第2章2.1～2.2 2010-9-7.ppt

Chapter 2: Deterministic Signal Analysis Dr. Li Hao Email: lhao@home.swjtu.edu.cn School of Information Science and Technology Southwest Jiaotong University 2010 Autumn Chapter 2 Deterministic Signal Analysis 2.1 Introduction 2.2 Fourier transform and spectra 2.3 Power spectral density (PSD) and autocorrelation function 2.4 Two important blocks: multiplier and filter 2.5 Hilbert transform 2.6 Complex envelope representation of bandpass signals 2.1 Introduction waveform classification signals or noise digital or analog deterministic or nondeterministic (random or stochastic) physically realizable or nonphysically realizable power or energy periodic or nonperiodic Time average operator Definition. The time average operator is given by Definition. The expected value, which is also called the ensemble average is given by where f(x) is the probability density function (PDF). Periodic waveform Definition: A waveform w(t) is periodic with period T0 if where T0 is the smallest positive number that satisfies this relationship. Theorem: If the waveform involved is periodic, the time average operator can be reduced to where T0 is the period of the waveform and a is an arbitrary real constant, which may be taken to zero. DC value Definition. The dc (direct current) value of a waveform w(t) is given by its time average Power Definition. Let v(t) denote the voltage across a set of circuit terminals, and let i(t) denote the current into the terminal. The instantaneous power (incremental work divided by incremental time) associated with the circuit is given by The average power is RMS value and normalized power Definition. The root-mean-square (rms) value of w(t) is Definition. The average normalized power is Energy and power waveforms Definition. w(t) is a power waveform if and only if the normalized average power of P is finite and nonzero (i.e., 0P?). Definition. w(t) is an energy waveform if and only if the total normalized energy is finite and nonzero