Synopsis
Understand how weighting a random signal reshapes its spectrum—and when high‑frequency content stays essentially the same.
This book examines weighted random processes and shows how multiplying a stationary process by a weight function affects its power spectrum. It provides clear results about when the spectrum of the weighted process closely matches the original at high frequencies, with practical implications for experiments and data analysis.
Using accessible math, the text links weighting to convolution of spectra and introduces conditions under which the two spectra align. It also discusses the idea of slowly varying spectra and how certain data windows influence measurements.
Readers will see how kernels like the Fejér window influence outcomes and encounter concrete examples relevant to communications and signal processing. The discussion stays focused on intuition, conditions, and outcomes that practitioners can apply.
- How y(t) = m(t)x(t) relates to the original stationary process x(t) through spectral convolution
- When the weighted spectrum approximates the original at high frequencies, and what can disrupt that
- The role of slowly varying spectra and common window functions in real data
- Practical implications for radio, measurements, and data window design
Ideal for readers interested in signal processing, stochastic theory, and practical analysis of noisy data.
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