Hello, 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. waiting for reply with regards praveen

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7/14/2003 4:39:48 PM

praveenkumar1979@rediffmail.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 ([1], 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 are: 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. [1] S. M. Kay, "Fundamentals of Statistical Signal Processing Vol 1: Estimation Theory", Prentice-Hall, 1993. Ciao, Peter K. -- Peter J. Kootsookos "Na, na na na na na na, na na na na" - 'Hey Jude', Lennon/McCartney

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7/15/2003 8:07:35 AM

"Peter J. Kootsookos" <p.kootsookos@remove.ieee.org> wrote > Kay's book ([1], 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 D'oh, I left out phi.... this should read something like: x[n] = A exp( j ( 2 pi f n + phi ) ) + complex white Gaussian noise -- Peter J. Kootsookos "Na, na na na na na na, na na na na" - 'Hey Jude', Lennon/McCartney

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7/15/2003 9:15:44 AM