Generation of Noise Time Series with arbitrary Power Spectrum

Noise simulation is a very powerful tool in signal analysis helping to foresee the system performance in real experimental situations. Time series generation is however a hard challenge when a robust model of the noise sources is missing. We present here a simple computational technique which allows the generation of noise samples of fixed length, given a desired power spectrum. A few applications of the method are also discussed.

💡 Research Summary

The paper addresses a practical problem in signal‑processing and experimental engineering: how to generate a finite‑length noise time series that exactly matches a desired power spectral density (PSD). Traditional approaches rely on parametric models such as ARMA processes, on filtering white Gaussian noise, or on detailed physical modeling of each noise source. These methods work only when the underlying noise statistics are well understood; they become cumbersome or inaccurate when the PSD is complex, contains multiple 1/f regions, narrow peaks, or is only known empirically.

The authors propose a simple, non‑parametric algorithm that builds a noise sequence directly from the target PSD. The core idea is to treat the PSD as a specification of the magnitude of the Fourier coefficients. For each discrete frequency bin k, the desired magnitude is set to the square‑root of the PSD, A(k)=√S_desired(k). A random phase φ(k) is drawn uniformly from