測試信號英文版課件：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) 主要內(nèi)容時(shí)域的有限化和離散化一頻域的有限化和離散化二誤差產(chǎn)生原因及解決辦法三譜分析時(shí)DFT參數(shù)的選擇四譜分析時(shí)DFT參數(shù)的選擇1）估計(jì)待分析信號中頻率范圍和頻率上限 。2）選定抽樣頻率 。3）根據(jù)分析精度，確定

4、數(shù)據(jù)有效長度 。4）確定點(diǎn)數(shù)N。5）選窗口。 6）采樣信號與長度為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畫圖法！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