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 [email protected] SIA Software Company, Inc One Main Street Whitinsville, MA 01588 508.234.9877
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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
SIA Software Company, Inc
One Main Street
Whitinsville, MA 01588
508.234.9877
www.siasoft.com
Fast Fourier Transforms“Our Friend the FFT”
Amp vs Time to Amp vs Freq
Waveform to Spectrum
A transform converts our data from one domain (view) to another.
Time Domain to Frequency Domain
Amp vs Time to Amp vs Freq
Waveform Spectrum
Frequency Resolution = 1/Time Constant
* Decimation – Varying SR & FFT to get constant res.*
FFT Parameters:Time Constant (TC) vs. Frequency Resolution (FR)
Linear Frequency Scale
TC = FFT/SR
FR = 1/TC
FFT Parameters:Time Constant (TC) vs. Frequency Resolution (FR)
Log Frequency Scale
Linear vs. Log Banding
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.
Linear banding has an increasing number of bands per octave as frequency increases, resulting in less energy per band in the HF.
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 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
Input
System
Output
A(¦)
H(¦)
B(¦)
Input Signal = A (¦) Output Signal = B(¦)
FrequencyResponse H(¦) = B(¦)/A(¦)
System
Output Signal
Input Signal
Measurement
Channel (RTA)
Transfer
Function
Reference
Channel (RTA)
System
Output Signal
Input Signal
Measurement
Channel (RTA)
Transfer
Function
Reference
Channel (RTA)
System
Output Signal
Input Signal
Measurement
Channel (RTA)
Transfer
Function
Reference
Channel (RTA)
Transfer Function . . . To . . . Impulse Response
FR = 1/TC
System
Output Signal
Input Signal
System
Input
Output
Measurement Signal
Reference Signal
Wave
System
Input
Output
FFT
=
Spectrograph
RTA
FFT
Wave
RTA
System
Input
Output
FFT
=
FFT
Transfer Function
(Frequency Resp.)
Wave
RTA
System
Input
Output
FFT
IFT
=
FFT
Transfer Function
(Frequency Resp.)
Impulse Resp.
Wave
RTA
Loudspeaker
& Room
Source
EQ / Processor
Amplifier
Microphone
Computer
w/ Stereo
line-level input
Mixer
EQ/Processor Control
Loudspeaker
& Room
Source
EQ / Processor
Amplifier
Control Data
Microphone
Computer
w/ Stereo
line-level input
Mixer
Remember:
Computers do what we tell them to do, not what we want them to do.
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.