Simple but Effective Spectrum Averaging
In this article, I provide a Matlab function that performs exponential PSD averaging, using first-order infinite impulse response (IIR) filtering to continuously average the PSD bins. This approach works well for computing the spectrum of a long-duration signal over time, because the spectrum is constantly updated as new PSD’s are computed. Conveniently, the time constant of the PSD averaging is determined by the single adjustable parameter α. I also provide a Matlab function for conventional (unweighted) PSD averaging. Neither function requires any canned code other than the Fast Fourier Transform (FFT), although I do use the Matlab hann window function for convenience.
Summary
This blog describes a lightweight Matlab implementation for exponential PSD averaging using a first-order IIR filter to continuously smooth FFT-based power spectral density estimates. The author explains the single-parameter α that controls the averaging time constant, provides a conventional (unweighted) PSD-averaging function for comparison, and shows how the approach supports continuous, low-complexity spectrum updates for long-duration signals.
Key Takeaways
- Implement exponential PSD averaging in Matlab using a first-order IIR (recursive) filter on FFT bins.
- Tune the single parameter α to control the averaging time constant and trade time resolution versus variance.
- Compare exponential (IIR) averaging to conventional unweighted/Welch-style averaging to choose the right estimator.
- Use the provided functions for streaming or long-duration signals to obtain continuously updated spectra with minimal code.
- Avoid common pitfalls by applying proper windowing (Hann) and normalization when computing PSDs.
Who Should Read This
Signal processing engineers or researchers with some Matlab experience who need simple, low-complexity methods for time-varying PSD estimation in audio, radar, or communications applications.
TimelessIntermediate
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