EE 435. Lecture 34. Spectral Performance Windowing Quantization Noise

Transcription

1 EE 435 Lecture 34 Spectral Performance Windowing Quantization Noise

2 . Review from last lecture. Are there any strategies to address the problem of requiring precisely an integral number of periods to use the FFT? Windowing is sometimes used Windowing is sometimes misused

3 . Review from last lecture. Windowing Windowing is the weighting of the time domain function to maintain continuity at the end points of the sample window Well-studied window functions: Rectangular (also with appended zeros) Triangular Hamming Hanning Blackman

4 . Review from last lecture. Rectangular Window

5 . Review from last lecture. Rectangular Window (with appended zeros)

6 . Review from last lecture. Triangular Window

7 . Review from last lecture. Hamming Window

8 . Review from last lecture. Hanning Window

9 . Review from last lecture. Comparison of 4 windows

10 . Review from last lecture. Comparison of 4 windows

11 Preliminary Observations about Windows Provide separation of spectral components Energy can be accumulated around spectral components Simple to apply Some windows work much better than others But windows do not provide dramatic improvement and

12 Comparison of 4 windows when sampling hypothesis are satisfied

13 Comparison of 4 windows

14 Preliminary Observations about Windows Provide separation of spectral components Energy can be accumulated around spectral components Simple to apply Some windows work much better than others But windows do not provide dramatic improvement and can significantly degrade performance if sampling hypothesis are met

15 Issues of Concern for Spectral Analysis An integral number of periods is critical for spectral analysis Not easy to satisfy this requirement in the laboratory Windowing can help but can hurt as well Out of band energy can be reflected back into bands of interest Characterization of CAD tool environment is essential Spectral Characterization of high-resolution data converters requires particularly critical consideration to avoid simulations or measurements from masking real performance

16 Spectral Characterization of Data Converters Distortion Analysis Time Quantization Effects of DACs of ADCs Amplitude Quantization Effects of DACs of ADCs

17 Spectral Characterization of Data Converters Distortion Analysis Time Quantization Effects of DACs of ADCs Amplitude Quantization Effects of DACs of ADCs

18 Quantization Effects on Spectral Performance and Noise Floor in DFT Assume the effective clock rate (for either an ADC or a DAC) is arbitrarily fast Without Loss of Generality it will be assumed that f SIG =50Hz Index on DFT will be listed in terms of frequency (rather than index number) Matlab File: afft_quantization.m

19 Quantization Effects 16,384 pts res = 4bits N P =25 20 msec

20 Quantization Effects 16,384 pts res = 4bits N P =25 20 msec

21 Quantization Effects 16,384 pts res = 4bits

22 Quantization Effects Simulation environment: N P =23 f SIG =50Hz V REF : -1V, 1V Res: will be varied N=2 n will be varied

23 Quantization Effects Res = 4 bits

24 Quantization Effects Res = 4 bits Axis of Symmetry

25 Quantization Effects Res = 4 bits Some components very small

26 Quantization Effects Res = 4 bits Set lower display limit at -120dB

27 Quantization Effects Res = 4 bits

28 Quantization Effects Res = 4 bits

29 Quantization Effects Res = 4 bits

30 Quantization Effects Res = 4 bits

31 Quantization Effects Res = 4 bits

32 Quantization Effects Res = 4 bits

33 Quantization Effects Res = 4 bits Fundamental

34 Quantization Effects Res = 10 bits

35 Quantization Effects Res = 10 bits

36 Quantization Effects Res = 10 bits

37 Quantization Effects Res = 10 bits

38 Quantization Effects Res = 10 bits

39 Quantization Effects Res = 10 bits

40 Quantization Effects Res = 10 bits

41 Quantization Effects Res = 10 bits

42 Quantization Effects Res = 10 bits

43 Quantization Effects Res = 10 bits

44 Quantization Effects Res = 10 bits

45 Quantization Effects Res = 10 bits

46 Quantization Effects Res = 10 bits

47 Quantization Effects Res = 10 bits Res 10 No. points 256 fsig= No. Periods Rectangular Window Columns 1 through Columns 6 through

