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EC3400: Introduction to Digital Signal Processing by Roberto Cristi Professor Dept. of ECE

EC3400: Introduction to Digital Signal Processing by Roberto Cristi Professor Dept. of ECE Naval Postgraduate School Monterey, CA 93943. Week 1 Topics:. Introduction Fourier Transform (Review) Sampling Reconstruction Digital Filtering Example: a Digital Notch Filter.

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EC3400: Introduction to Digital Signal Processing by Roberto Cristi Professor Dept. of ECE

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  1. EC3400: Introduction to Digital Signal Processing by Roberto Cristi Professor Dept. of ECE Naval Postgraduate School Monterey, CA 93943

  2. Week 1 Topics: • Introduction • Fourier Transform (Review) • Sampling • Reconstruction • Digital Filtering • Example: a Digital Notch Filter

  3. Introduction Objectives In this course we introduce techniques to process signals by digital computers. A signal can come from a number of different sources: • filtered signal: • reject disturbances. sonar DSP Hardware Software radar • transformed signal: • detection • compression audio video ...

  4. A Digital Filter ADC LPF DSP DAC LPF LPF LPF DSP ADC DAC antialiasing reconstruction

  5. We review the relations between the spectra of the signals in the following operations: LPF LPF DAC Sampling: Digital Filtering: Reconstruction:

  6. LPF Structure of a Digital Filter continuous time discrete time continuous time ADC DAC LPF ZOH anti-aliasing filter reconstruction filter clock Problem: determine the continuous time frequency response.

  7. Recall: • the Fourier Transform of a continuous time signal • the Discrete Time Fourier Transform of a discrete time signal

  8. Sampling of a continuous time signal: ADC mathematical model of the sampler: it appends a to each sample

  9. We can write the same expression in two different ways: FT FT since since

  10. As a consequence:

  11. Particular case: if the signal is bandlimited as then LPF Notice: F is in Hz (1/sec), is in radians/sample (no dimension).

  12. DAC ZOH Reconstruction: the Zero Order Hold where g(t) is the pulse associated to each sample. Then, its FT is computed as: where G(F)=FT[g(t)] is given by

  13. ADC DAC LPF ZOH LPF anti-aliasing filter reconstruction filter clock Finally, put everything together and assume ideal analog filters:

  14. reconstruction filter

  15. Example: suppose we design a notch discrete time filter with transfer function with zeros and poles and sampling frequency . Determine the magnitude of its frequency response in the continuous time domain. z-plane

  16. Solution: from what we have seen the frequency response is given by

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