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) having significant nonzero values over a composite time interval that is finite Its spectrum having significant values over a composite frequency interval that Is fInite being a continuous function of time; having a finite peak value The waveform having only real values. That is, at any time, it cannot have a complex value a+bi where b is nonzero
3 2.1 Properties of signal and Noise (Properties of Physical Waveform) • having significant nonzero values over a composite time interval that is finite; • Its spectrum having significant values over a composite frequency interval that is finite; • being a continuous function of time; • having a finite peak value; • The waveform having 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 Wa to zero before to zero before 3T 5T 6T (a) Physical Waveform (t) Waveform extends Waveform extends 5T6 (b)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 T/2 =lim T/2 Periodic waveform with period To O(1)=(t+0) for all t(2-3) Time average operator for periodic waveform T/2)+ T/2)+a
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 dt T T a T a