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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

- 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”

- 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

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

- 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

- Larger Time Window:
- 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/SR

FR = 1/TC

- 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

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

- 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!

- Analyzers are our tools for finding problems
- Different measurements are good for finding different problems

- Single Channel: Absolute
- Dual Channel: Relative - In vs Out

A(¦)

H(¦)

B(¦)

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

FrequencyResponse H(¦) = B(¦)/A(¦)

- SPL & VU
- Wave Form
- Amplitude vs. Time

- Spectrum
- Amplitude vs. Frequency

- Transfer Function: Frequency Response
- Phase vs. Frequency
- Magnitude vs Frequency

- Impulse Response
- Magnitude vs Time
- “Echo structure”

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)

- IFT produces impulse response
Transfer Function . . . To . . . Impulse Response

- *So . . . If Frequency Response can be measured source independently - so can Impulse Response*

- Window Length vs Resolution
FR = 1/TC

- Source Independence
- Propagation Time
- Linearity
- Noise
- Averaging
- Coherence

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.

- Verify that we are making our measurements properly.
- Verify that it is an appropriate measurement for our purpose.

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.