136). 5.7.4 Practical application: computing oscillator phase noise spectra The theory above relates the stochastics of an injected stationary noise process u(T) to that of an oscillator's random phase behavior. In a next step, we need to figure out the impact this random phase behavior has on the PSD of the oscillator's output signal, i.e. on its phase-noise spectrum. The ultimate goal is to determine the relation between the PSD of the input noise process u(t) and the phase-noise spectrum. In [Vana03c], we present a semi-analytic method to do SO. For input noise processes that vary sufficiently fast over time, we derived an analytic expression. For cases that do not satisfy these conditions, we developed a numerical algorithm that computes corrections to this ex- pression. These corrections mainly concern the shape of the very-close-in phase-noise 5.7.4 Practical application: computing oscillator phase noise spectra spectrum. Either way, the computation of the oscillator's entire phase-noise spectrum is accomplished in only a few minutes. This is a huge improvement over methods that rely on lengthy simulations and a numerical discrete Fourier transformation. Moreover, our work in [Vana03c] allows the accurate computation of the very-close-in phase-noise spectrum, i.e. for frequency offsets down to a few Hz and below. In what follows, we summarize the main results. For details, we refer to [Vana03c]. The phase noise spectrum Sx.k(Af) near the k-th harmonic of an oscillator's output signal is related to the stochastic phase behavior described by (5.126) and (5.133) by means of the equation14 (5.138) Here, Af is the frequency offset to the k-th harmonic frequency kfo. Furthermore, the Fourier transform in (5.138) is computed with respect to the unnormalized time variable t. If the averaged noise process () varies sufficiently fast over time, then it is shown that [Vana03c] (5.139) Here, Snn(Af)=F{nn(2rfot)} is the PSD of the averaged noise process (). Again, the Fourier transform is with respect to unnormalized ti