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Sinusoid with unknown frequency

A very popular assumption is that the input signal is a sinusoid with unknown frequency. In the time domain:

Vin(t) = VAsin(ωt). (12)
Let vin(s) be the Laplace transform of Vin(t) . If the transfer function in the Laplace domain from the input of the filter to the output of integrator i is fi :

fi(s) = $\displaystyle {\frac{{x_i(s)}}{{v_{\hbox{in}}(s)}}}$, (13)
the amplitude of the signal at the output of this integrator will be

| xi()| = | fi()| VA (14)
Let the maximum output signal amplitude at the output of any integrator be Vmax . The maximum filter input amplitude Vmax, in is then:

Vmax, in = $\displaystyle {\frac{{V_{\hbox{max}}}}{{\max_{i, \omega}\vert f_i(j\omega)\vert}}}$ (15)
and the maximum filter output signal level is

Vmax, out = Vmax, in$\displaystyle \max_{\omega}^{}$(| H()|). (16)
The mean-squared maximal output level is

$\displaystyle \overline{{V_{\hbox{max,out}}^2}}$ = $\displaystyle {\frac{{V_{\hbox{max,out}}^2}}{{2}}}$ (17)

FA will use this assumption to calculate the maximum output signal level and the dynamic range if the scale_inf flag is set by

set: scale_inf
This is the default.


next up previous contents
Next: Wide-band signal Up: Maximum Signal Level Previous: Maximum Signal Level   Contents
2009-06-03