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Digital Signal Processing: A Merger of Math and Machines

Explore signals, sounds, and signal processing concepts in this 2002 summer youth program by Michigan Tech University. Learn about sinusoids, DTMF signals, and Fourier theory. Discover applications in speech and speaker recognition. Study analog vs. digital signals, sampling, and digital filtering. Gain insights into filter design, software, and hardware systems. Join the transformation from analog to digital!

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Digital Signal Processing: A Merger of Math 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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