Lecture 5: Signal Processing II

1. Lecture 5: Signal Processing II EEN 112: Introduction to Electrical and Computer Engineering Professor Eric Rozier, 2/20/13

2. SOME DEFINITIONS

3. Decibels • Logarithmic unit that indicates the ratio of a physical quantity relative to a specified level. • 10x change is 10 dB change. 2x change ~3dB change. • Remember • L_dB = 10 log_10 (P1/P0) for power • L_db = 20 log_10 (A1/A0) for amplitude • (Power ~ Amplitude^2)

4. Period • A measurement of a time interval • A periodic signal that repeats every 10s • Periodic observation, count the number of students who are asleep every 1 minute

5. Rate • 1/period • If I count the number of students who are asleep every minute, I do so with the rate of 1/60s, or at a rate of 0.0166667 Hertz

6. Hertz • Instances per second • kHz, MHz, GHz – standard SI-prefixes for hertz

7. Rate and Time • If a period is 10s, the rates is 1/10s. • Hertz is cycles per second

8. Bandwidth(signal processing) • Difference between the upper and lower frequencies in a continuous set that carry information of interest. • Not to be confused with data bandwidth, which while related is not the same concept

9. SAMPLING CONTINUOUS SIGNALS

10. Sampling • Conversion of continuous time signals into discrete time signals. • How frequently we record, witness, or store, some signal. • Frame rates, movies typically play at 24 frames/second (rate) • What is the period?

11. Sampling • Affects how much data we have to store to represent a signal. • The more we store, the more space it takes! • The less we store, the more error is introduced! How do we know how much is enough?

12. Digital Sampling

13. Sampling Issues

14. Sampling Issues

15. The Problem

16. Fixing the Problem

17. Sampling • Nyquist Theorem (sampling theorem) • An analog signal of bandwidth B Hertz when sampled at least as often as once every 1/2B seconds (or at 2B Hertz), can be exactly converted back to the analog original signal without any distortion or loss of information. • This rate is called the Nyquist sampling rate.

18. Nyquist in Practice • Telephone speech has a bandwidth of 3500 Hz • At what rate should it be sampled? • 7000 Hz • In practice it is sampled at 8000 Hz, to avoid conversion factors • (Once every 124 microseconds)

19. Acoustic Signals • Acoustic signals are audible up to 24 kHz • What is the corresponding Nyquist sampling rate?

20. Acoustic Signals • Industrial standards • 6000 Hz • 8000 Hz • 11025 Hz • 16000 Hz • 22050 Hz • 32000 Hz • 32075 Hz • 44100 Hz • 48000 Hz

21. Spoken Sentence

22. Spoken Sentence

23. Spoken Sentence • 16000 Hz • 11025 Hz • 8000 Hz • 6000 Hz

24. Piano

25. Piano

26. Spoken Sentence • 16000 Hz • 11025 Hz • 8000 Hz • 6000 Hz

27. SPECTROGRAMS

28. Spectrogram Visual representation of frequencies in a signal. Sometimes called, spectral waterfalls, or voiceprints/voicegrams Can identify spoken words phonetically. Also used in sonor, radar, seismology, etc.

29. Spectrogram Frequency vs Time Color or height mapped to dB

30. Spectrogram – Speech16000 Hz

31. Spectrogram – Speech11025 Hz

32. Spectrogram – Speech8000 Hz

33. Spectrogram – Speech6000 Hz

34. Spectrogram – Piano16000 Hz

35. Spectrogram – Piano11025 Hz

36. Spectrogram – Piano8000 Hz

37. Spectrogram – Piano6000 Hz

38. ANALOG TO DIGITAL CONVERSION

39. A2D: Analog to Digital • Two steps • Sampling (which we just covered) • Quantization

40. Quantization • Analog signals take any value between some minimum and maximum • Infinite possible values • We need a finite set of values

41. Why do we need finite values?

42. State in Digital Logic • Flip-flops store state for sequential logic (vscombinatorical logic) • Each one can hold a 0 or 1, one bit • Put X together and we have X bits worth of state we can store

43. How do we get this?

44. How to quantize • Informally • If we have N bits per value, we have how many states? • Values from [min, max] (inclusive) • Each state provided by our bit vector needs to cover of the range

45. How to quantize • Simple algorithm, assume 2-bits, how many states?

46. How to quantize • Simple algorithm, assume 2-bits, how many states? • First state is min. We now have (4-1) = 3 states left to cover the range (Max – Min) • 00 – Min • 01 – Min + (Max – Min)/3 • 10 – Min + 2(Max – Min)/3 • 11 – Min + 3(Max – Min)/3 = Max

47. How to quantize • What do we do with data in between these values? • Let’s refine our algorithm

48. Quantization • Classification rule • Tells us which state of our bit vector the value corresponds to • Reconstruction rule • Tells us how to interpret a state of the bit vector

49. QuantizationClassification Rule • A general classification rule

50. QuantizationReconstruction Rule • A general reconstruction rule