FFT and Windowing

[JMB]

I was hoping to open up a discussion amongst you EE types to expound upon the advantages and disadvantages in different windows in different situations. Would anyone be kind enough to explain this in light of frequency response, THD and IMD measurements, burst measurements, and CSD? John K had advised to just stick with Blackmann Harris for SE while the ARTA manual suggests different windows for different circumstances. thnx.

 

[SY]

Surprisingly, the Wikipedia article is pretty comprehensive (though it leaves out my beloved H-G window):
Window function - Wikipedia, the free encyclopedia

National Instruments has a very clear tutorial:
Windowing: Optimizing FFTs Using Window Functions - National Instruments

Note the summary in Figure 8, which I think is exactly what you're looking for.

 

[Elias]

Very surprisingly, they also have window function and accompanied Fourier transform for Taj Mahal:

 

[JMB]

Thanks, SY. I had seen those links and several others. I am not able to make the leap from leakage, side lobes, etc. to which works best for what function in loudspeaker measurement. An impulse windowing in loudspeaker measurement for dummies would be great! thnx

 

[SY]

What are you trying to measure and how? Frequency response is one thing, distortion is another. Impulse vs. MLS will also influence your choice.

Blackman-Harris is a good default choice if you're not sure.

 

[JMB]

First an impulse response is obtained. I then process it with either Soundeasy or ARTA to derive frequency response, CSD, Tone Burst, etc. IMD and THD both use their own signals to obtain their results. IMD uses two separate frequencies to measure while THD uses Stepped Sine, I believe, in SE and I believe it uses swept sine in ARTA.

 

[SY]

For the frequency response measurements, B-H is likely your best bet.

For IMD and THD, use a flat-top, or if that's not an option, a Hanning. You'll get some side lobes which you should ignore- you're interested in the ratios of the peak values of the fundamental and the harmonics.

 

[JMB]

Thanks, SY. Any chance that you might explain the why of this? I can see the differences in side lobes and in the rate of decent from the peak of the signal under each window but I am trying to understand where there is benefit to each window and why.

I guess to be more specific, why is B-H better than Hanning or flat top, etc for FR? Why Flat top or Hanning and not Uniform for IMD or THD? What about each window profile makes it preferable to the others? Thanks in advance. Jay

 

[SY]

The "why" is mathematical. The practicalities are that, in choosing a window or apodization, you're trading freedom from skirts or spreading in the frequency domain for accuracy of peak height. Peak height accuracy is what you want in distortion measurement since distortion percentage is defined by the ratios of the harmonics and intermod products to the fundamental(s); the spreading isn't very critical.

There's lots of different measurement situations, so there's lots of tools! For example, if I wanted to resolve sidebands from power supply intermodulation or two closely spaced tones, I'd want to choose an apodization that had the least spreading so they wouldn't get buried in the mathematical noise around the test frequency.

 

[JMB]

Thanks for your patience and for your explanation. For FR you want the most accurate frequency data; would this be reflected by the lowest side lobes, greatest side lobe roll off (I guess reflected by the -3dB bandwidth), or a combination of the two (or am I way off base here)?

 

[SY]

Nope, you're right on base.

 

[JMB]

Thanks. Then to take it one step further, I assume one would use the same windows that you have used for FR for CSD and for Tone burst and for the same reasons?

 

[Jay]

. Would anyone be kind enough to explain this in light of frequency response, THD and IMD measurements, burst measurements, and CSD? John K had advised to just stick with Blackmann Harris for SE while the ARTA manual suggests different windows for different circumstances. thnx.

I don't know why you ask this because it is clear that each windowing has compromises so you will want to compromise frequency accuracy or transient accuracy depends on the information you want to seek and the nature of the input signal.

If you know too much about the subject of course it is good to use the most appropriate windowing for each cases. But let me tell you that the interpretation of measurement regardless of accuracy is still a weakest link. So you will need long time to be able to well interpret the result of any windowing. In your situation it is best to stick with one type. A type that is in the middle compromise for general purpose measurement is probably the BH4. I choose Hann because most important masurements require the frequency domain accuracy.


Windowing option is also related with FFT size and processing speed. For final measurement the accuracy should be better than trials.

 

[scott wurcer]

FFT size and processing speed.

No longer relevant in most cases.

 

[Jay]

No longer relevant in most cases.

I don't know what you mean with no longer relevant but I think it was me who is not clear about what I was saying. My main point was about choosing different "accuracy" for trial and final. Because the more accurate the measurement the more processing is required hence time. I'm not talking about BH7 for final and no windowing for trials, no, but in general term including choosing the sample size.

 

[jcx]

if you are using the same clock, say a soundcard or DAQ, for both source, record then you can skip windowing altogether if you make any frequency input an exact integer fit

asynchronus frequency interference like power line noise will splatter though

 

[Jay]

Btw, my computer was top when I bought it, now I realized that I'm way behind. Actually I work with computers but that feeling when I bought my computer blinded me that my computer is only 2GHz and 2G RAM when the last time I checked.

Indeed software development is left way behind hardware development. And I don't play games so Photoshop is the critical software for me then

 

[JMB]

Thanks all, for helping me to better understand this. Sy, between your explanation and feyz over at the PE forum

FFT and Windowing

along with the links:

Windowing: Optimizing FFTs Using Window Functions - National Instruments
The Fundamentals of FFT-Based Signal Analysis and Measurement in LabVIEW and LabWindows/CVI - National Instruments
Characteristics of Different Smoothing Windows - LabVIEW 8.2 Help

, I feel like I have a much better ability to apply this.

Jay

 

[SY]

Wow, he's a more prolific typer than I am!

The value of a tool is proportional to the user's understanding of it. You're taking the right approach.

 

[scott wurcer]

I don't know what you mean with no longer relevant but I think it was me who is not clear about what I was saying. My main point was about choosing different "accuracy" for trial and final. Because the more accurate the measurement the more processing is required hence time. I'm not talking about BH7 for final and no windowing for trials, no, but in general term including choosing the sample size.

My bad, I misunderstood your comment.