Hi Don

I haven't really used "dynamic" analyzers in the audio sense as my work is much higher speed. However, I can define what some of the basic instruments do... Let me think on this a bit. For now, I need to toddle off and practice.

Forgot about this one, sorry... Here's a quick off-the-cuff guess:

Network analyzers are used to measure the frequency response of networks. They do not intrinsically operate in the time domain, but many include an inverse-FFT function that provides a calculated time response to a step or impulse input. Think of a box with two ports, but you can't see inside. You apply a signal to one port and measure at the other, and repeat in the other direction (most do the switching automatically to measure both ports). The network analyzer measures the frequency response, the transfer function, from one port to the other by sweeping the signal frequency at one port and measuring the resulting signal at the other. From that you may infer some of the properties of the box. Thus, a network analyzer includes a source (sweep generator) and receiver that are synchronized to provide the response at each frequency point in the sweep. Simple ones measure the magnitude only; more complex models measure magnitude and phase and thus provide vector information.

A spectrum analyzer measures the frequency spectrum of an input signal and is what one uses to determine discrete frequency components in a signal. A spectrum analyzer does not include a source. It can be used to measure the signal-to-noise ratio (SNR) by summing all the frequency components except the fundamental (test tone) and comparing the magnitude of the sum to the magnitude of the test tone. Similarly, it is used to provide the distortion (THD, IMD) of a test tone by comparing the magnitude of the fundamental to the sum of all the distortion components. (Not that the “sum” is actually a root-sum-square, the square root of the sum of all tones squared.) You could make a network analyzer by synchronizing a sweep generator and a spectrum analyzer.

A signal analyzer is generally a multi-function device that measures frequency response, SNR, THD, IMD, etc. Most audio test instruments are multi-purpose devices, including a signal source to provide fixed or swept tones and a sensitive receiver that can serve in a network or spectrum analyzer role.

Dynamic analyzers allow you to measure signals over time, allowing you to perform for example a plot of the decay in frequencies over time in a room, or plots of distortion vs. power over multiple sweeps.

The output of a network analyzer is a frequency sweep like this:


The output of a spectrum analyzer looks like this:

Nicely done as always Don.

Don,

One aspect that has always bothered me is the technique used to implement most signal analyzers. We can find either instruments based in sweep, pink noise or maximum-lengthsequence (MLS) techniques. As expected, each developer claims better results using the technique he implements. Do you have a feeling on which would be more appropriate for room measurements? I am not considering loudspeaker development, that has different requirements.

microstrip said:

Do you have a feeling on which would be more appropriate for room measurements?

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I'm not Don, but for me the overwhelming advantage of sweep tones over noise is the software can apply a tracking filter to increase the s/n ratio. This is why most modern software like Room EQ Wizard and ETF etc use a sweep.

--Ethan

+1 (Good to see you chime in, Ethan!) Also, swept tones are well-defined in frequency and amplitude, unlike pink noise or MLS that is statisical. Meaning you need to takes lots of measurements over time to get the details. Pink noise is great for averaging over time to get a general idea of the response and is often used with a spectrum analyzer to provide a look at the overall FR of a system. However, you cannot (ideally) predict the power (voltage, phase, etc.) of any given frequency at any given time, making it a poor choice compared to the precision of a network analyzer or other swept system. I have almost no experience with MLS systems for audio.

For a quick look at the overall response pink noise is great. For detailed measurements and fine-tuning I use a sweeper (frequency domain) and/or (im)pulse functions (time domain).

Thanks to both of you.

Just a few hours ago I found in the "A Sound Engineers Guide to Audio Test and Measurement " the following sentence "The advantage of the MLS is its excellent noise immunity and fast measurement time, making it a favorite of loudspeaker designers. A disadvantage is that the noise-like stimulus can be annoying, sometimes requiring that measurements be done after hours. The use of MLS has waned in recent years to log-swept sine measurements made on dual-channel FFT analyzers" . So, thanks also to google books!

This is a great thread so far!

Thanx to you folks. :b

microstrip said:

Just a few hours ago I found in the "A Sound Engineers Guide to Audio Test and Measurement " the following sentence "The advantage of the MLS is its excellent noise immunity and fast measurement time, making it a favorite of loudspeaker designers. A disadvantage is that the noise-like stimulus can be annoying, sometimes requiring that measurements be done after hours. The use of MLS has waned in recent years to log-swept sine measurements made on dual-channel FFT analyzers" . So, thanks also to google books!

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Another good read is the article (PDF file) Transfer-Function Measurement with Sweeps, which also includes a nice history going back to Heyser's invention of Time Delay Spectrometry.

Great article, thanks Andy! I forgot to mention one of features highlighted by the opening lines in that article: sweeps allow the instrument to reject all noise and distortion except at the desired frequency, making it much easier to get a good (valid) FR plot.

It's a neat trick how the distortion components show up in "negative time" in the impulse response .

I have not had time to read it yet (just looked at the pictures ). I assume there is delay in the system to make it look non-causal...

DonH50 said:

I have not had time to read it yet (just looked at the pictures ). I assume there is delay in the system to make it look non-causal...

