2. Digital Signal Processing A Merger of Mathematics and Machines 2002 Summer Youth Program Electrical and Computer Engineering Michigan Technological University

3. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Signals and Sounds l The simplest signal is the sinusoid: t t t t frequency = 500 Hz frequency = 1 KHz frequency = 2 KHz frequency = 4 KHz

4. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Signals and Sounds l Sums of sinusoids 00.0050.010.0150.02 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 time (seconds) amplitude 941 1209f ‘spectral’ representation

5. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Signals and Sounds 123 456 789 *0# 697 Hz 941 Hz 852 Hz 770 Hz 1209 Hz 1336 Hz1477 Hz Dual-tone multiple frequency (DTMF) Frere Jacques Olympic Fanfare

6. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Signals and Sounds Olympic Fanfare

7. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Signals and Sounds l What other signals (or sounds) can we make from sinusoids? –Answer: ALL OF THEM! l This is Fourier theory and it forms the basis for many branches of electrical engineering.

8. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program The Common Loon

9. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Pied-Billed Grebe

10. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Tundra Swan (Whistling Swan)

11. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Signals and Sounds 00.0020.0040.0060.0080.010.0120.0140.016 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 time (seconds) amplitude 250 1250 7501750 2250 f Signal Spectrum

12. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Signals and Sounds 00.0020.0040.0060.0080.010.0120.0140.016 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 time (seconds) amplitude 250 f Signal Spectrum 00.0020.0040.0060.0080.010.0120.0140.016 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 time (seconds) amplitude

13. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Filtering l 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

14. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Filtering + noise

15. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Filtering 050010001500200025003000350040004500 0 50 100 150 200 250 300 frequency (Hz) gain frequency response H(f)

16. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Filtering + noise

17. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Filtering H(f) 020004000600080001000012000 0 0.5 1 1.5 2 2.5 3 3.5 frequency (Hz) gain frequency response

18. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Digital Signal Processing A-to-DD-to-ADSP analog digital Analog signals are continuous in time and amplitude. Digital signals are discrete in time and amplitude.

19. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Sampling l 16 bits gives 2 16 = 65,536 amplitude levels l 8 bits gives 2 8 = 256 amplitude levels l 4 bits gives 2 4 = 16 amplitude levels

20. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Sampling of Sound l 16 bits (CD quality) l 12 bits l 8 bits (phone quality) l 16 bits / 8 bits l 8 bits / 6 bits l 8 bits / 4 bits l 8 bits / 2 bits

21. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Digital Signal Processing l Digital filters are really simple! –four-sample moving average filter –recursive (feedback) filter

22. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program Pictures Too!

23. Department of Electrical and Computer Engineering Copyright Michigan Technological University 2002 Summer Youth Program So What Do You Need To Learn? l Signal and System Theory –Spectral analysis –Filter design l Digital Signal Processing –Software systems –Hardware systems