Tutorial - FFT size

This will be a mostly visual guide to FFT size and effect on frequency resolution and bin residual noise.

Each of the following graphs are the exact same measurement of an ADI-2 Pro DAC output looped back to ADC input using HpW Works.

Test conditions:
DAC reference level 0dBFS = +19 dBu
DAC filter is SD Sharp,
DAC output adjusted to -20 dBFS which translates to -1 dBu
DAC output looped back to ADC input
ADC reference level = +19 dBu
Sample rate is 44.1 KHz

The only change between each graph is the FFT size and thus bin frequency resolution. They represent the same measurement with different FFT resolutions. Notice how the SNR, THD and THD+N are relatively consistent in all graphs. The residual energy per bin lowers as the FFT size increases. Visually it becomes easier to see harmonics and distinguish from noise spurs at higher resolutions. By 8M points it becomes debatable if there is any further information to be gained by increased resolution for this particular measurement.

Look carefully at all the information on each graph. Outside of my tongue-in-cheek labels, the following information can be seen:
1. Y axis units
2. Number of measurements averaged together
3. FFT size in number of points
4. Date and Time of measurement
5. X axis units
6. SNR
7. THD
8. THD+N
9. DC level
10. RMS level of measurement signal
11. Sample rate
12. Channel displayed
13. FFT window used
14. Bandwidth filter if any
15. Weighting filter if any

FFT = 4K


FFT = 16K


FFT = 65K


FFT = 262K


FFT = 1M


FFT = 8M


FFT = 16M


FFT = 33M


This last graph is an overlay consisting of the 4K, 262K and 16M FFT measurements.

 

In this example a Bottlehead Crack is measured at 40 Hz.

This BH Crack has the following modifications:
Tungsram e80cc (PS rebiased for this driver tube)
Chatham 5998 output tube
No speedball upgrade
Output caps are 820 uF Nichicon electrolytics
1 uF film bypass capacitors to signal path electrolytics
1 uF film bypass cap to last C in power supply filter
First R in power supply filter replaced with Triad C7X choke (10H, 270R)

Test conditions:
RME ADI-2 Pro used for stimulus and response measurement
DAC and ADC Reference 0 dBFS = +19 dBu
DAC filter SD Sharp
Sample rate = 44.1 KHz
Signal level presented to BH Crack = -11 dBu (conveniently -30 dBFS)
BH Crack gain knob adjusted for input to output gain = 0 dB
BH Crack output load = 300R

FFT bins are distributed linearly through the frequency domain. But we wish to display with a logarithmic frequency x axis to more closely match how the Human Auditory System perceives sound. Note how the bins at low frequency cover more Hz per bin than at higher frequencies. Our measurements have greater resolution at high frequency than low frequency. FFT size should be chosen carefully with this in mind. Another thing to keep in mind is higher FFT sizes require longer measurement and computation times. 65K runs in a few seconds while 16M can take 13 minutes for a single measurement at 44.1 KHz.

FFT = 4K

4K is not a good choice in this measurement as we are unable to discriminate the fundamental (40 Hz), bins for 2nd (80 Hz) and 3rd (120 Hz) harmonics are too broad in the frequencies they represent.

FFT = 16K

16K offers improvement in identifying 40, 80 and 120 Hz components

FFT = 65K

65K appears to be a reasonable choice for compromise between resolution and time for measurement.

FFT = 262K

Greater frequency resolution at 262K is apparent. Beginning to notice 40 Hz is really a little above 40Hz as the signal generator was set for coherent operation. This nudges the desired test frequency a little to minimize issues with FFT windows (another topic for another post.)

FFT = 1M

Notice the 3rd harmonic identifier on the graph dropped to half the height of the displayed spur. Now consider that the nudged signal generation was from 40 Hz to 40.375 Hz and that second harmonic of power supply mains in this lab is 120 Hz, which is also 3rd harmonic of 40 Hz.

FFT = 8M

Again the 3rd harmonic identifier is at half height of the displayed spur. Also note increased frequency resolution dropped residual energy per bin below our current Y axis minimum of -160 dBFS

FFT = 8M with Y axis raised

Raising the Y axis allows us to see the residual energy per FFT bin again.

FFT = 8M with X axis zoomed

Remember the nudged signal generation was from 40 Hz to 40.375 Hz and that second harmonic of power supply mains in this lab is 120 Hz, which is 3rd harmonic of 40 Hz. On this expanded graph we see the separation of the power supply 2nd harmonic of 120 Hz from the stimulus signal 3rd harmonic of 121.13 Hz. So why don't we always perform 8M FFT's? 3.5 minute measurement times. Maybe a better solution would be to choose a different stimulus frequency taking into account the power supply mains frequency and harmonics. See the next post.

 

BH Crack with 45 Hz stimulus.

FFT = 16K with 45 Hz stimulus

At this resolution power supply mains 2nd harmonic and stimulus 3rd harmonic are still visually co-mingled.

FFT = 32K with 45 Hz stimulus

Visual separation of power supply mains 2nd harmonic and stimulus 3rd harmonic are clearly visible.

FFT = 65K with 45 Hz stimulus

Greater resolution again provides enhanced visual resolution for discriminating between stimulus frequency + harmonics (45, 90, 135 Hz) and power supply mains + harmonics (60, 120 Hz), though once again an overlap will occur at 180 Hz. So we solved on problem but created another. Maybe a better choice for the future would be 42 or 43 Hz.

FFT = 262K with 45 Hz stimulus

 

Thanks @atomicbob for such a good visualisation. I find it helpful to understand that the noise floor drops with larger FFT sizes due to each individual bin becoming proportionately narrower. The narrower the bin, the less bandwidth it has, and noise is measured by bandwidth (sqrt Hz).

 

Thanks @atomicbob and other more educated and sharper than I...I'll be trying to understand this in more technical detail as the thread evolves. Pointers to resources for the untrained would be welcome.

 

The header of my more recent Technical Measurements posts include the following:

If you are unfamiliar with audio measurements please use a search engine with the query:
"audio measurements" or "audio measurement handbook"
Look for publications by Richard C. Cabot and also by Bob Metzler, both from Audio Precision. There are other useful publications as well. These will provide basic knowledge.

Also note that I have added material to posts 2 and 3 above.

 

Weird that this handbook isn't included with the fancy APx555

 

Those spurs at 160db are disturbing. Put that ADI-2 in the garbage.

 

Unfortunately the only prerequisite to owning expensive test equipment is sufficient funds. AP makes really good equipment, as do Prism Sound. Rohde & Schwarz, and a number of other vendors.

I was enduring another cardiac episode while posting the updates today. This made me really laugh, thank-you!

 

Your measurements are always appreciated but health comes first. Look after yourself Bob.

 

Thank-you for the kind sentiments, which I receive often from a great number of people.

Paroxysmal atrial fibrillation is a way of life for millions of people on the planet. There are dietary restrictions, meds, cardiac procedures, etc to manage the issue. Some more or less successfully. I've had one procedure and likely need another. Meanwhile I have my regimen with oversight of several cardiologists. It is a matter of episode management. Calming music and keeping the mind occupied are also helpful in my case. However I avoid any critical decision making during an episode. Sitting and stewing about it makes my episodes worse so it is a good time to stay busy with something useful. This FFT tutorial has served just such a purpose.

 

Thanks Bob, great stuff.

...on account of which I am now imagining Head-Fi HQ like this: