The Power Spectrum
Often, when calculating the spectrum of a sampled signal, we are interested in relative powers, and we don't care about the absolute accuracy of the y axis. However, when the sampled signal represents an analog signal, we sometimes need an accurate picture of the analog signal's power in the frequency domain. This post shows how to calculate an accurate power spectrum.
Summary
This blog explains how to compute an accurate analog power spectrum from sampled signals, rather than only relative spectral magnitudes. It guides the reader through the correct FFT scaling, window and averaging corrections, and practical calibration steps needed to report power in physical units.
Key Takeaways
- Convert DFT/FFT outputs to physical power units (e.g., V^2 and V^2/Hz) by applying the correct length and sampling-rate scalings.
- Apply window-correction factors and choose coherent/incoherent averaging methods to preserve accurate power estimates.
- Use the correct one-sided/two-sided conventions and factor-of-two adjustments for real-valued signals.
- Calibrate the measurement chain (sensor/ADC gain and anti-alias filters) to recover the analog signal's true power.
Who Should Read This
Intermediate-level DSP engineers and researchers who design or verify measurement systems in audio, communications, or radar and need accurate analog-domain power spectra.
TimelessIntermediate
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