1. ni.com Data Analysis: Time and Frequency Domain

2. ni.com Typical Data Acquisition System

3. ni.com Digitization An analog signal is sampled at a point in time and converted to a time series

4. ni.com Digitization Each sampled signal value is digitized using and analog-to-digital converter Parameters: –Resolution: number of bits used to represent the analog signal –Range: min. and max. voltage ADC can span (-5V to +5V) –Gain: range scale factor (gain factor of 10 means that a range spans 1/10 of the original range). –Polarity: single (-5 to 5V) or double (0 to 10V) Each sampled signal value is digitized using and analog-to-digital converter Parameters: –Resolution: number of bits used to represent the analog signal –Range: min. and max. voltage ADC can span (-5V to +5V) –Gain: range scale factor (gain factor of 10 means that a range spans 1/10 of the original range). –Polarity: single (-5 to 5V) or double (0 to 10V)

5. ni.com Code Width (LSB) Number of codes is a function of resolution: #of codes = 2 Code width (vertical sensitivity is the amount of voltage corresponding to a one-bit increment in code number LSB = Number of codes is a function of resolution: #of codes = 2 Code width (vertical sensitivity is the amount of voltage corresponding to a one-bit increment in code number LSB = resolution range gain x #of codes

6. ni.com Code Value to Voltage Conversion : voltage = (code) x code_width + Conversion : voltage = (code) x code_width + Bottom of range gain

7. ni.com When to Sample? Settling time is important desired measured desired

8. ni.com When to Sample?

9. ni.com Improperly sampled Properly sampled f N = f s /2f s : sampling frequency Sampling Guidelines Nyquist Theorem sampling rate > 2 x maximum frequency of signal Nyquist Frequency (f N ) maximum frequency that can be analyzed Frequencies above Nyquist Frequency cause aliasing Nyquist Theorem sampling rate > 2 x maximum frequency of signal Nyquist Frequency (f N ) maximum frequency that can be analyzed Frequencies above Nyquist Frequency cause aliasing

10. ni.com What is Aliasing? (Time Domain) Samples acquired at 1 kHz 150 Hz sine tone ? 850 Hz sine tone ? (1000 Hz – 150 Hz) 1150 Hz sine tone ? (1000 Hz + 150 Hz)

11. ni.com  n * F sampling  150 Hz Aliasing (Frequency Domain) 150, 850, and 1150 Hz

12. ni.com f1f1 f1f1 f3f3 f3f3 f s /2 fsfs fsfs alias free bandwidth f1f1 f1f1 f s /2 fsfs fsfs anti-aliasing filter anti-aliasing filter f2f2 f2f2 attenuated f 2 attenuated f 2 alias f 3 alias f 3 f4f4 f4f4 RAW SIGNAL ACQUIRED SIGNAL Time Domain Considerations Alias Free Bandwidth Nyquist Frequency Sample Frequency

13. ni.com Removes frequencies higher than Nyquist frequency Analog low-pass filter Before sampling Removes frequencies higher than Nyquist frequency Analog low-pass filter Before sampling Time Domain Considerations Anti-Aliasing Filter Flat Frequency Response Sharp Roll-off

14. ni.com Anti-Aliasing Filter (Analog Only) Analog anti-aliasing filter –Passband – DC to 400 Hz –Stopband – 600 Hz  Analog anti-aliasing filter –Passband – DC to 400 Hz –Stopband – 600 Hz 

15. ni.com Anti-Aliasing Filter (Analog+Digital) Analog filter –Passband – DC to 400 Hz –Stopband – 1600 Hz  Analog filter –Passband – DC to 400 Hz –Stopband – 1600 Hz  Digital filter (2X decimation) Passband – DC to 400 Hz Stopband – 600 to 1400 Hz Digital filter (2X decimation) Passband – DC to 400 Hz Stopband – 600 to 1400 Hz

16. ni.com Sampling Methods Simultaneous Sampling Interval Sampling Continuous Sampling Random Sampling Multiplexing Simultaneous Sampling Interval Sampling Continuous Sampling Random Sampling Multiplexing

