测试信号英文版课件：Chapter3-Lecture-2-Key-Points

1、Chapter 3 Discrete-Time Signals in the Transform DomainLecture 2Key PointsDiscretization in Time-domain and Frequency-domain2Time-domainSamplingFrequency-domainSamplingDTFTDFT (using FFT)DefinitionInverse discrete-time Fourier transform3Discrete Fourier TransformTransformation method NameTime domain

2、transform domainTransformation method Continuous-time Fourier Transform (CTFT)Discrete-Time Fourier Transform (DTFT)Discrete Fourier Transform (DFT)45Discrete Fourier TransformSampling theory in frequency domain6xn length-M N DFT parameteryn sequence by applying N-point IDFT on the N-point DFT of xn

3、General Properties of DFT7Numerical Computation of the DTFT Using the DFT82) Compute M-point DFT of the length-M sequence - M is an integer power of 2 - use FFT to obtain DFT1) Zero-padding (MN) 主要内容时域的有限化和离散化一频域的有限化和离散化二误差产生原因及解决办法三谱分析时DFT参数的选择四谱分析时DFT参数的选择1）估计待分析信号中频率范围和频率上限 。2）选定抽样频率 。3）根据分析精度，确定

4、数据有效长度 。4）确定点数N。5）选窗口。 6）采样信号与长度为N的窗口相乘， 再利用FFT算法做N-point DFT。Circular time-domain operationsCircular Shift of a SequenceCircular time-reversalCircular Convolution11画图法！Condition of equivalence between circular convolution and linear convolutionSummaryProvided that the length of Circular Convolution

5、 is not less than N+M1 where N and M are the lengths of the two sequences involved, the procedure of circular convolution is equivalent to that of linear convolution12Linear Convolution of Two Finite-Length SequencesLet gn and hn be two finite-length sequences of length N and M, respectivelyDenoteDe

6、fine two length-L sequences13Linear Convolution of Two Finite-Length SequencesThenThe corresponding implementation scheme is illustrated below*LZero-paddingwithpoint DFTZero-paddingwithpoint DFTgnhnLength-Npoint IDFTLength-MLength-14DFT parameter-NWhenever you need to apply DFT in signal analysis and processing, you should always ask yourself a question