4.1  To Learn in This Chapter
4.2  Introduction
4.3  Windows for spectral analysis
4.3.1  Popular windows
4.3.2  Figures of merit applied to windows
4.3.3  Leakage
4.3.4  Picket-fence effect
4.3.5  Advanced: Only a bin-centered sinusoid leads to an FFT without visible leakage
4.3.6  Summarizing leakage and picket-fence effect
4.3.7  Example of using windows in spectral analysis
4.4  The ESD, PSD and MS Spectrum functions
4.4.1  Energy spectral density (ESD)
4.4.2  Advanced: Units of ESD when angular frequencies are adopted
4.4.3  Power spectral density (PSD)
4.4.4  Advanced: Fourier modulation theorem applied to PSDs
4.4.5  Mean-square (MS) spectrum
4.5  Filtering Random Signals and the Impact on PSDs
4.5.1  Response of LTI systems to random inputs
4.5.2  Filtering continuous-time signals that have a white PSD
4.5.3  Advanced: Filtering discrete-time signals that have a white PSD
4.6  Nonparametric PSD Estimation via Periodogram
4.6.1  Periodogram of periodic signals and energy signals
4.6.2  Examples of continuous-time PSD estimation using periodograms
4.6.3  Relation between MS spectrum and periodogram
4.6.4  Estimation of discrete-time PSDs using the periodogram
4.6.5  Examples of discrete-time PSD estimation
4.6.6  Estimating the PSD from Autocorrelation
4.7  Nonparametric PSD Estimation via Welch’s method
4.7.1  The periodogram variance does not decrease with N
4.7.2  Welch’s method for PSD estimation
4.8  Parametric PSD Estimation via Autoregressive (AR) Modeling
4.8.1  Advanced: Spectral factorization
4.8.2  AR modeling of a discrete-time PSD
4.8.3  AR modeling of a continuous-time PSD
4.8.4  Advanced: Yule-Walker equations and LPC
4.8.5  Examples of autoregressive PSD estimation
4.9  Time-frequency Analysis using the Spectrogram
4.9.1  Definitions of STFT and spectrogram
4.9.2  Advanced: Wide and narrowband spectrograms
4.10  Applications
4.11  Comments and Further Reading
4.12  Exercises
4.13  Extra Exercises