dual-channel fft analysis: a presentation prepared for syn-aud-con: test and measurement seminars...

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, 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

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


System

=

Input Output

FFT

FFT Transfer Function(Frequency Resp.)

RTAWave


System

=

Input Output

FFT

FFT

IFT

Transfer Function(Frequency Resp.)

RTA

Impulse Resp.

Wave


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

dual-channel fft analysis: a presentation prepared for syn-aud-con: test and measurement seminars...

Documents