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№1 слайд![Fast Frequency and Response](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img0.jpg)
Содержание слайда: Fast Frequency and Response Measurements using FFTs
Alain Moriat,
Senior Architect
Fri. 12:45p
Pecan (9B)
№2 слайд![Accurately Detect a Tone What](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img1.jpg)
Содержание слайда: 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?
№3 слайд![Presentation Overview Why use](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img2.jpg)
Содержание слайда: Presentation Overview
Why use the frequency domain?
FFT – a short introduction
Frequency interpolation
Improvements using windowing
Error evaluation
Amplitude/phase response measurements
Demos
№4 слайд![Clean Single Tone Measurement](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img3.jpg)
Содержание слайда: Clean Single Tone Measurement
Clean sine tone
Easy to measure
№5 слайд![Noisy Tone Measurement Noisy](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img4.jpg)
Содержание слайда: Noisy Tone Measurement
Noisy signal
Difficult to measure in the time domain
№6 слайд![Fast Fourier Transform FFT](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img5.jpg)
Содержание слайда: Fast Fourier Transform (FFT) Fundamentals (Ideal Case)
The tone frequency is an exact multiple of the frequency resolution (“hits a bin”)
№7 слайд![FFT Fundamentals Realistic](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img6.jpg)
Содержание слайда: FFT Fundamentals (Realistic Case)
The tone frequency is not a multiple of the frequency resolution
№8 слайд![Input Frequency Hits Exactly](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img7.jpg)
Содержание слайда: Input Frequency Hits Exactly a Bin
Only one bin is activated
№9 слайд![Input Frequency is . Bin off](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img8.jpg)
Содержание слайда: Input Frequency is +0.01 Bin “off”
More bins are activated
№10 слайд![Input Frequency is . Bin off](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img9.jpg)
Содержание слайда: Input Frequency is +0.25 Bin “off”
№11 слайд![Input Frequency is . Bin off](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img10.jpg)
Содержание слайда: Input Frequency is +0.50 Bin “off”
Highest side-lobes
№12 слайд![Input Frequency is . Bin off](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img11.jpg)
Содержание слайда: Input Frequency is +0.75 Bin “off”
The Side lobe levels decrease
№13 слайд![Input Frequency is . Bin off](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img12.jpg)
Содержание слайда: Input Frequency is +1.00 Bin “off”
Only one bin is activated
№14 слайд![The Envelope Function](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img13.jpg)
Содержание слайда: The Envelope Function
№15 слайд![The Mathematics Envelope](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img14.jpg)
Содержание слайда: The Mathematics
Envelope function:
Bin offset:
Real amplitude:
№16 слайд![Demo Amplitude and frequency](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img15.jpg)
Содержание слайда: Demo
Amplitude and frequency detection by Sin(x) / x interpolation
№17 слайд![Aliasing of the Side-Lobes](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img16.jpg)
Содержание слайда: Aliasing of the Side-Lobes
№18 слайд![Weighted Measurement Apply a](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img17.jpg)
Содержание слайда: Weighted Measurement
Apply a Window to the signal
№19 слайд![Weighted Spectrum Measurement](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img18.jpg)
Содержание слайда: Weighted Spectrum Measurement
Apply a Window to the Signal
№20 слайд![Rectangular and Hanning](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img19.jpg)
Содержание слайда: Rectangular and Hanning Windows
Side lobes for Hanning Window are significantly lower than for Rectangular window
№21 слайд![Input Frequency Exactly Hits](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img20.jpg)
Содержание слайда: Input Frequency Exactly Hits a Bin
Three bins are activated
№22 слайд![Input Frequency is . Bin off](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img21.jpg)
Содержание слайда: Input Frequency is +0.25 Bin “off”
More bins are activated
№23 слайд![Input Frequency is . Bin off](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img22.jpg)
Содержание слайда: Input Frequency is +0.50 Bin “off”
Highest side-lobes
№24 слайд![Input Frequency is . Bin off](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img23.jpg)
Содержание слайда: Input Frequency is +0.75 Bin “off”
The Side lobe levels decrease
№25 слайд![Input Frequency is . Bin off](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img24.jpg)
Содержание слайда: Input Frequency is +1.00 Bin “off”
Only three bins activated
№26 слайд![The Mathematics for Hanning](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img25.jpg)
Содержание слайда: The Mathematics for Hanning ...
Envelope:
Bin Offset:
Amplitude:
№27 слайд![A LabVIEW Tool Tone detector](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img26.jpg)
Содержание слайда: A LabVIEW Tool
Tone detector LabVIEW virtual instrument (VI)
№28 слайд![Demo Amplitude and frequency](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img27.jpg)
Содержание слайда: 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
№29 слайд![Frequency Detection Resolution](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img28.jpg)
Содержание слайда: Frequency Detection Resolution
№30 слайд![Amplitude Detection Resolution](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img29.jpg)
Содержание слайда: Amplitude Detection Resolution
№31 слайд![Phase Detection Resolution](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img30.jpg)
Содержание слайда: Phase Detection Resolution
№32 слайд![Conclusions Traditional](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img31.jpg)
Содержание слайда: 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
№33 слайд![Conclusions Notes Page Only](/documents_6/1a1063b0fc3a9e5705397c64e3070099/img32.jpg)
Содержание слайда: 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 Amplitude and Phase