Chapter 2 Signals and Spectra
1 Chapter 2 Signals and Spectra
Introduction Basic signal properties(dc, rms, dBm, and power) Fourier transform and spectra Linear systems and linear distortion Bandlimited signal and sampling Discrete fourier transform · Bandwidth of signal
2 Introduction • Basic signal properties(dc, rms,dBm, and power) • Fourier transform and spectra • Linear systems and linear distortion • Bandlimited signal and sampling • Discrete Fourier transform • Bandwidth of signal
2.1 Properties of signal and Noise (Properties of Physical Waveform) the waveform has significant nonzero values over a composite time interval that is finite The spectrum of the waveform has significant values over a composite frequency interval that is finite The waveform is a continuous function of time The waveform has a finite peak value The waveform has only real values. That is, at any time, it cannot have a complex value atbi where b is nonzero
3 2.1 Properties of signal and Noise (Properties of Physical Waveform) • the waveform has significant nonzero values over a composite time interval that is finite • The spectrum of the waveform has significant values over a composite frequency interval that is finite • The waveform is a continuous function of time • The waveform has a finite peak value • The waveform has only real values. That is, at any time, it cannot have a complex value a+bj, where b is nonzero
2.1 Properties of signal and Noise (t) Waveform decays Waveform decays to zero before to zero before t =+oo 5T 6T (a)Physical Waveform 0(t Waveform extends Waveform extends 5T 6T () )Math Model Waveform Figure 2-1 Physical and mathematical waveforms
4 2.1 Properties of signal and Noise
2.1 Properties of signal and Noise Time average operator 少= limD(2 Periodic waveform with period To a(t=a(t+To) for allt (2-3) Time average operator for periodic waveform 1r(T/2)+a T/2)+a 5
5 2.1 Properties of signal and Noise • Time average operator (2 -1) 1 lim / 2 / 2 dt T T T T → − • = • • Periodic waveform with period T0 ( ) ( ) for all t (2 - 3) T0 t = t + • Time average operator for periodic waveform (2 - 4 ) 1 ( / 2) ( / 2) 0 d t T T a T a + − + • = •