Sinusoid with unknown frequency

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

V_in(t) = V_Asin(ωt). (12)

Let v_in(s) be the Laplace transform of V_in(t) . If the transfer function in the Laplace domain from the input of the filter to the output of integrator i is f_i :

$${\frac{{x_i(s)}}{{v_{\hbox{in}}(s)}}}$$ (13)

the amplitude of the signal at the output of this integrator will be

| x_i(jω)| = | f_i(jω)| V_A (14)

Let the maximum output signal amplitude at the output of any integrator be V_max . The maximum filter input amplitude V_{max, in} is then:

$${\frac{{V_{\hbox{max}}}}{{\max_{i, \omega}\vert f_i(j\omega)\vert}}}$$ (15)

and the maximum filter output signal level is

$$\max_{\omega}^{}$$ (16)

The mean-squared maximal output level is

$$\overline{{V_{\hbox{max,out}}^2}} {\frac{{V_{\hbox{max,out}}^2}}{{2}}}$$ (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.