6. Time and Frequency Characterization of Signals and Systems

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Presentation transcript:

6. Time and Frequency Characterization of Signals and Systems 6 Time and frequency characterization of S&S 6. Time and Frequency Characterization of Signals and Systems 6.1 The Magnitude-phase Representation of the Fourier Transform For signal x(t) :

6 Time and frequency characterization of S&S

6 Time and frequency characterization of S&S

6 Time and frequency characterization of S&S

6 Time and frequency characterization of S&S

6.2 The Magnitude-phase Representation of 6 Time and frequency characterization of S&S 6.2 The Magnitude-phase Representation of the Frequency Response of LTI System System characterization: Impulse response: Frequency response:

6.2.1 Linear and Nonlinear Phase 6 Time and frequency characterization of S&S 6.2.1 Linear and Nonlinear Phase Linear phase: Nonlinear phase: Example: Effect: Linear phase means non-distortion of signal transmission.

6 Time and frequency characterization of S&S ( Linear phase ) ( Original signal ) ( Nonlinear phase )

Distortionless system: is flat. 6 Time and frequency characterization of S&S 6.2.2 Group Delay Definition: Example: Distortionless system: is flat.

6 Time and frequency characterization of S&S

6.2.3 Log-Magnitude and Bod Plots 6 Time and frequency characterization of S&S 6.2.3 Log-Magnitude and Bod Plots Magnitude spectrum: Phase spectrum:

6 Time and frequency characterization of S&S

6.3 Time-Domain Properties of Ideal Frequency- selective Filters 6 Time and frequency characterization of S&S 6.3 Time-Domain Properties of Ideal Frequency- selective Filters Lowpass filter: (1) Continous time: (2) Discrete time:

6 Time and frequency characterization of S&S

6 Time and frequency characterization of S&S

6 Time and frequency characterization of S&S

6 Time and frequency characterization of S&S

6.4 Time-Domain and Frequency-domain Aspects of Non-ideal Filters 6 Time and frequency characterization of S&S 6.4 Time-Domain and Frequency-domain Aspects of Non-ideal Filters Basic parameter of lowpass filter:

6 Time and frequency characterization of S&S

6 Time and frequency characterization of S&S

6 Time and frequency characterization of S&S

6 Time and frequency characterization of S&S Problems: 6.5 6.23 6.27