英文版《信号与系统》第678章讲义

1、Chapter 6Time and Frequency Characterizationof Signals and Systems1 Chapter 6 Time and Frequency CharacterizationTime-Domain:Frequency-Domain:6.1 The Magnitude-Phase Representation 幅度-相位 of the Fourier TransformMagnitude Energy-Density2 Chapter 6 Time and Frequency Characterization6.2 The Magnitude-

2、Phase Representation of the Frequency Response of LTI SystemsGain Phase Shift3 Chapter 6 Time and Frequency Characterization6.2.1 Linear and Nonlinear Phase1. Linear Phase4 Chapter 6 Time and Frequency Characterization2. Nonlinear Phase5 Chapter 6 Time and Frequency CharacterizationHomework: 6.5 6.2

3、366.5 Consider a continuous-time ideal bandbass filter whose frequency response is Chapter 6 Problem SolutionIf is the impulse response of this filter, determine a function such that (b) As is increased, does the impulse response of the filterget more concentrated or less concentrated about the orig

4、in?Solution (b) It will get more concentrated about the origin.(a)7 Chapter 6 Problem Solution6.23 Shown in Figure 6.23 is for a lowpass filter. Determine and sketch the impulse response of the filter for each of the following phase characteristics: (a) (b) , where T is a constant.8(c) Chapter 6 Pro

5、blem Solution9 Chapter 7 Sampling Chapter 7 Sampling10 Chapter 7 Sampling-T 0 T 2T t 11 Chapter 7 Sampling7.1 The Sampling Theorem 7.1.1 Impulse-Train Sampling-3T -2T -T 0 T 2T 3T 4T t 12 Chapter 7 SamplingSampling Theorem:Let be a band-limited signal withThen is uniquely determined by its samples i

6、f where13 Chapter 7 SamplingWhen aliasing occurs,Homework: 7.1 7.2 7.3 7.6 7.97.3 The Effect of Undersampling: Aliasing 欠采样 混叠14 Chapter 7 Problem Solution7.1 A real-valued signal is known to be uniquely determined by its samples when the sampling frequency is . For what values of is guaranteed to b

7、e zero?15 Chapter 7 Problem Solution7.2 A continuous-time signal is obtained at the output of an ideal lowpass filter with cutoff frequency . If impulse-train sampling is performed on ,which of the following sampling periods would guarantee that can be recovered from its sampled version using an app

8、ropriate lowpass filter? (a) T=0.510-3 (b) T=210-3 (c) T=10-4(a) and (c)Sampling interval16 Chapter 7 Problem Solution7.3 Determine the Nyquist rate corresponding to each of the following signals:17 Chapter 7 Problem Solution7.6 Determine the maximum sampling interval T such that is recoverable from

9、 through the use of an ideal LPF.Nyquist ratemaximum sampling interval18 Chapter 7 Problem Solution7.9 Consider the signalwhich we wish to sample with a sampling frequency ofto obtain a signal with Fourier transform . Determinethe maximum value of for which it is guaranteed that19 Chapter 8 Communic

10、ation Systems20 Chapter 8 Communication SystemsModulation :The general process of embedding an information-bearing signal into a second signal.Extracting the information-bearing signal.Demodulation :Modulation :Amplitude Modulation (AM)Frequency Modulation (FM)Phase Modulation (PM)ModulatingSignal C

11、arrier Signal ModulatedSignal Amplitude Modulation21 Chapter 8 Communication Systems8.1 Complex Exponential and Sinusoidal Amplitude Modulation8.1.1 Amplitude Modulation with a Complex Exponential Carriercarrier frequencyinitial phaseModulation :Demodulation :22 Chapter 8 Communication Systems8.1.2

12、Amplitude Modulation with a Sinusoidal CarrierModulation :23DemodulationSynchronous Demodulation （同步解调）Asynchronous Demodulation （非同步解调） Chapter 8 Communication SystemsEnvelope 24 Chapter 8 Communication SystemsCommunicationChannel 8.2.1 Synchronous Demodulation Transmitter Modulation ReceiverSynchr

13、onous DemodulationLPFsameLPF25 Chapter 8 Communication SystemsSuppose the modulator and demodulator are not synchronized in phase.Transmitter Carrier Complex Exponential CarrierReceiverCarrierWhen ,26 Chapter 8 Communication Systems Sinusoidal CarrierTransmitter CarrierReceiverCarrierModulationDemod

14、ulationThe output of LPF is:Be out of the passband of LPF27 Chapter 8 Communication Systems2. Suppose the modulator and demodulator are not synchronized in frequency.Transmitter CarrierReceiverCarrierThe output of LPF is:Be out of the passband of LPF28 Chapter 8 Communication Systems298.3 Frequency-

15、Division Multiplexing频分复用 Chapter 8 Communication SystemsBPFBPFBPF30 Chapter 8 Communication SystemsBPFReceiver LPFBPFLPFBPFLPF31 Chapter 8 Communication SystemsHomework: 8.1 8.3 8.2232 Chapter 8 Problem Solution8.1 Determine a signal such that Solution 33 Chapter 8 Problem Solution8.3 Determine . L

16、PF Solution Be out of the passband of LPF34 8.22In Figure (a) ,a system is shown with input and outputThe input signal has the Fourier transform shown in Figure (b)Determine and sketch . Chapter 8 Problem SolutionFigure (a)Figure (b)35-7W -5W -3W 0 3W 5W 7W -5W -3W 0 3W 5W -8W -6W -2W 0 2W 6W 8W -2W

17、 0 2W Chapter 8 Problem Solution36Problems for Fourier AnalysisA period of Example 1 Determine the Fourier transform of37Example 2 A real continuous-time signal with Fourier transform , and If is even, determine .If is odd, determine .Problems for Fourier AnalysisIf is real ,even38Problems for Fouri

18、er Analysis2. If is real ,odd39Problems for Fourier AnalysisExample 3 Consider the following LTI systems with impulse response:1. 2.3.If the input is Determine the output 1. Solution :40Problems for Fourier Analysis2.3.41Problems for Fourier AnalysisExample 5 In Figure (a), a system is shown with input signal and output signal . If the following information are given.1. Determine 2. Determine the impulse response of the whole system .If the input signal , determine the output signal +-42Problems for Fourier Analysis1. Determine