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Author Topic: Fun with Tone Bursts  (Read 536 times)

Frank Koenig

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Fun with Tone Bursts
« on: August 28, 2018, 10:33:06 pm »

In the Frequency Dependent Resistance thread I alluded to my fascination with tone bursts as test signals. Here are a few simulations. They look pretty cool on measured data, too. The excitation in each case is a burst of 4 cycles of a sine wave windowed with a raised cosine (Von Hann, or "Hanning") window. It turns out the window type is not critical in these representations and even a rectangular window behaves pretty well.

The tone bursts are centered at zero time, hence the negative time values in the plots. All the filters are centered at 1 kHz and the plots run from 250 Hz to 4 kHz in the x direction and -8 ms to 8 ms in the y direction. Color represents amplitude ranging from blue (neg) through black (0) to red and white (pos).

No filter


4th order Butterworth low-pass


4th order Butterworth high-pass


2nd order all-pass (sum of 3rd order Butterworth high- and low-pass)
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John Roberts {JR}

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Re: Fun with Tone Bursts
« Reply #1 on: August 29, 2018, 09:39:09 am »

I did a lot of bench testing with tone bursts back in the 70s-80s when designing dynamics processors, and companding NR.

Tone bursts are not naturally occuring waveforms in the real world, but excellent for stressing dynamics.

I designed my own specialized gate circuitry that would mute and unmute whatever audio input I fed it. I coordinated the muting to occur at zero-crossings (to reduce HF clicks), and even insured that it presents even numbers of sine wave cycles, to avoid DC content from a gated half cycle.

I had a variable depth of mute (on/off ratio), so i could could even punch up the crest factor of normal music (again useful for dynamics design.)

JR
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Langston Holland

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Re: Fun with Tone Bursts
« Reply #2 on: August 29, 2018, 06:41:46 pm »

Hartley should have paid John more - a primary reason for the Hanning windowing Frank used was to suppress the side lobe "noise", or clicks in John's case. You need near zero amplitude at the beginning and end of the burst for a useful result regardless of method. A zero cross gate - Ha! :)

So... What happens if you draw a line on one of Franks plots through the center region of the burst data? A group delay plot!

So... What happens when you take one of Frank's plots, flip it around backwards, then turn it 90˚ clockwise? A wavelet plot!

Measurement systems like CLIO, FIR Capture and ARTA* also use this kind of windowing on an FFT of the time domain data converted to frequency. Mathematically it is identical to using separate tone bursts to measure the dynamic behavior of the DUT. Mechanically it is different because an actual burst is a dynamic event, whereas the log swept sine derived tone bursts as typically shown in a wavelet plot result from a continuous sweep. The results are identical as long as the DUT remains linear, although the sweep method has much higher S/N and thus is much more helpful with low level stuff**. OTOH, the actual bursts are much better at studying nonlinear behavior such as harmonic distortion. Finally, shaped (Gaussian or Hanning) tone bursts have bell-shaped envelopes instead of the instant-on/off edges of unwindowed sines and thus are much more like naturally occurring sound.

What software did you use to do that Frank?

*ARTA calls it a burst decay plot and displays in waterfall format instead of the "normal" 2D wavelet plot. Same thing, just a different way of looking at the data.

**Analogous to room acoustics measurements using balloon pops vs. sweeps through dodecahedron loudspeakers.
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Frank Koenig

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Re: Fun with Tone Bursts
« Reply #3 on: August 29, 2018, 07:24:36 pm »

Thanks for the replies. I'm away from the computer but will respond in detail and can post source code, etc. when I get back. --Frank
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Frank Koenig

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Re: Fun with Tone Bursts
« Reply #4 on: August 30, 2018, 08:58:28 pm »

What software did you use to do that Frank?
I've been using the R language to do my playing around and it works pretty well for me. I probably should be using Python but that's not the road I started down. Matlab would be the traditional tool but it's not free. While a little fast and loose compared with, say, C, R is really quick for mocking up little simulations with graphical output.  What's changed from the way I used to do things is that I debug almost entirely graphically. I don't insert printfs but rather plot.defaults. The R "console window" let's you run arbitrary snippets of code or type and run code on the fly to, say, evaluate an intermediate result. R was written by and for statisticians and some of the nomenclature is unfamiliar to electrical engineers, but not hard to figure out. And there's tons of statistics stuff in there I have no clue about.

I use ARTA to capture the impulse responses and, at this point, calculate everything from them. It's just easier to have a common format for the raw data. I use Smaart for field alignments, health checks, and playing around with the measurement mic to see "what if". It's really good for that. I've never had the opportunity to try Systune.

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*ARTA calls it a burst decay plot and displays in waterfall format instead of the "normal" 2D wavelet plot. Same thing, just a different way of looking at the data.
I've looked at ARTA's burst-decay plots. They are more-or-less the same thing but viewed a different way. While they look very cool, I have not found their representation that useful. The lateral ridges tell you the frequencies where there are resonances. But in pretty much every case you already know where the resonances are by looking at the local peaks in the magnitude. My representation is more time oriented and lets you see how the carrier cycles line up across frequency. I find this confidence-building when, say, working on crossovers. You can usually see, for example, if you are off by an entire cycle, or might be better off inverting polarity and delaying by a half-cycle. With well-behaved phase overlaps you can see that from the relative phase slopes, too. But sometimes they are not that well behaved. I recently worked with a little 6.5 in. coax with an ~2 kHz crossover where there wasn't much overlap to go on. The ridge of the envelopes does indeed represent group delay and is a direct consequence of the definition of group delay that holds it to be the delay of the envelope of an amplitude modulated signal.

I've been interested in time-frequency-energy (TFE) representations of systems for a long time (35+ years, since school). I fooled around with short-time Fourier transforms, the Wigner distribution (and its 2-D Fourier transform, the ambiguity function) and others. The one I've found most interesting for audio, other than these wormy tone-burst plots, is what I call the "short-frequency Fourier transform". This is the log-magnitude of the IDFT of the constant octave-bandwidth Gaussian windowed frequency response. Only the positive frequencies pass through the window so, in effect, the IDFT performs a discrete Hilbert transform (DHT) and generates the analytic signal in the time domain. The ridge of this TFE is also an estimate of the group delay. (No phase unwrapping required.)

--Frank
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