Hilbert transform and SSB power??

I have a question on the power of SSB (Single side band) AM.

if transmitted signal is expressed as: 
 
u(t)=Ac*m(t)*cos(2pi*fc*t) plus minus Ac*H[m(t)]*sin(2*pi*fc*t),

Ac=carrier amplitude, fc=carrier frequency, m(t)=message signal, and
H[m(t)] is Hilbert transform of m(t). What is the equation for
received power (Pr) in terms of power of message signal (Pm)?

Some books say Pr=[(Ac^2)*Pm]/4, but other books say Pr=(Ac^2)*Pm.  
Which is right??

Thanks for the help.  This problem is really killing me. =)

Bob wrote:

> I have a question on the power of SSB (Single side band) AM.
> 
> if transmitted signal is expressed as: 
>  
> u(t)=Ac*m(t)*cos(2pi*fc*t) plus minus Ac*H[m(t)]*sin(2*pi*fc*t),
> 
> Ac=carrier amplitude, fc=carrier frequency, m(t)=message signal, and
> H[m(t)] is Hilbert transform of m(t). What is the equation for
> received power (Pr) in terms of power of message signal (Pm)?
> 
> Some books say Pr=[(Ac^2)*Pm]/4, but other books say Pr=(Ac^2)*Pm.  
> Which is right??
> 
> Thanks for the help.  This problem is really killing me. =)

Do the math for m(t) = 1, keeping in mind that H[m(t)] = 0.  Then you'll 
know.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com