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Data Analysis: Time and Frequency Domain

Data Analysis: Time and Frequency Domain. Typical Data Acquisition System. Digitization. An analog signal is sampled at a point in time and converted to a time series. Digitization. Each sampled signal value is digitized using and analog-to-digital converter Parameters:

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Data Analysis: Time and Frequency Domain

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  1. Data Analysis: Time and Frequency Domain

  2. Typical Data Acquisition System

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

  4. 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)

  5. 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 = resolution range gain x #of codes

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

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

  8. When to Sample?

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

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

  11. n * Fsampling±150 Hz Aliasing (Frequency Domain) • 150, 850, and 1150 Hz

  12. f1 alias f3 attenuated f2 Time Domain ConsiderationsAlias Free Bandwidth Nyquist Frequency Sample Frequency fs /2 fs RAW SIGNAL f1 f2 f3 f4 alias free bandwidth fs /2 fs anti-aliasing filter ACQUIRED SIGNAL

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

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

  15. Sampling Methods • Simultaneous Sampling • Interval Sampling • Continuous Sampling • Random Sampling • Multiplexing

  16. Simultaneous Sampling • Critical time relation btw. signals • Requires: • Sample-and-hold circuits OR • Individual ADC’s

  17. Interval Sampling • Simulate simultaneous sampling for low-frequency signals

  18. Continuous Sampling • Sampling multiplexed channels at constant rate. • Causes phase skew btw. Channels • Use only if time relation btw. Channels is not important

  19. 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

  20. 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

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

  22. 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

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

  24. Additional Time Domain Considerations • D/S 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

  25. Time Domain ConsiderationsSmoothing Windows • Reduces spectral leakage • Window selection depends on the application • PC Based instruments greatly facilitate transient analysis No windowing Nonintegral number of cycles Window Windowing

  26. Time vs Frequency Domain

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

  28. Frequency Domain Analysis • FFT analysis • Octave analysis • Swept sine analysis

  29. 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 fs: sampling frequency T: total acquisition time N: FFT block size

  30. 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

  31. Zoom FFT Analysis • 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

  32. Zoom FFT Analysis Baseband FFT Analysis Zoom FFT Analysis

  33. 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) 220 Hz 440 Hz 880 Hz A A A

  34. 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

  35. Swept Sine Analysis Device • Source steps through a range of frequencies • Analyzer measures frequency amplitude and phase at each step • Non-FFT based Under Test Frequency Source Response

  36. Channel A Channel B Swept Sine Analysis 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

  37. 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

  38. 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

  39. Next Lecture • Output signals • Servo-control systems

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