Fourier transform analysis of 1/f noise index of a gated integrator having a trapezoidal waveform

The step, delta and 1/f noise index of a pulse shaper obtained by the frequency-domain analysis have the same results as those obtained by the time-domain analysis respectively. This fundamental relationship is proved by the method of Fourier transformation of the weighting function of the pulse-shaper filter and is referred to as Parsevalʹs Theorem. Noise indices of a trapezoidal shaper that is composed of a rectangular prefilter and a gated integrator are obtained. The results are compared with those two similar gated integrators having an integrator and a differentiator pre-filter to focus attention on their 1/f noise indices.