48 Columns 11 through Columns 16 through Columns 21 through Columns 26 through Columns 31 through

49 Columns 36 through Columns 41 through Columns 46 through Columns 51 through Columns 56 through

50 Columns 61 through Columns 66 through Columns 71 through Columns 76 through Columns 81 through

51 Columns 86 through Columns 91 through

52 Spectral Characterization of Data Converters Distortion Analysis Time Quantization Effects of DACs of ADCs Amplitude Quantization Effects of DACs of ADCs

53 Spectral Characteristics of DACs and ADCs

54 Spectral Characteristics of DAC t Periodic Input Signal Sampling Clock T SIG t Sampled Input Signal (showing time points where samples taken)

55 Spectral Characteristics of DAC T SIG Quantization Levels T PERIOD Quantized Sampled Input Signal (with zero-order sample and hold)

56 Spectral Characteristics of DAC T DFT WINDOW T PERIOD T SIG T CLOCK Sampling Clock T DFT CLOCK DFT Clock

57 Spectral Characteristics of DAC T DFT WINDOW T PERIOD T SIG T CLOCK Sampling Clock T DFT CLOCK DFT Clock

58 Spectral Characteristics of DAC Sampling Clock DFT Clock

59 Spectral Characteristics of DAC Sampled Quantized Signal (zoomed) DFT Clock Sampling Clock

60 Spectral Characteristics of DAC Consider the following example f SIG =50Hz k 1 =230 k 2 =23 N P =1 n res =8bits Xin(t) =.95sin(2πf SIG t) (-.4455dB) Thus N P1 =23 θ SR =5 f CL /f SIG =10 Matlab File: afft_quantization_dac.m

61 DFT Simulation from Matlab n sam =

62 DFT Simulation from Matlab Expanded View n sam = Width of this region is f CL Analogous to the overall DFT window when directly sampled but modestly asymmetric

63 DFT Simulation from Matlab Expanded View n sam =

64 DFT Simulation from Matlab Expanded View n sam =

65 DFT Simulation from Matlab Expanded View n sam =

66 f SIG =50Hz, k 1 =23, k 2 =23, N P =1, n res =8bits Xin(t) =sin(2πf SIG t) N=32768 Columns 1 through Columns 8 through Columns 15 through Columns 22 through Columns 29 through

67 f SIG =50Hz, k 1 =23, k 2 =23, N P =1, n res =8bits Xin(t) =sin(2πf SIG t) N=32768 Columns 36 through Columns 43 through Columns 50 through Columns 57 through Columns 64 through

68 f SIG =50Hz, k 1 =23, k 2 =23, N P =1, n res =8bits Xin(t) =sin(2πf SIG t) N=32768 Columns 71 through Columns 78 through Columns 85 through Columns 92 through Columns 99 through

69 DFT Simulation from Matlab n sam =

70 DFT Simulation from Matlab Expanded View n sam =

71 DFT Simulation from Matlab Expanded View n sam =

72 DFT Simulation from Matlab Expanded View nsam =

73 Summary of time and amplitude quantization assessment Time and amplitude quantization do not introduce harmonic distortion Time and amplitude quantization do increase the noise floor

74 Quantization Noise DACs and ADCs generally quantize both amplitude and time If converting a continuous-time signal (ADC) or generating a desired continuoustime signal (DAC) these quantizations cause a difference in time and amplitude from the desired signal First a few comments about Noise

75 Noise We will define Noise to be the difference between the actual output and the desired output of a system Types of noise: Random noise due to movement of electrons in electronic circuits Interfering signals generated by other systems Interfering signals generated by a circuit or system itself Error signals associated with imperfect signal processing algorithms or circuits

76 Noise We will define Noise to be the difference between the actual output and the desired output of a system All of these types of noise are present in data converters and are of concern when designing most data converters Can not eliminate any of these noise types but with careful design can manage their effects to certain levels Noise (in particular the random noise) is often the major factor limiting the ultimate performance potential of many if not most data converters

77 Noise We will define Noise to be the difference between the actual output and the desired output of a system Types of noise: Random noise due to movement of electrons in electronic circuits Interfering signals generated by other systems Interfering signals generated by a circuit or system itself Error signals associated with imperfect signal processing algorithms or circuits Quantization noise is a significant component of this noise in ADCs and DACs and is present even if the ADC or DAC is ideal

78 End of Lecture 34