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Bài giảng Xử lý tín hiệu số: Sampling and Reconstruction - Ngô Quốc Cường (ĐH Sư phạm Kỹ thuật)

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Bài giảng Xử lý tín hiệu số: Sampling and Reconstruction - Ngô Quốc Cường (ĐH Sư phạm Kỹ thuật)

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Bài giảng "Xử lý tín hiệu số: Sampling and Reconstruction" cung cấp cho người học các kiến thức: Introduction, review of analog signal, sampling theorem, analog reconstruction. Mời các bạn cùng tham khảo nội dung chi tiết.

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Nội dung Text: Bài giảng Xử lý tín hiệu số: Sampling and Reconstruction - Ngô Quốc Cường (ĐH Sư phạm Kỹ thuật)

  1. Xử lý tín hiệu số Sampling and Reconstruction Ngô Quốc Cường ngoquoccuong175@gmail.com Ngô Quốc Cường sites.google.com/a/hcmute.edu.vn/ngoquoccuong
  2. Sampling and reconstruction • Introduction • Review of analog signal • Sampling theorem • Analog reconstruction 2
  3. 1.1 Introduction Digital processing of analog signals proceeds in three stages: 1. The analog signal is digitized, that is, it is sampled and each sample quantized to a finite number of bits. This process is called A/D conversion. 2. The digitized samples are processed by a digital signal processor. 3. The resulting output samples may be converted back into analog form by an analog reconstructor (D/A conversion). 3
  4. 1.2 Review of analog signal • An analog signal is described by a function of time, say, x(t). The Fourier transform X(Ω) of x(t) is the frequency spectrum of the signal: • The physical meaning of X(Ω) is brought out by the inverse Fourier transform, which expresses the arbitrary signal x(t) as a linear superposition of sinusoids of different frequencies: 4
  5. 1.2 Review of analog signal • The response of a linear system to an input signal x(t): • The system is characterized completely by the impulse response function h(t). The output y(t) is obtained in the time domain by convolution: 5
  6. 1.2 Review of analog signal • In the frequency domain by multiplication: • where H(Ω) is the frequency response of the system, defined as the Fourier transform of the impulse response h(t): 6
  7. 1.2 Review of analog signal 7
  8. CT Fourier Transforms of Periodic Signals Source: Jacob White 8
  9. Fourier Transform of Cosine Source: Jacob White 9
  10. Impulse Train (Sampling Function) Note: (period in t) T (period in ) 2/T Source: Jacob White 10
  11. 1.3 Sampling theorem • The sampling process is illustrated in Fig. 1.3.1, where the analog signal x(t) is periodically measured every T seconds. Thus, time is discretized in units of the sampling interval T: 11
  12. 1.3 Sampling theorem • For system design purposes, two questions must be answered: 1. What is the effect of sampling on the original frequency spectrum? 2. How should one choose the sampling interval T? 12
  13. 1.3 Sampling theorem • Although the sampling process generates high frequency components, these components appear in a very regular fashion, that is, every frequency component of the original signal is periodically replicated over the entire frequency axis, with period given by the sampling rate: • Let x(t) = xc(t), sampling pulse s(t) 13
  14. 1.3 Sampling theorem Source: Zheng-Hua Tan 14
  15. 1.3 Sampling theorem Source: Zheng-Hua Tan 15
  16. 1.3 Sampling theorem Source: Zheng-Hua Tan 16
  17. 1.3 Sampling theorem Source: Zheng-Hua Tan 17
  18. 1.3 Sampling theorem Source: Zheng-Hua Tan 18
  19. 1.3 Sampling theorem Source: Zheng-Hua Tan 19
  20. 1.3 Sampling theorem • The sampling theorem provides a quantitative answer to the question of how to choose the sampling time interval T. • T must be small enough so that signal variations that occur between samples are not lost. But how small is small enough? • It would be very impractical to choose T too small because then there would be too many samples to be processed. 20
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