Đang chuẩn bị liên kết để tải về tài liệu:
Lecture Signals, systems & inference – Lecture 19: Einstein-Wiener-Khinchin theorem, PSD applications, modeling filters

Hải Nhi 70 9 pdf

Đang chuẩn bị nút TẢI XUỐNG, xin hãy chờ Tải xuống

The following will be discussed in this chapter: Einstein-Wiener-Khinchin theorem, periodogram averaging (illustrating the Einstein-Wiener-Khinchin theorem), respiratory model, modeling filters. | Lecture Signals, systems & inference – Lecture 19: Einstein-Wiener-Khinchin theorem, PSD applications, modeling filters Einstein-Wiener-Khinchin theorem, PSD applications, modeling filters 6.011, Spring 2018 Lec 19 1 Periodograms (e.g., 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 0.5 1 0 0.5 1 0 0.5 1 0 0.5 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 |XT (j!)|2 Periodogram = 0 0 2T 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 v/(2p) v/(2p) M = 16, T = 50 M = 16, T = 200 4 DT case: XN (ej⌦ ) $ x[n]4 windowed to [ N, N ] 3 3 2 2 |XN (ej⌦ )|2 1 Periodogram 1 2 = 0 0 2N + 1 Einstein-Wiener-Khinchin theorem 1 h i 2 sin (!T ) 2 E |XT (j!)| = Sxx (j!) ? 2T ⇡! 2 T sin2 (!T ) Since lim 2 = (!) , T !1 ⇡! T 1 h i 2 lim E |XT (j!)| = Sxx (j!) T !1 2T 3 Periodogram averaging (illustrating the Einstein-Wiener-Khinchin theorem) 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 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 v/(2p) v/(2p) v/(2p) v/(2p) M = 4, T = 50 M = 4, T = 200 4 4 3 3 2 2 1 1 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 v/(2p) v/(2p) M 16, T 50 M 16, T 200 4 4 3 3 2 2 4 1 1 Periodogram averaging (illustrating the Einstein-Wiener-Khinchin theorem) 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 0.5 1 0 0.5 1 0 0.5 1 0 0.5 1 v/(2p) v/(2p) v/(2p) v/(2p) M = 4, T = 50 M = 4, T = 200 4 4 3 3 2 2 1 1 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 v/(2p) v/(2p) M = 16, T = 50 M = 16, T = 200 4 4 3 3 2 2 1 1 0 5 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 v/(2p) v/(2p) Respiratory model cf. Khoo’s 6 textbook for N=1 Heart rate variability ECG signal 1.2 1 0.8 ECG amplitude (mV) 0.6 0.4 0.2

TÀI LIỆU LIÊN QUAN

Lecture Signals, systems & inference – Lecture 1: Introduction

Lecture Signals, systems & inference – Lecture 2: Transforms

Lecture Signals, systems & inference – Lecture 3: Energy spectral density

Lecture Signals, systems & inference – Lecture 4: State-Space Models

Lecture Signals, systems & inference – Lecture 5: State-space models, equilibrium, linearization

Lecture Signals, systems & inference – Lecture 6: Modal solution of undriven CT LTI state-space models

Lecture Signals, systems & inference – Lecture 7: Full modal solution, asymptotic stability, reachability and observability

Lecture Signals, systems & inference – Lecture 8: Matrix exponential, ZIR+ZSR, transfer function, hidden modes, reaching target states

Lecture Signals, systems & inference – Lecture 9: Observers for state estimation

Lecture Signals, systems & inference – Lecture 10: Observers, state feedback

Đã phát hiện trình chặn quảng cáo AdBlock

Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.