Correlation and Power Spectrum
In the signals and systems course and in the first course in digital signal processing, a signal is, most often, characterized by its amplitude spectrum in the frequency-domain and its amplitude profile in the time-domain. So much a student gets used to this type of characterization, that the student finds it difficult to appreciate, when encountered in the ensuing statistical signal processing course, the fact that a signal can also be characterized by its autocorrelation function in the time-domain and the corresponding power spectrum in the frequency-domain and that the amplitude characterization is not available. In this article, the characterization of a signal by its autocorrelation function in the time-domain and the corresponding power spectrum in the frequency-domain is described. Cross-correlation of two signals is also presented.
Summary
This article explains how signals can be characterized in the time domain by their autocorrelation function and in the frequency domain by the corresponding power spectrum. It guides the reader through the theoretical link between autocorrelation and power spectral density and highlights practical implications for signal analysis and estimation.
Key Takeaways
- Understand the role of the autocorrelation function in characterizing stochastic signals and its relationship to the power spectral density via the Wiener–Khinchin theorem.
- Compute a power spectrum from an autocorrelation sequence and interpret differences between amplitude spectra and power spectra.
- Apply practical PSD estimation techniques (e.g., periodogram, averaging) and recognize the effects of windowing, bias, and variance.
- Relate autocorrelation and PSD concepts to problems in communications and detection where amplitude-phase information may be unavailable.
Who Should Read This
Intermediate DSP students, signal processing engineers, and researchers who need to understand autocorrelation-based signal characterization and power spectral density estimation for analysis and system design.
TimelessIntermediate
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