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Digital Signal Processing A Merger of Mathematics and Machines

Digital Signal Processing A Merger of Mathematics and Machines. 2002 Summer Youth Program Electrical and Computer Engineering Michigan Technological University. Signals and Sounds. The simplest signal is the sinusoid:. frequency = 500 Hz. t. frequency = 1 KHz. t. frequency = 2 KHz. t.

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Digital Signal Processing A Merger of Mathematics and Machines

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  1. Digital Signal ProcessingA Merger of Mathematics and Machines 2002 Summer Youth Program Electrical and Computer Engineering Michigan Technological University

  2. Signals and Sounds • The simplest signal is the sinusoid: frequency = 500 Hz t frequency = 1 KHz t frequency = 2 KHz t frequency = 4 KHz t

  3. 1 0.8 ‘spectral’ representation 0.6 0.4 0.2 amplitude 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.005 0.01 0.015 0.02 941 1209 f time (seconds) Signals and Sounds • Sums of sinusoids

  4. Signals and Sounds Dual-tone multiple frequency (DTMF) 1336 Hz 1477 Hz 1209 Hz Frere Jacques 1 2 3 697 Hz 4 5 6 770 Hz 7 8 9 852 Hz Olympic Fanfare * 0 # 941 Hz

  5. Signals and Sounds Olympic Fanfare

  6. Signals and Sounds • What other signals (or sounds) can we make from sinusoids? • Answer: ALL OF THEM! • This is Fourier theory and it forms the basis for many branches of electrical engineering.

  7. The Common Loon

  8. Pied-Billed Grebe

  9. Tundra Swan (Whistling Swan)

  10. 1 0.8 0.6 0.4 0.2 amplitude 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 time (seconds) Signals and Sounds Signal Spectrum 750 1750 f 250 1250 2250

  11. 1 0.8 0.6 0.4 0.2 amplitude 0 -0.2 -0.4 -0.6 -0.8 -1 1 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 time (seconds) 0.8 0.6 0.4 0.2 amplitude 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 time (seconds) Signals and Sounds Signal Spectrum f 250

  12. Filtering • One of the key concepts in signal processing is the idea that systems can be built to analyze or modify a signal’s spectrum. • Applications: • speech recognition • speaker recognition • noise removal

  13. Filtering + noise

  14. frequency response 300 250 200 gain 150 100 50 0 0 500 1000 1500 2000 2500 3000 3500 4000 4500 frequency (Hz) Filtering H(f)

  15. Filtering + noise

  16. frequency response 3.5 3 2.5 2 gain 1.5 1 0.5 0 0 2000 4000 6000 8000 10000 12000 frequency (Hz) Filtering H(f)

  17. Digital Signal Processing analog analog digital digital A-to-D DSP D-to-A Analog signals are continuous in time and amplitude. Digital signals are discrete in time and amplitude.

  18. Sampling • 16 bits gives 216 = 65,536 amplitude levels • 8 bits gives 28 = 256 amplitude levels • 4 bits gives 24 = 16 amplitude levels

  19. Sampling of Sound • 16 bits (CD quality) • 12 bits • 8 bits (phone quality) • 16 bits / 8 bits • 8 bits / 6 bits • 8 bits / 4 bits • 8 bits / 2 bits

  20. Digital Signal Processing • Digital filters are really simple! • four-sample moving average filter • recursive (feedback) filter

  21. Pictures Too!

  22. So What Do You Need To Learn? • Signal and System Theory • Spectral analysis • Filter design • Digital Signal Processing • Software systems • Hardware systems

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