fast frequency and response measurements using ffts

8/14/2019 Fast Frequency and Response Measurements Using FFTs

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www.natinst.comwww.natinst.com

Fast Frequency and Response

Measurements using FFTs

Fast Frequency and Response

Measurements using FFTs

Alain Moriat,

Senior ArchitectFri. 12:45p

Pecan (9B)

Alain Moriat,

Senior ArchitectFri. 12:45p

Pecan (9B)


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Accurately Detect a ToneAccurately 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?

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 OverviewPresentation Overview

Why use the frequency domain?

FFT a short introduction

Frequency interpolation

Improvements using windowing

Error evaluation

Amplitude/phase response measurements Demos

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 MeasurementClean Single Tone Measurement

Clean sine tone Easy to measure

Clean sine tone Easy to measure

Clean tone spectrum

Clean tone spectrum

2

-2

-1

0

1

1.00.0 0.2 0.4 0.6 0.8

Time signal 20

-60

-40

-20

0

500 5 10 15 20 25 30 35 40 45

FFT SpectrumVolt

mskHz

dBV


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2

-2

-1

0

1

1.00.0 0.2 0.4 0.6 0.8

Time signal 20

-60

-40

-20

0

500 5 10 15 20 25 30 35 40 45

FFT SpectrumVolt

mskHz

dBV

Noisy Tone MeasurementNoisy Tone Measurement

Noisy signal Difficult to measure in

the time domain

Noisy signal Difficult to measure in

the time domain

Noisy signal spectrum Easier to measure

Noisy signal spectrum Easier to measure

Our signal


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Fast Fourier Transform (FFT)

Fundamentals (Ideal Case)

Fast Fourier Transform (FFT)

Fundamentals (Ideal Case)

The tone frequency is an exact multiple of the frequencyresolution (hits a bin)

The tone frequency is an exact multiple of the frequencyresolution (hits a bin)

2

-2

-1

0

1

0.50.0 0.1 0.2 0.3 0.4

Time signal 20

-60

-40

-20

0

500 5 10 15 20 25 30 35 40 45

FFT SpectrumVolt

ms

kHz

dBV

Fsampling = 100 kHz Record size = 50 samples

Time res = 10 us Freq. res = 2 kHz


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FFT Fundamentals (Realistic Case)FFT Fundamentals (Realistic Case)

The tone frequency is not a multiple of the

frequency resolution

The tone frequency is not a multiple of the

frequency resolution

2

-2

-1

0

1

0.50.0 0.1 0.2 0.3 0.4

Time signal 20

-60

-40

-20

0

500 5 10 15 20 25 30 35 40 45

FFT SpectrumVolt

ms

kHz

dBV

Fsampling = 100 kHz Record size = 50 samples

Time res = 10 us Freq. res = 2 kHz


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Input Frequency Hits Exactly a BinInput Frequency Hits Exactly a Bin

Only one bin

is activated

Only one bin

is activated

0

-60

-50

-40

-30

-20

-10

6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

dB

Bin


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Input Frequency is +0.01 Bin offInput Frequency is +0.01 Bin off

More bins

are

activated

More bins

are

activated

0

-60

-50

-40

-30

-20

-10

6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

dB

Bin


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0

-60

-50

-40

-30

-20

-10

6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

dB

Bin


Real top

Highest Bin

Next Highest

Bin


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Highest

side-lobes

Highest

side-lobes

0

-60

-50

-40

-30

-20

-10

6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

dB

Bin


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The Side

lobe levels

decrease

The Side

lobe levels

decrease

0

-60

-50

-40

-30

-20

-10

6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

dB

Bin


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Only one

bin is

activated

Only one

bin is

activated

0

-60

-50

-40

-30

-20

-10

6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

dB

Bin


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1.1

-0.3-0.2

0.0

0.2

0.4

0.6

0.8

1.0

4-4 -3 -2 -1 0 1 2 3 Bin

The Envelope FunctionThe Envelope Function

Real top

Highest Bin = a

Next highestBin = b


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The MathematicsThe Mathematics

Envelope function:

Bin offset:

Real amplitude:

Envelope function:

Bin offset:

Real amplitude:

bin)(

bin)Sin(Env

=

b)(a

bbin

+=

bin)Sin(bin)(aAmp

=


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DemoDemo

Amplitude and frequency detection by

Sin(x) / x interpolation

Amplitude and frequency detection by

Sin(x) / x interpolation


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0

-60

-50

-40

-30

-20

-10

100 1 2 3 4 5 6 7 8 9

dB

Bin

Aliasing of the Side-LobesAliasing of the Side-LobesHighest Bin =

Bin 4

Aliased Bin =

Negative Bin 4


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Weighted MeasurementWeighted Measurement

Apply a Window to the signal Apply a Window to the signal

2

-2

-1

0

1

0.50.0 0.1 0.2 0.3 0.4

Volt

ms

2

-2

-1

0

1

0.50.0 0.1 0.2 0.3 0.4

Volt

ms

2

-2

-1

0

1

0.50.0 0.1 0.2 0.3 0.4

Volt

ms

Hanning windowone period of ( 1 - COS )


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Weighted Spectrum MeasurementWeighted Spectrum Measurement

Apply a Window to the Signal Apply a Window to the Signal

20

-60

-40

-20

0

250 5 10 15 20

Without Window

kHz

dBV

20

-60

-40

-20

0

250 5 10 15 20

With Hanning Window

kHz

dBV


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Rectangular and Hanning WindowsRectangular and Hanning Windows

Side lobes

for Hanning

Window aresignificantly

lower than

for

Rectangularwindow

Side lobes

for Hanning

Window aresignificantly

lower than

for

Rectangularwindow

0

-60

-50

-40

-30

-20

-10

6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

dB

Bin


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Input Frequency Exactly Hits a BinInput Frequency Exactly Hits a Bin

Three bins

are

activated

Three bins

are

activated

0

-60

-50

-40

-30

-20

-10

6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

dB

Bin


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More bins

are

activated

More bins

are

activated

0

-60

-50

-40

-30

-20

-10

6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

dB

Bin


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Highest

side-lobes

Highest

side-lobes

0

-60

-50

-40

-30

-20

-10

6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

dB

Bin


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The Side

lobe levels

decrease

The Side

lobe levels

decrease

0

-60

-50

-40

-30

-20

-10

6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

dB

Bin


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Only three

bins

activated

Only three

bins

activated

0

-60

-50

-40

-30

-20

-10

6-6 -5 -4 -3 -2 -1 0 1 2 3 4 5

dB

Bin


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The Mathematics for Hanning ...The Mathematics for Hanning ...

Envelope:

Bin Offset:

Amplitude:

Envelope:

Bin Offset:

Amplitude:

)bin(1bin)(

bin)Sin(Env

2

=

b)(a

2b)-(abin

+=

)bin1(bin)Sin(

bin)(aAmp 2

=


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A LabVIEW ToolA LabVIEW Tool

Tone detector LabVIEW virtual instrument (VI) Tone detector LabVIEW virtual instrument (VI)


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DemoDemo

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

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 ResolutionFrequency Detection Resolution1000.00

0.01

0.10

1.00

10.00

100.00

1001 10

Freq error (ppm)ppm

Signal periods


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Amplitude Detection ResolutionAmplitude Detection Resolution1000.00

0.01

0.10

1.00

10.00

100.00

1001 10

Amplitude error (ppm)

Signal periods

ppm


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Phase Detection ResolutionPhase Detection Resolution1000.00

0.01

0.10

1.00

10.00

100.00

1001 10

Phase error (mdeg)

Signal periods

mdeg.


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ConclusionsConclusions

Traditional counters resolve 10 digits in one

second

FFT techniques can do this in much less than100 ms

Another example of 10X for test

Similar improvements apply to amplitude and

phase

Traditional counters resolve 10 digits in one

second

FFT techniques can do this in much less than100 ms


Similar improvements apply to amplitude and

phase


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www natinst comwww natinst com

Conclusions (Notes Page Only)Conclusions (Notes Page Only)

Traditional Counters Resolve 10 digits in one

second

FFT Techniques can do this in much lessthan 100 ms


Similar improvements apply to Amplitude and

Phase

Traditional Counters Resolve 10 digits in one

second

FFT Techniques can do this in much lessthan 100 ms


Similar improvements apply to Amplitude and

Phase

fast frequency and response measurements using ffts

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