Dual-Channel FFT Analysis: A Presentation Prepared for Syn-Aud-Con: Test and Measurement Seminars
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Dual-Channel FFT Analysis:
A Presentation Prepared for Syn-Aud-Con: Test and Measurement Seminars
Louisville, KY Aug. 28-30, 2002
Presenter
• Jamie Anderson– SIA Product Manager – Jamie@SIASoft.com
SIA Software Company, IncOne Main Street
Whitinsville, MA 01588508.234.9877
www.siasoft.com
Fast Fourier Transforms“Our Friend the FFT”
The Fourier Transform
• Jean Baptiste Joseph Fourier– All complex waves are composed of a
combination of simple sine waves of varying amplitudes and frequencies
Amp vs Time to Amp vs Freq
Waveform to Spectrum
TransformsA transform converts our data from one domain (view) to
another.– Same data
• Is reversible via Inverse Transform
– Unlike a conventional RTA using a bank of analog filters, FFT’s yield complex data: Magnitude and Phase information
Amp vs Time to Amp vs FreqWaveform Spectrum
Time Domain to Frequency Domain
FFT Resolution
• Reciprocal Bandwidth: FR=1/TC Frequency Resolution = 1/Time Constant
– Larger Time Window:• Higher Resolution• Slower (Longer time window and more data to crunch)
– Smaller Time Window:• Lower Resolution• Faster
• Time Constant = Sample Rate x FFT Length
* Decimation – Varying SR & FFT to get constant res.*
FFT Parameters:Time Constant (TC) vs. Frequency Resolution (FR)
Linear Frequency Scale TC = FFT/SRFR = 1/TC
FFT Resolution
• FFT’s yield linear data– Constant bandwidth instead of constant Q– FFT data must be “banded” to yield fractional-
octave data.
• FFT must be windowed– FFT’s assume data is continuous & repeating so
wave form must begin and end at 0.– Windows are amplitude functions on data
FFT Parameters:Time Constant (TC) vs. Frequency Resolution (FR)
Log Frequency Scale
Linear vs. Log Banding
Linear banding has an increasing number of bands per octave as frequency increases, resulting in less energy per band in the HF.
Pink Noise (equal energy per octave) shown w/ linear and log banding.
Fractional–octave (log) banding has an equal number of bands per octave, resulting in equal energy per band.
FFT Data Windows
An FFT assumes that a waveform that it has sampled (defined by its time window) is infinite and repeating. So if the waveform does not begin and end at the same value, the waveform will effectively be “distorted”.
FFT Data WindowsData Windows
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Sample
Ma
gn
itu
de
Hamming (t)
Hanning
Blackman
Parzen
Rect
Window FFT's
-90
-80
-70
-60
-50
-40
-30
-20
-10
0
1 6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
10
1
10
6
11
1
11
6
12
1
12
6
13
1
13
6
14
1
14
6
15
1
15
6
Frequency
Ma
gn
itu
de Hamming (f)
Hanning
Blackman
Rect
FFT data windows force the sampled waveform to zero at the beginning and end of the time record, thereby reducing the impact of the “Infinite and Repeating” assumption.
Each data window has a corresponding spectral distribution (analogous to filter shape.)
The FFT data window being used and its corresponding distribution must be taken into consideration when banding the resulting spectral data into fractional-octave bands.
Dual-Channel Measurement
Systems
Input OutputSystem
Note: These systems can be anything from a single piece of wire to a multi-channel sound system with electrical, acoustic and electro-acoustic elements, as well as wired and wireless connections.
And remember, it only takes one bad cable to turn a $1,000,000 sound system into an AM radio!
Measurement Types
• Analyzers are our tools for finding problems
• Different measurements are good for finding different problems
Measurement Types: Single Channel vs. Dual Channel
• Single Channel: Absolute
• Dual Channel: Relative - In vs Out
A() B()H()
Frequency Response H() = B()/A()
Input Signal = A () Output Signal = B()
Measurement Types:Single Channel
• SPL & VU
• Wave Form– Amplitude vs. Time
• Spectrum– Amplitude vs. Frequency
Measurement Types: Dual Channel
• Transfer Function: Frequency Response
– Phase vs. Frequency
– Magnitude vs Frequency
• Impulse Response– Magnitude vs Time– “Echo structure”
Transfer Function
MeasurementChannel (RTA)
ReferenceChannel (RTA)
TransferFunction
System
Input Signal Output Signal
Transfer Function
MeasurementChannel (RTA)
ReferenceChannel (RTA)
TransferFunction
System
Input Signal Output Signal
Transfer Function
MeasurementChannel (RTA)
ReferenceChannel (RTA)
TransferFunction
System
Input Signal Output Signal
What do you get if you transform a transfer function?
• IFT produces impulse response
Transfer Function . . . To . . . Impulse Response
*So . . . If Frequency Response can be measured source independently - so can Impulse Response*
Dual-Channel FFT Issues
• Window Length vs Resolution FR = 1/TC
• Source Independence• Propagation Time• Linearity• Noise
– Averaging– Coherence
System
Input Signal Output Signal
How Dual-Channel FFT Analyzers Work
SystemInput Output
Wave
Measurement Signal
Reference Signal
SystemInput Output
FFT
FFT
RTA
=
Wave
SpectrographRTA
How Dual-Channel FFT Analyzers Work
System
=
Input Output
FFT
FFT Transfer Function(Frequency Resp.)
RTAWave
How Dual-Channel FFT Analyzers Work
System
=
Input Output
FFT
FFT
IFT
Transfer Function(Frequency Resp.)
RTA
Impulse Resp.
Wave
How Dual-Channel FFT Analyzers Work
Basic Measurement Set-up
Source EQ / Processor AmplifierLoudspeaker
& Room
Microphone
Computer w/ Stereo
line-level input
Mixer
Basic Measurement Set-up
Source EQ / Processor AmplifierLoudspeaker
& Room
Microphone
Computer w/ Stereo
line-level input
Mixer
Control Data
EQ/Processor Control
Any idiot can get squiggly line to appear on an analyzer screen.
Our goal is to make ones we can make decisions on.
Remember:Computers do what we tell them to do, not what we want them to do.
To use an analyzer, we must first:
1. Verify that we are making our measurements properly.
2. Verify that it is an appropriate measurement for our purpose.
An analyzer is only a tool: YOU make the decisions
You decide what to measure.
You decide which measurements to use.
You decide what the resulting data means.
And you decide what to do about it.
Our goal is to fix our systemnot the trace on the screen.
Decimation
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