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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 [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


Presenter
Presenter

  • Jamie Anderson

    • SIA Product Manager

    • [email protected]

SIA Software Company, Inc

One Main Street

Whitinsville, MA 01588

508.234.9877

www.siasoft.com


Fast fourier transforms our friend the fft

Fast Fourier Transforms“Our Friend the FFT”


The fourier transform
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


Transforms
Transforms

A 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

Time Domain to Frequency Domain

Amp vs Time to Amp vs Freq

Waveform Spectrum


Fft resolution
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

FFT Parameters:Time Constant (TC) vs. Frequency Resolution (FR)

Linear Frequency Scale

TC = FFT/SR

FR = 1/TC


Fft resolution1
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 fr1

FFT Parameters:Time Constant (TC) vs. Frequency Resolution (FR)

Log Frequency Scale


Linear vs log banding

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.


Fft data windows
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 windows1
FFT Data Windows

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.



Systems
Systems

Input

System

Output

  • 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
Measurement Types

  • Analyzers are our tools for finding problems

  • Different measurements are good for finding different problems


Measurement types single channel vs dual channel
Measurement Types: Single Channel vs. Dual Channel

  • Single Channel: Absolute

  • Dual Channel: Relative - In vs Out

A(¦)

H(¦)

B(¦)

Input Signal = A (¦) Output Signal = B(¦)

FrequencyResponse H(¦) = B(¦)/A(¦)


Measurement types single channel
Measurement Types: ChannelSingle Channel

  • SPL & VU

  • Wave Form

    • Amplitude vs. Time

  • Spectrum

    • Amplitude vs. Frequency


Measurement types dual channel
Measurement Types: ChannelDual Channel

  • Transfer Function: Frequency Response

    • Phase vs. Frequency

    • Magnitude vs Frequency

  • Impulse Response

    • Magnitude vs Time

    • “Echo structure”


Transfer function
Transfer Function Channel

System

Output Signal

Input Signal

Measurement

Channel (RTA)

Transfer

Function

Reference

Channel (RTA)


Transfer function1
Transfer Function Channel

System

Output Signal

Input Signal

Measurement

Channel (RTA)

Transfer

Function

Reference

Channel (RTA)


Transfer function2
Transfer Function Channel

System

Output Signal

Input Signal

Measurement

Channel (RTA)

Transfer

Function

Reference

Channel (RTA)


What do you get if you transform a transfer function
What do you get if you transform a transfer function? Channel

  • 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
Dual-Channel FFT Issues Channel

  • Window Length vs Resolution

    FR = 1/TC

  • Source Independence

  • Propagation Time

  • Linearity

  • Noise

    • Averaging

    • Coherence

System

Output Signal

Input Signal


How dual channel fft analyzers work
How Dual-Channel FFT Analyzers Work Channel

System

Input

Output

Measurement Signal

Reference Signal

Wave


How dual channel fft analyzers work1
How Dual-Channel FFT Analyzers Work Channel

System

Input

Output

FFT

=

Spectrograph

RTA

FFT

Wave

RTA


How dual channel fft analyzers work2
How Dual-Channel FFT Analyzers Work Channel

System

Input

Output

FFT

=

FFT

Transfer Function

(Frequency Resp.)

Wave

RTA


How dual channel fft analyzers work3
How Dual-Channel FFT Analyzers Work Channel

System

Input

Output

FFT

IFT

=

FFT

Transfer Function

(Frequency Resp.)

Impulse Resp.

Wave

RTA


Basic measurement set up
Basic Measurement Set-up Channel

Loudspeaker

& Room

Source

EQ / Processor

Amplifier

Microphone

Computer

w/ Stereo

line-level input

Mixer


Basic measurement set up1
Basic Measurement Set-up Channel

EQ/Processor Control

Loudspeaker

& Room

Source

EQ / Processor

Amplifier

Control Data

Microphone

Computer

w/ Stereo

line-level input

Mixer


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
To use an analyzer, we must first: screen.

  • Verify that we are making our measurements properly.

  • Verify that it is an appropriate measurement for our purpose.


An analyzer is only a tool you make the decisions
An analyzer is only a screen. 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 system not the trace on the screen
Our goal is to fix our system screen. not the trace on the screen.


Decimation
Decimation screen.


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