1. DSP

2. What is DSP? DSP: Digital Signal Processing---Using a digital process (e.g., a program running on a microprocessor) to modify a digital representation of a signal DSP: Digital Signal Processor---a specialized microprocessor designed for handling DSP tasks.

3. Types of Signals Analog signal: A continuous signal in both value (magnitude) and time Digital: A signal that is discrete in both value and time (or other dimension such as space)

4. Transducers convert analog signals to time-varying electrical voltages P3 fig1-1

5. Source of analog signals and how they are converted to digital ones P20 table 2-1

6. Nyquist’s Sampling Theorem Analog to digital conversion: the analog signal must be sampled at twice the highest frequency component of the signal to avoid distortion. Example, for digital audio CD, the sampling rate is 44.1 kHz (based on the highest human audible frequency of around 20 KHz)

7. Illustration of the Sampling Process P4 fig 1-2

8. Speed of DSP Critical for Real- Time Applications Example: sampling rates are 44.1 kHz for audio CD and 48 kHz for digital audio tape (DAT) unit. A DSP CD-to-tape converter must be ready to accept a new sample every 22.6  sec (or 1/44100 sec) from the CD source and produce a new output sample for the DAT every 20.8  sec (1/48000 sec).

9. Advantages of DSP over analog signal processing (ASP) Insensitive to environment Insensitive to component tolerances Predictable, repeatable (exact) behavior Programmability (flexibility) Size: small than analog counterpart in general Continued rapid advancement of VLSI technology Capacity utilization of high BW transmission links Design tools are available

10. Applications of DSP P8 tab 1-1

11. Major DSP Vendors Analog Devices AT&T Lucent Motorola NEC Texas Instruments Zoran

12. Fourier Analysis

13. Fourier Analysis (continued)

18. Sinusoidal components (continued): 1 Hz square wave P30 fig 2-9, 10

19. Frequency components of 1 Hz squarewave

20. Visualization of a signal (Dual Tone Multiple Frequency) in time and frequency domain P23 fig 2-3, 4

21. Fourier series: sinusoidal components of a signal P 28 fig 2-7, 8

22. Filters Filter is used to “shape” (selectively change or modify the magnitude and phase of the input signal as a function of frequency) the signals.

23. Functions of Filters Remove noise/interference Spectral analysis: analyze the frequency contents of a signal Synthesis: generate simple tones to human voice …

24. Types of filters Low-pass High-pass All-pass (amplifier) Band-pass Band-stop (notch) Arbitrary pass-band comb

25. Ideal versus real filter: low-pass P67 fig 3-3

26. The meaning of db or decibel P45 tab 2-3

27. Bassband and bandpass filters P38 fig 2-18

28. Types of filters High pass & bandpass p70

29. Types of filters (continued) Bandpass & bandstop P71 fig 3-8

30. Types of filters (continued) Comb filter p74 fig 3-12

31. The characteristics of a real baseband (lowpass) filter P41 fig 2-21

32. Implementation of filters Analog filters Digital filters: one of the major applications of DSP; offer many advantages over their analog counterpart as described earlier.

33. Example of filter (notch filter) application: removal of noise P66 fig 3-2

34. Correlation: compare earlier sections of signals with current section (auto- correlation); special case of filtering.

35. A typical DSP chip (IC) P11 tab 1-2

36. Limitations of DSP Speed: being programmable means 10 to 100 times slower than the hardwired tech. Processing: program is simple but needs be done quickly (lots of MAC instructions) Precision: use fixed point format with limited precision to save chip space Digital signal required more BW than the corresponding analog signal

37. Visualizing analog signals in time domain P22 figs 2-1 & 2-2

38. Human Speech Spectrum

39. Describing a system in time domain: the impulse response An impulse (math.) excites a system equally at all frequencies. P47 fing 2-23

40. Labeling a system in time domain P49 fig 2-25

41. Impulse response of an elliptical filter P48 fig 2-24

42. The frequency response function H(j  ), where  ( or  ) is signal frequency; it is also known as the transfer function H(j  ) can be generalized to H(s), the system function, where s =  + j , a quantity known as complex frequency. Depending on whether  is positive or negative, the signal strength increases or decreases in time, as show in the following example.

43. Example of complex frequency P54 fig 2-30

44. The complex frequency s-plane P57 fig 2-31

45. Properties of a linear system P59 fig 2-33

46. Poles and zeros of the transfer function P85 equations

47. Poles and zeros (continued) P86 equation & fig 3-22

48. Poles and zeros example

49. Poles and zeros (continued) P88 fig 3-24

50. Poles and zeros (continued) P89 fig 3-25

51. Analog, discrete-time, and digital signals P94 fig 4-1

52. Sampling: 1st step to convert an analog signal to digital one Nyquist rate: minimum sampling frequency to avoid undesirable effect (aliasing) p96 fig 4-2

53. Sampling theorem

54. Sampling theorem (continued)

56. Describing discrete-time system H(z): the system or transfer function, where z is the complex frequency in polar coordinates

57. The polar coordinate and z-plane P110 fig 4-14

58. More on H(z) and z-plane P111 equations, p112 fig 4-15

59. More on H(z)

60. Example for a simple system P113 fig 4-16

61. H(z) and the difference equations H(s): Laplace transformation of h(t) H(z): z-transformation of the DT (discrete time) impulse response of h(n) h(t) is a differential equation h(n) is described using difference equations, meaning current output of the system is a linear combination of current input samples, past input samples, and past output samples.

62. The difference equations General form: p116 equation 4-14 Difference equations can be translated easily into computer programs (run on DSP)

63. Digital filters The IIR (infinite impulse response) filter p148 fig 4-33

64. The FIR (finite impulse response) filter P149 fig 4-34

65. IIR versus FIR digital filters P152 tab 4-6

66. DSP implementation of filters DSP architecture: