1. FFT Window Functions Practical Applications
Bob Smith
SoundSmith Labs

2. Overview Analyzer Architectures
Comparison of several FFT window functions
Example measurement setups
In part 1 jj described the problem of discontinuities created by differences between sampled signals and FFT size, and how they may be addressed by FFT window functions. In this part I will briefly review typical audio measurement tools that utilize FFT analysis and where the FFT window selection resides in those analyzers. Then I will demonstrate a specific measurement repeated with different FFT windows for comparison. Finally we will look at examples of measurement situations and which windows might be best for each.

3. Analyzer Examples Analysis SW
APx555 + proprietary SW – PrismSound dScope + proprietary SW – ADI-2 Pro + HpW Works SW
Analysis SW

4. Fundamentals of Modern Audio Measurement Journal of the AES, Sep 1999
Signal Generator – Stimulus on left Measurement System on Right Note complexity of AP audio analyzer - advance slide to locate Window Function setting in DSP block
Fundamentals of Modern Audio Measurement
Journal of the AES, Sep 1999
Richard C. Cabot, AES Fellow
Audio Precision, Inc.

5. HpW Works simplified architecture
Stimulus
Discuss stimulus to DUT: analog / digital signal generator, wavefiles with test signals types of DUTs – smartphone, portable personal listening device, amplifier, DAC, etc. Highlight location of the Window Function setting which resides in FFT & Spectrum box
DUT: Device Under Test

6. HpW Works Architecture Diagram
HpW works analyzer architecture Discuss ADI-2 Pro audio interface used in Sound Card Block
ADI-2 Pro – all features off
Ref +19 dBu
Gain -29 dBFS
Output: -10 dBu Vrms output

7. “There are approximately as many different window functions as there are papers about windowing. Everyone has designed their own, probably so they can put their name on it and get a piece of fame.
From a practical viewpoint, very few windows are necessary for audio measurements.”
- Richard C. Cabot, Fundamentals of Modern Audio Measurement
Notable quote from AES fellow

8. Reason for this presentation – 39 windows in HpW works from which to choose as an example

9. Display orientation – discuss axis, Averaging, Fs, FFT size N

10. Live demonstration begins with asynchronous stimulus and Rectangular window

11. Add Hamming windowed FFT of same asynchronous stimulus

12. Add Hann windowed FFT – note small peaks at 450 and 550 Hz

13. Add Blackman – Harris 7 term FFT to reveal spurs existing at 450 and 550 Hz

14. Frequency axis zoom to see lobe steepness vs frequency specificity

15. Asynchronous vs. Coherent Signal Stimulus
Frequency generator settings before coherent adjustment

16. Asynchronous vs. Coherent Signal Stimulus
Frequency generator settings before coherent adjustment

17. When synchronous stimulation possible Rectangular window provides better frequency selectivity along with steep lobes – noise and harmonics must be low enough not to create discontinuity at sample window edges.

18. FFT size and averaging
Larger FFT size increases resolution and greater computational expense
Averaging reduces random bin noise at expense of multiple FFT measurements
May run several larger FFT measurements and change averages to make point – otherwise live demonstration ends here
1M FFT takes 22 S per measurement Avg 88 S on this laptop

19. Segal’s Law Man with one clock always know the time.
Man with two clocks never certain.

20. Asynchronous Stimulus Examples
Separate signal generator and measurement system each with own clock, or signal generator might be analog such as HP339A distortion analyzer
Dragon Inspire IHA rectifier tube – 6SN7 amp

21. Asynchronous Stimulus Examples

22. Synchronous Stimulus Examples
Signal generator and measurement system contained in one analyzer with common clock