17. ni.com Simultaneous Sampling Critical time relation btw. signals Requires: –Sample-and-hold circuits OR –Individual ADC’s Critical time relation btw. signals Requires: –Sample-and-hold circuits OR –Individual ADC’s

18. ni.com Interval Sampling Simulate simultaneous sampling for low- frequency signals

19. ni.com Continuous Sampling Sampling multiplexed channels at constant rate. Causes phase skew btw. Channels –Use only if time relation btw. Channels is not important Sampling multiplexed channels at constant rate. Causes phase skew btw. Channels –Use only if time relation btw. Channels is not important

20. ni.com Classic Multiplexed MIO Low cost/flexible –No anti-aliasing filters –Only one A/D converter for all channels Conflicts with some common requirements of many applications that require dynamic signal acquisition –Aliasing protection –Simultaneous sampling Low cost/flexible –No anti-aliasing filters –Only one A/D converter for all channels Conflicts with some common requirements of many applications that require dynamic signal acquisition –Aliasing protection –Simultaneous sampling

21. ni.com Multiplexing: Some Definitions Channels – the actual number of input channels scanned by the board Scan clock – the output data rate for each channel Decimation factor (D) – the acquisition over- sampling factor for each channel A/D clock – the actual sample rate of the multiplexing A/D converter A/D clock = channels * decimation * scan clock Channels – the actual number of input channels scanned by the board Scan clock – the output data rate for each channel Decimation factor (D) – the acquisition over- sampling factor for each channel A/D clock – the actual sample rate of the multiplexing A/D converter A/D clock = channels * decimation * scan clock

22. ni.com Multiplexing Identical Input 4 channels (same input signal on all channels) Scan clock = 1 kHz A/D clock = 4 kHz 4 channels (same input signal on all channels) Scan clock = 1 kHz A/D clock = 4 kHz

23. ni.com Resulting Delayed Acquisitions Our four channels appear to have different phases even though we input the same signal to each Scan clock = 1 kHz A/D clock = 4 kHz Our four channels appear to have different phases even though we input the same signal to each Scan clock = 1 kHz A/D clock = 4 kHz

24. ni.com Relative Phase Responses: Skew 4 channels Scan clock = 1 kHz A/D clock = 16 kHz (over-sampled 4X) 4 channels Scan clock = 1 kHz A/D clock = 16 kHz (over-sampled 4X)

25. ni.com Additional Time Domain Considerations  analog to digital converter –High resolution –Built-in anti-aliasing filters –Suited for sound and vibration measurements Simultaneous sampling and triggering –Phase relationship between signals Programmable gain Overload detection  analog to digital converter –High resolution –Built-in anti-aliasing filters –Suited for sound and vibration measurements Simultaneous sampling and triggering –Phase relationship between signals Programmable gain Overload detection

26. ni.com Time Domain Considerations Smoothing Windows Nonintegral number of cycles Reduces spectral leakage Window selection depends on the application PC Based instruments greatly facilitate transient analysis Reduces spectral leakage Window selection depends on the application PC Based instruments greatly facilitate transient analysis No windowing Windowing Window

27. ni.com Time vs Frequency Domain

28. ni.com Sample Time Domain Signal Sample Time Domain Signal FFT Anti-Alias Filter Anti-Alias Filter Octave Acquire Waveform Acquire Waveform Basics of Frequency Measurements Signal Conditioning Signal Conditioning Frequency Analysis Frequency Analysis

29. ni.com Frequency Domain Analysis FFT analysis Octave analysis Swept sine analysis FFT analysis Octave analysis Swept sine analysis

30. ni.com FFT Analysis Time domain in discrete values Use Discrete Fourier Transform (DFT) Fast Fourier Transform (FFT) Optimized version of DFT Highest frequency that can be analyzed Frequency resolution Time domain in discrete values Use Discrete Fourier Transform (DFT) Fast Fourier Transform (FFT) Optimized version of DFT Highest frequency that can be analyzed Frequency resolution f s : sampling frequency T : total acquisition time N : FFT block size T : total acquisition time N : FFT block size

