Ni.com Data Analysis: Time and Frequency Domain. ni.com Typical Data Acquisition System

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Data Analysis: Time and Frequency Domain

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Typical Data Acquisition System

SignalSource

SignalConnection

SignalConditioning

+-

SignalMeasurement

ADC

Analog

Digital

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DigitizationDigitization

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

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

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DigitizationDigitization

• 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)

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Code Width (LSB)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

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Code Value to VoltageCode Value to Voltage

• Conversion :

voltage = (code) x code_width +

• Conversion :

voltage = (code) x code_width + Bottom of range

gain

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When to Sample?When to Sample?

• Settling time is important• Settling time is important

desiredmeasured

measureddesired

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When to Sample?When to Sample?

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Improperly sampledImproperly sampled Properly sampledProperly sampled

fN = fs/2 fs: sampling frequencyfN = fs/2 fs: sampling frequency

Sampling GuidelinesSampling 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

• 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

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What is Aliasing? (Time Domain)What is Aliasing? (Time Domain)

• Samples acquired at 1 kHz• Samples acquired at 1 kHz

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150 Hz sine tone ? 150 Hz sine tone ?

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850 Hz

850 Hz sine tone ? (1000 Hz – 150 Hz) 850 Hz sine tone ? (1000 Hz – 150 Hz)

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150 Hz

850 Hz

1150 Hz

1150 Hz sine tone ? (1000 Hz + 150 Hz) 1150 Hz sine tone ? (1000 Hz + 150 Hz)

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n * Fsampling 150 Hz n * Fsampling 150 Hz

Aliasing (Frequency Domain)Aliasing (Frequency Domain)

• 150, 850, and 1150 Hz• 150, 850, and 1150 Hz

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f1f1 f3f3

fs /2fs /2 fsfs

alias free bandwidthalias free bandwidth

f1f1

fs /2fs /2 fsfs

anti-aliasingfilteranti-aliasingfilter

f2f2

attenuatedf2

attenuatedf2

aliasf3

aliasf3

f4f4

RAW SIGNALRAW SIGNAL

ACQUIRED SIGNALACQUIRED SIGNAL

Time Domain ConsiderationsAlias Free BandwidthTime Domain ConsiderationsAlias Free Bandwidth Nyquist FrequencyNyquist Frequency Sample FrequencySample Frequency

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• 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 ConsiderationsAnti-Aliasing FilterTime Domain ConsiderationsAnti-Aliasing Filter

Flat FrequencyResponse

SharpRoll-off

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AA-Filter

Anti-Aliasing Filter (Analog Only)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

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Sampling MethodsSampling Methods

• Simultaneous Sampling

• Interval Sampling

• Continuous Sampling

• Random Sampling

• Multiplexing

• Simultaneous Sampling

• Interval Sampling

• Continuous Sampling

• Random Sampling

• Multiplexing

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Simultaneous SamplingSimultaneous 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

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Interval SamplingInterval Sampling

• Simulate simultaneous sampling for low-frequency signals

• Simulate simultaneous sampling for low-frequency signals

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Continuous SamplingContinuous 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

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Classic Multiplexed MIOClassic 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

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Multiplexing: Some DefinitionsMultiplexing: 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

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Multiplexing Identical InputMultiplexing 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

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Analog In

Chan. 0

Chan. 1

Chan. 2

Chan. 3

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Resulting Delayed AcquisitionsResulting 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

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Chan. 0

Chan. 1

Chan. 2

Chan. 3

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Relative Phase Responses: SkewRelative 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)

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Chan. 0

Chan. 1

Chan. 2

Chan. 3

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Degrees

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Additional Time Domain ConsiderationsAdditional 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

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Time Domain ConsiderationsSmoothing WindowsTime Domain ConsiderationsSmoothing Windows

Nonintegral number of cyclesNonintegral 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

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Time vs Frequency DomainTime vs Frequency Domain

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Sample TimeDomain SignalSample Time

Domain Signal

FFTFFT

Anti-Alias Filter

Anti-Alias Filter

OctaveOctave

Acquire WaveformAcquire

Waveform

Basics of Frequency MeasurementsBasics of Frequency Measurements

SignalConditioning

SignalConditioning

FrequencyAnalysis

FrequencyAnalysis

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Frequency Domain AnalysisFrequency Domain Analysis

• FFT analysis

• Octave analysis

• Swept sine analysis

• FFT analysis

• Octave analysis

• Swept sine analysis

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FFT AnalysisFFT 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

2maxsfF fs : sampling frequencyfs : sampling frequency

N

f

Tf s

1 T : total acquisition time

N : FFT block size

T : total acquisition time

N : FFT block size

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FFT AnalysisFFT 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

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• 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 AnalysisZoom FFT Analysis

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Zoom FFT AnalysisZoom FFT Analysis

Baseband FFT AnalysisBaseband FFT Analysis

Zoom FFTAnalysis

Zoom FFTAnalysis

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Octave AnalysisOctave 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)

ff/2f/4 4 f2 f

1 octave

F

A

0220 Hz220 Hz 440 Hz440 Hz 880 Hz880 HzAA AAAA

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Octave AnalysisOctave 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

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Swept Sine AnalysisSwept 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

FrequencyResponse

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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 AnalysisSwept Sine Analysis

Gain

Chan A

Gain

Chan BSource Channel B

Channel A

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Swept Sine AnalysisSwept 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

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Comparison of Frequency Analysis MethodsComparison 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

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Next LectureNext Lecture

• Output signals

• Servo-control systems

• Output signals

• Servo-control systems