email@example.com (praveen) writes:
> I am finding the amplitude of the signal using complex demodulation
> (quadrature demodulation). I wanted to know maximum accuracy to
> which the amplitude of the one of the frequency contained in phase
> modulated signal(which is the input) can be estimated. The accuracy
> to which the amplitude obtained should be 10^-8 (between actual and
> estimated by this method). So i wanted to know if there is any
> cramer rao bound (accuracy to which amplitude of the signal can be
> estimated). The SNR of the signal is about 55 to 60 dB.
Kay's book (, page 542) says that the CRLBs for estimating A, f and phi in:
x[n] = A exp( j 2 pi f n ) + complex white Gaussian noise
var(Ahat) >= sigma^2 / ( 2 N )
var(fhat) >= 6 sigma^2 / ( (2 pi)^2 A^2 N (N^2-1) )
var(phihat) >= sigma^2 ( 2 N - 1 ) / ( A^2 N (N + 1) )
where sigma^2 is the complex noise variance, N is the number of
samples of x[n] that you have.
 S. M. Kay, "Fundamentals of Statistical Signal Processing Vol 1:
Estimation Theory", Prentice-Hall, 1993.
Peter J. Kootsookos
"Na, na na na na na na, na na na na"
- 'Hey Jude', Lennon/McCartney