31. ni.com FFT Analysis FFT gives magnitude and phase information –Magnitude = sqrt(Real^2 + Imag^2) –Phase = Tan -1 (Imag / Real) Power Spectrum reflects the energy content –Power Spectrum = Mag^2 Applications Vibration analysis Structural dynamics testing Preventative maintenance Shock testing FFT gives magnitude and phase information –Magnitude = sqrt(Real^2 + Imag^2) –Phase = Tan -1 (Imag / Real) Power Spectrum reflects the energy content –Power Spectrum = Mag^2 Applications Vibration analysis Structural dynamics testing Preventative maintenance Shock testing

32. ni.com Concentrates (“zooms”) FFT on a narrow band of frequencies Improves frequency resolution Distinguishes between closely-spaced frequencies Baseband analysis requires longer acquisition time for better resolution – requires more computation Concentrates (“zooms”) FFT on a narrow band of frequencies Improves frequency resolution Distinguishes between closely-spaced frequencies Baseband analysis requires longer acquisition time for better resolution – requires more computation Zoom FFT Analysis

33. ni.com Zoom FFT Analysis Baseband FFT Analysis Zoom FFT Analysis Zoom FFT Analysis

34. ni.com Zoom FFT Analysis – How It’s Done f1f1 f1f1 f2f2 f2f2 f 1 + f 2 f 1 - f 2 f1f1 f2f2 f 1 – f 2

35. ni.com Octave Analysis Analysis performed through a parallel bank of bandpass filters –One octave corresponds to the doubling of the frequency –Reference frequency is 1 kHz (audio domain) Analysis performed through a parallel bank of bandpass filters –One octave corresponds to the doubling of the frequency –Reference frequency is 1 kHz (audio domain) 220 Hz 440 Hz 880 Hz A A A A A A

36. ni.com Octave Analysis Octave analysis gives log-spaced frequency information –Similar to human perception of sound –1/1, 1/3, 1/12, and 1/24 octave analysis FFT gives linearly-spaced frequency information Applications –noise emissions testing –acoustic intensity measurement –sound power measurement –audio equalization Octave analysis gives log-spaced frequency information –Similar to human perception of sound –1/1, 1/3, 1/12, and 1/24 octave analysis FFT gives linearly-spaced frequency information Applications –noise emissions testing –acoustic intensity measurement –sound power measurement –audio equalization

37. ni.com Swept Sine Analysis Source steps through a range of frequencies Analyzer measures frequency amplitude and phase at each step Non-FFT based Source steps through a range of frequencies Analyzer measures frequency amplitude and phase at each step Non-FFT based Source Device Under Test Frequenc y Respon se

38. ni.com Auto-ranging: dynamic range optimized at each frequency Adjust source amplitude Adjust input range Both improve dynamic range at particular frequencies –Can get 140 dB effective dynamic range Auto-ranging: dynamic range optimized at each frequency Adjust source amplitude Adjust input range Both improve dynamic range at particular frequencies –Can get 140 dB effective dynamic range Swept Sine Analysis Channel B Channel A

39. ni.com Swept Sine Analysis Auto-resolution –Sweep optimized - more time at lower frequencies, less time at higher –Increases frequency resolution on rapidly changing responses Applications –Speaker testing –Cell phone testing –Electronic equipment characterization Auto-resolution –Sweep optimized - more time at lower frequencies, less time at higher –Increases frequency resolution on rapidly changing responses Applications –Speaker testing –Cell phone testing –Electronic equipment characterization

40. ni.com Comparison of Frequency Analysis Methods FFT analysis –Very fast –Linear frequency scale –Based on discrete Fourier transform Octave analysis –Logarithmic frequency scale –Set of filters dividing frequency into bands –Similar to how human ear perceives sound Swept sine analysis –Good dynamic range –Source and analyzer step across frequency range –Slower response FFT analysis –Very fast –Linear frequency scale –Based on discrete Fourier transform Octave analysis –Logarithmic frequency scale –Set of filters dividing frequency into bands –Similar to how human ear perceives sound Swept sine analysis –Good dynamic range –Source and analyzer step across frequency range –Slower response

41. ni.com Next Lecture Output signals Servo-control systems Output signals Servo-control systems