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It's been quite some time since I last read it, but I believe they do some sort of one-sided windowing in the time domain before doing further computation, since the nonlinear distortion terms at "negative time" are unwanted.

I had always wondered what detrimental effect small amounts of nonlinear distortion would have in these sorts of calculations, since they assume a linear system. So I guess this is one more advantage of the swept-sine approach: the ability to isolate and remove errors due to small amounts of nonlinear distortion in the device under test (which I assume is dominated by the speaker system in this case).

Yeah, delay everything, but delay part less the the rest, and you get "negative time". Unless he is describing the time equivalent of negative frequency in an FFT ( a consequence of the math). Too bad such "negative time" systems tend to be unstable...

It's been a while since I looked, and I can't say I looked closely then, but IIRC MLS uses 1/0 weighting and is fairly sensitive to almost anything that messes up the weighting. I actually thought the combination of fairly low sensitivity, requiring fairly high output, and resulting nonlinearities was one of the biggest drawbacks of MLS testing. Modern DSP may help with that, but we are getting above my (almost nil) knowledge of the subject...

DonH50 said:

Yeah, delay everything, but delay part less the the rest, and you get "negative time". Unless he is describing the time equivalent of negative frequency in an FFT ( a consequence of the math). Too bad such "negative time" systems tend to be unstable...

Click to expand...

In normal computation of the system impulse response h(t), one assumes a linear system. The ratio of the FFT of the output to the FFT of the input is taken, then h(t) is calculated as the inverse FFT of that ratio.

But in a nonlinear system, the output time function is not related to the input time function by just its convolution with the impulse response. That relationship, for a time-invariant nonlinear system, is a Volterra series. Aside from a DC term, the first term is the normal convolution integral from linear system theory, but the second-order distortion term is a double integral, a convolution of the second-order Volterra kernel with the input time function. Likewise, the third-order distortion term is a triple integral with the third-order Volterra kernel and the input, the fourth-order term is a quadruple integral with the fourth-order Volterra kernel and the input, and so on. For a memoryless nonlinearity, the Volterra series reduces to just the Taylor series one might typically use for simplified analysis of distortion.

What you want is for the computation of, for lack of a better term, the "pseudo impulse response" (impulse response including distortion effects) to have the second and higher order convolution results from the Volterra series separated in time from the normal impulse response term from linear system theory so they can be windowed out for the purpose of obtaining the true impulse response, or "windowed in" so they can be studied individually as distortion. The math behind this is described in reference 2 of the Muller article. It's an AES article by Farina, titled Simultaneous Measurement of Impulse Response and Distortion with a Swept-sine technique.

I haven't gone completely through all the math yet though.

To me the big problem of attempting to understand how a component performs using techniques like this is that it takes no account of the history of signals fed to it. Assume a speaker driver: in first instance it is dead cold, in the second it has been conditioned to a "normal" operating state by being fed normal musical signals, at reasonable listening levels over many hours, in the third instance it has been fed a diet of heavy metal tracks at head banging levels for an hour or so. Would someone, with hand over their heart, claim that the MLS output would be identical in each of these situations?

Frank

fas42 said:

To me the big problem of attempting to understand how a component performs using techniques like this is that it takes no account of the history of signals fed to it. Assume a speaker driver: in first instance it is dead cold, in the second it has been conditioned to a "normal" operating state by being fed normal musical signals, at reasonable listening levels over many hours, in the third instance it has been fed a diet of heavy metal tracks at head banging levels for an hour or so. Would someone, with hand over their heart, claim that the MLS output would be identical in each of these situations?

Click to expand...

You are right - a loudspeaker is neither linear nor time invariant in the strict sense of the terms. But the idea is not to claim perfection in the measurement, but to do the best one can. One would hope that the measurement is good enough to give a reasonably good characterization of the kinds of changes that take place under the conditions you're talking about.

@Frank: Because of other effects, like thermal in the voice coils, I doubt anything would show exact equality in your test case. There are also many other variables, like changing preamp and amp bias levels, temperature and humidity change in the room, etc. I cannot point to them but i recall studies showing the changes in results when performing swept tones over time and at various power levels. IIRC, the changes were pretty small, however, and probably inaudible though I cannot say for sure.

@Andy: Thanks for the overview. FFTs and Taylor series I am familiar with, at least from the hairy-knuckled engineer's side, and have been exposed to Volterra series because it is used in e.g. RF/microwave large-signal steady-state analysis (simulators), plus I have lecture notes from Ray Maas' seminar. That was long ago and I have mercifully forgotten most of it, however. I have a hand-waving idea of combining impulse and swept tones (the program I use does that, in fact) but have never really looked into the math behind it. I designed data converters and associated circuits for decades, so had to have at least a passing glance at nonlinear systems (they are not LTI and a converter's front end is subject to charge-based hysteresis and thermal effects). However, I am a circuit designer and do not have the scientist's depth in the math (always too busy getting the next latest greatest thing out the door). I need to find time to follow up; I'd love to have a better understanding of all this. Maybe when I retire and finish my PhD!