Презентация «Fast Frequency and Response Measurements using FFTs»

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Презентация «Fast Frequency and Response Measurements using FFTs»

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Fast Frequency and Response Measurements using FFTs Alain Moriat, Senior Architect Fri. 12:45p Pecan
Fast Frequency and Response Measurements using FFTs Alain Moriat, Senior Architect Fri. 12:45p Pecan (9B)
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Accurately Detect a Tone What is the exact frequency and amplitude of a tone embedded in a complex s
Accurately Detect a Tone What is the exact frequency and amplitude of a tone embedded in a complex signal? How fast can I perform these measurements? How accurate are the results?
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Presentation Overview Why use the frequency domain? FFT – a short introduction Frequency interpolati
Presentation Overview Why use the frequency domain? FFT – a short introduction Frequency interpolation Improvements using windowing Error evaluation Amplitude/phase response measurements Demos
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Clean Single Tone Measurement Clean sine tone Easy to measure
Clean Single Tone Measurement Clean sine tone Easy to measure
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Noisy Tone Measurement Noisy signal Difficult to measure in the time domain
Noisy Tone Measurement Noisy signal Difficult to measure in the time domain
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Fast Fourier Transform (FFT) Fundamentals (Ideal Case) The tone frequency is an exact multiple of th
Fast Fourier Transform (FFT) Fundamentals (Ideal Case) The tone frequency is an exact multiple of the frequency resolution (“hits a bin”)
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FFT Fundamentals (Realistic Case) The tone frequency is not a multiple of the frequency resolution
FFT Fundamentals (Realistic Case) The tone frequency is not a multiple of the frequency resolution
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Input Frequency Hits Exactly a Bin Only one bin is activated
Input Frequency Hits Exactly a Bin Only one bin is activated
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Input Frequency is +0. 01 Bin “off” More bins are activated
Input Frequency is +0. 01 Bin “off” More bins are activated
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Input Frequency is +0. 25 Bin “off”
Input Frequency is +0. 25 Bin “off”
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Input Frequency is +0. 50 Bin “off” Highest side-lobes
Input Frequency is +0. 50 Bin “off” Highest side-lobes
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Input Frequency is +0. 75 Bin “off” The Side lobe levels decrease
Input Frequency is +0. 75 Bin “off” The Side lobe levels decrease
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Input Frequency is +1. 00 Bin “off” Only one bin is activated
Input Frequency is +1. 00 Bin “off” Only one bin is activated
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The Envelope Function
The Envelope Function
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The Mathematics Envelope function: Bin offset: Real amplitude:
The Mathematics Envelope function: Bin offset: Real amplitude:
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Demo Amplitude and frequency detection by Sin(x) / x interpolation
Demo Amplitude and frequency detection by Sin(x) / x interpolation
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Aliasing of the Side-Lobes
Aliasing of the Side-Lobes
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Weighted Measurement Apply a Window to the signal
Weighted Measurement Apply a Window to the signal
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Weighted Spectrum Measurement Apply a Window to the Signal
Weighted Spectrum Measurement Apply a Window to the Signal
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Rectangular and Hanning Windows Side lobes for Hanning Window are significantly lower than for Recta
Rectangular and Hanning Windows Side lobes for Hanning Window are significantly lower than for Rectangular window
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Input Frequency Exactly Hits a Bin Three bins are activated
Input Frequency Exactly Hits a Bin Three bins are activated
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Input Frequency is +0. 25 Bin “off” More bins are activated
Input Frequency is +0. 25 Bin “off” More bins are activated
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Input Frequency is +0. 50 Bin “off” Highest side-lobes
Input Frequency is +0. 50 Bin “off” Highest side-lobes
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Input Frequency is +0. 75 Bin “off” The Side lobe levels decrease
Input Frequency is +0. 75 Bin “off” The Side lobe levels decrease
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Input Frequency is +1. 00 Bin “off” Only three bins activated
Input Frequency is +1. 00 Bin “off” Only three bins activated
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The Mathematics for Hanning . . . Envelope: Bin Offset: Amplitude:
The Mathematics for Hanning . . . Envelope: Bin Offset: Amplitude:
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A LabVIEW Tool Tone detector LabVIEW virtual instrument (VI)
A LabVIEW Tool Tone detector LabVIEW virtual instrument (VI)
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Demo Amplitude and frequency detection using a Hanning Window (named after Von Hann) Real world demo
Demo Amplitude and frequency detection using a Hanning Window (named after Von Hann) Real world demo using: The NI-5411 ARBitrary Waveform Generator The NI-5911 FLEXible Resolution Oscilloscope
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Frequency Detection Resolution
Frequency Detection Resolution
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Amplitude Detection Resolution
Amplitude Detection Resolution
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Phase Detection Resolution
Phase Detection Resolution
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Conclusions Traditional counters resolve 10 digits in one second FFT techniques can do this in much
Conclusions Traditional counters resolve 10 digits in one second FFT techniques can do this in much less than 100 ms Another example of 10X for test Similar improvements apply to amplitude and phase
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Conclusions (Notes Page Only) Traditional Counters Resolve 10 digits in one second FFT Techniques ca
Conclusions (Notes Page Only) Traditional Counters Resolve 10 digits in one second FFT Techniques can do this in much less than 100 ms Another example of 10X for test Similar improvements apply to …


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