in general $\Delta \mu^j$ is not small.

Let the data vector be $${\bf x} = \check A {\bf h}(\check \mu^j) + {\bf n},$$ where $\check A$ is the amplitude of the signal and $\check \mu^j$ are the remaining parameters. We have separated the amplitude as it occurs in the signal as just a scale factor multiplying the signal. The SNR is defined as, $$\label{SNR}
\rho =  \left\langle{\bf s}(\check{\bbox{\mu}}),{\bf 
s}(\check{\bbox{\mu}})\right\rangle^{1/2} = {\check A}.$$ From eqs. (\[FT\]) and (\[scal\]) we see that the SNR is equal to the amplitude parameter of the signal, $\check A$.

When we consider an ensemble of noise realisations, the $c(\mu^j)$ becomes a random variable. For a fixed set of parameters $\mu^j$, $c(\mu^j)$ is a Gaussian random variable since it is a linear function of the noise (eqn. (\[cor\]). The process of maximization over the parameters is however a nonlinear process and hence the statistics of $c(\mu^j)$ will be non-Gaussian. For a given realization of noise, we assume that the global maximum of $c(\mu^j)$ will also be a local maximum. This assumption depends on the specific nature of the waveform and the filter bank. The equations which will be satisfied at the estimated parameters $\mu^j={\hat\mu^j}$, are, $$\begin{aligned}
\label{m1}
