signal m(t).Not exactly. An offset is added to the modulating signal to keep it from becoming negative.> In angle modulation, the phase or derivative of > the phase is modulated according to m(t). In both case we have a real > signal.All signals are real. You couldn't measure them otherwise.> What is the advantage of associating the analytic signal to the real > modulated signal?It simplifies the equations.> The analytic signal has its imaginary part equal to the Hilbert transform > if its real part...Does it have to do with respecting causality? > I think the analytic signal should offer an easier way to de-modulated the > modulated signal and extract the message m(t). Does it work only in AM or > also in PM and FM? > Why is it hard to separate the phase and magnitude if we don't use the > analytic signal but stick with the real representation of the modulated > signal? > > Any simple example? > > x(t)= A(t) cos(w*t) is the modulated AM signal....Wrong. You want x(t)= (A(t)+M)*cos(wt), where w is the carrier, and M is a constant equal to or larger than the peak value of A(t). If x(t) is a sinusoid, say cos(w_m) and the carrier is cos(w_c), that becomes (1 + cos(w_m))*cos(w_c)> we just need to detect its envelope to detect m(t)..How would you do that digitally? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●October 30, 20092009-10-30
On Oct 30, 10:40�am, Jerry Avins <j...@ieee.org> wrote:> fisico32 wrote: > > Hello Forum, > > > in AM modulation, a carrier (pure monochromatic signal) is multiplied by > > the message signal m(t). > > Not exactly. An offset is added to the modulating signal to keep it from > becoming negative. > > > � � � � � � �In angle modulation, the phase or derivative of > > the phase is modulated according to m(t). In both case we have a real > > signal. > > All signals are real. You couldn't measure them otherwise. > > > What is the advantage of associating the analytic signal to the real > > modulated signal? > > It simplifies the equations. > > > The analytic signal has its imaginary part equal to the Hilbert transform > > if its real part...Does it have to do with respecting causality? > > I think the analytic signal should offer an easier way to de-modulated the > > modulated signal and extract the message m(t). Does it work only in AM or > > also in PM and FM? > > Why is it hard to separate the phase and magnitude if we don't use the > > analytic signal but stick with the real representation of the modulated > > signal? > > > Any simple example? > > > x(t)= A(t) cos(w*t) is the modulated AM signal.... > > Wrong. You want x(t)= (A(t)+M)*cos(wt), where w is the carrier, and M is > a constant equal to or larger than the peak value of A(t). If x(t) is a > sinusoid, say cos(w_m) and the carrier is cos(w_c), that becomes > � � � � � � � � �(1 + cos(w_m))*cos(w_c) > > > we just need to detect its envelope to detect m(t).. > > How would you do that digitally?One "real" way is to take the absolute value of each sample (digital full-wave rectifier), followed by a low-pass digital filter (FIR or IIR).
Reply by ●October 30, 20092009-10-30
Darol Klawetter wrote:> On Oct 30, 10:40 am, Jerry Avins <j...@ieee.org> wrote: >> fisico32 wrote: >>> Hello Forum, >>> in AM modulation, a carrier (pure monochromatic signal) is multiplied by >>> the message signal m(t). >> Not exactly. An offset is added to the modulating signal to keep it from >> becoming negative. >> >>> In angle modulation, the phase or derivative of >>> the phase is modulated according to m(t). In both case we have a real >>> signal. >> All signals are real. You couldn't measure them otherwise. >> >>> What is the advantage of associating the analytic signal to the real >>> modulated signal? >> It simplifies the equations. >> >>> The analytic signal has its imaginary part equal to the Hilbert transform >>> if its real part...Does it have to do with respecting causality? >>> I think the analytic signal should offer an easier way to de-modulated the >>> modulated signal and extract the message m(t). Does it work only in AM or >>> also in PM and FM? >>> Why is it hard to separate the phase and magnitude if we don't use the >>> analytic signal but stick with the real representation of the modulated >>> signal? >>> Any simple example? >>> x(t)= A(t) cos(w*t) is the modulated AM signal.... >> Wrong. You want x(t)= (A(t)+M)*cos(wt), where w is the carrier, and M is >> a constant equal to or larger than the peak value of A(t). If x(t) is a >> sinusoid, say cos(w_m) and the carrier is cos(w_c), that becomes >> (1 + cos(w_m))*cos(w_c) >> >>> we just need to detect its envelope to detect m(t).. >> How would you do that digitally? > > One "real" way is to take the absolute value of each sample (digital > full-wave rectifier), followed by a low-pass digital filter (FIR or > IIR).Fifty-percent oversampling provides only three samples per carrier cycle. It is not unrealistic to imagine that few samples fall near a carrier peak. The apparent envelope is likely be very distorted then. Greatly oversampling, or interpolating to achieve a high sample rate after the signal has been acquires can overcome that. A Hilbert transform to get the quadrature signal and then calculating the envelope as the sqrt(Im^2+Re^2) is a sounder way Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
