On Digital Signal Processing of Time Series for Spectrum Estimation

Area of Science:

• Digital signal processing
• Spectrum analysis
• Radiometry

Background:

• Digital radiometry involves obtaining radiation spectra from digitally sampled signals.
• Accurate power spectral density (PSD) estimation is crucial for analyzing such data.
• Existing methods may have limitations in precision and computational efficiency.

Purpose of the Study:

• To develop and evaluate an optimal method for power spectral density (PSD) estimation from time-domain data.
• To generalize PSD estimation using a quadratic estimator framework.
• To quantify the uncertainty (variance and bias) in non-ideal PSD estimation.

Main Methods:

• Generalized quadratic estimator for PSD estimation.
• Minimization of mean squared error to determine optimal window functions.
• Formulation of bounds for variance and bias.
• Comparison of windowed estimates based on computational efficiency and precision.

Main Results:

• The study presents a generalized quadratic estimator for PSD estimation.
• Optimal window selection is achieved by minimizing mean squared error.
• Quantified bounds for variance and bias provide uncertainty measures.
• Windowed estimates demonstrate trade-offs between computational efficiency and amplitude precision.

Conclusions:

• The proposed quadratic estimator offers a generalized approach to PSD estimation.
• Optimal window selection is critical for accurate spectrum measurements.
• The formulated bounds are essential for understanding uncertainty in digital signal processing.
• The findings are applicable to real-world applications such as digital radiometry.