TAILIEUCHUNG - Lecture Signals, systems & inference – Lecture 18: Power Spectral Density (PSD)

The following will be discussed in this chapter: iid signal x[n], uniform in []; extracting the portion of x(t) in a specified frequency band; questions (warm-up for Quiz 2!); periodograms (., a unit-intensity “white” process); periodogram averaging (illustrating the Einstein-Wiener-Khinchin theorem). | Lecture Signals, systems & inference – Lecture 18: Power Spectral Density (PSD) Power Spectral Density (PSD) , Spring 2018 Lec 18 1 iid signal x[n], uniform in [] 2 y[.] obtained by passing x[.] through resonant 2nd-order filter H(z), poles at ±{jπ/3} 3 Extracting the portion of x(t) in a specified frequency band x(t) H(jv) y(t) H(jv) ¢ ¢ 1 -v0 v0 4 Questions (warm-up for Quiz 2!) WSS process x[·] with Cxx [m] = ⇢ [m 1] + [m] + ⇢ [m + 1] . What is the largest magnitude ⇢ can have? WSS process x(·) with mean µx and PSD Sxx (j!). What is its FSD? Zero-mean WSS process x(·) with 1 Sxx (j!) = 1 + !2 2 and let y(t) = Z +x(t), where Z has zero mean, variance , and is uncorrelated with x(·). What are µy and Syy (j!)? 5 Periodograms (., a unit-intensity “white” process) M = 1, T = 50 M = 1, T = 50 M = 1, T = 50 M = 1, T = 50 4 4 4 4 3 3 3 3 2 2 2 2 1 1 1 1 0 0 0 0 0 1 0 1 0 1 0 1 v/(2p) v/(2p) v/(2p) v/(2p) M = 4, T = 50 M = 4, T = 200 4 4 3 CT case: XT (j!) $ x(t) 3 windowed to [ T, T ] 2 2 1 1

• Kĩ thuật Viễn thông
• Signals systems
• Lecture Signals systems
• Time invariant system models
• System models in continuous
• Linear system models
• State–space models
• Power Spectral Density
• Lecture ELEC2400 signals and systems
• ELEC2400 signals and systems
• Signal types and operations
• Operations on Signals
• Types of Signals
• Signals and systems using MATLAB
• Systems using MATLAB
• From the ground up
• Continuous time signals
• Continuous time systems
• The laplace transform
• Frequency analysis
• Frequency domain analysis
• Fourier transform
• Frequency response of LTI systems
• Energy spectral density
• State Space Models
• Matrix exponential
• Transfer function
• Observers for state estimation
• State feedback
• Observer based feedback
• Probabilistic models
• Random variables
• Correlation coefficient
• LTI filtering
• WSS processes
• Wiener filtering
• Wiener filtering illustrations
• Hypothesis testing