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EC3400: Introduction to Digital Signal Processing

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Presentation on theme: "EC3400: Introduction to Digital Signal Processing"— Presentation transcript:

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 LPF LPF ADC DSP LPF antialiasing
DAC LPF LPF ADC DSP DAC LPF antialiasing reconstruction

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

6 Structure of a Digital Filter
continuous time discrete time continuous time ADC DAC LPF ZOH LPF 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 Reconstruction: the Zero Order Hold
DAC ZOH 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 Finally, put everything together and assume ideal analog filters:
ADC DAC ZOH clock LPF anti-aliasing filter reconstruction

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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