As an approximation to the integrate-and-dump detector in Figure 9.3(a), we replace the integrator with a low pass RC filter with frequency response function 

where f₃ is the 3-dB cut off frequency 

Figure 9.3(a)

(a) Find s₀₂, (T) / E{n²₀(t)}, where s₀(T) is the value of the output signal at t = T due to +A being applied at t = 0, and n₀ (t) is the output noise. (Assume that the filter initial conditions are zero.)

(b) Find the relationship between T and f₃ such that the signal-to-noise ratio found in part (a) is maximized. (Numerical solution required.)

H(f) = 1+ j(f/f3) t = to + T to + T ()dt () Threshold device > 0: choose +A < 0: choose A (a)