My Site and Blog are back Up.

According to This preceding posting, this site had experienced some down-time, due to a problem with my router. I’m happy to say, that the router is working fine again, and that therefore, my blog is back Up.

I did nothing successful, that would have brought the malfunction to a stop. I can only guess then, that my ISP must have downloaded a firmware update to the router, which fixed the problem. Yay! :-) Yes, this router is managed in such a way, that my ISP can just flash it.

Dirk

 

Problems with my DSL. Downtime.

One of the peculiarities with which I host this blog, is that I use a home PC as a Web-server, that’s meant to be visible to the entire Internet. I don’t really recommend that other people do this; this just happens to be what I do. As a result, the visibility of my site and blog on the Internet, are limited by the behaviors of my home Internet as well as by the modem / router that I use. This one happens to be owned by my ISP.

As recently as last Wednesday, which was December 12, 2018, this blog went off-line, due to some problem with the router, which was similar to the problem I posted about Here.

This time around, there is no firm estimate, of when the problem will be fixed. I’m hoping that this will be resolved, by the time the next firmware update for this router is downloaded by the ISP, but that can take an unpredictably long time.

My own personal use of the Internet remains unaffected.

Dirk

 

An observation about computing the Simpson’s Sum, as a numerical approximation of an Integral.

One of the subjects which I posted about before, is the fact that in practical computing, often there is an advantage to using numerical approximations, over trying to compute Algebraically exact solutions. And one place where this happens, is with integrals. The advantage can be somewhere, between achieving greater simplicity, and making a solution possible. Therefore, in Undergraduate Education, emphasis is placed in Calculus 2 courses already, on not just computing certain integrals Algebraically, but also, on understanding which numerical approximations will give good results.

One numerical approximation that ‘gives good results’, is The so-called Simpson’s Sum. What it does, is to perform a weighted summation of the most-recent 3 data-points, into an accumulated result. And the version of it which I was taught, sought to place a weight of 2/3 on the Midpoint, as well as to place a weight of 1/3 on the Trap Sum.

In general, the direction in which the Midpoint is inaccurate, will be opposite to the direction in which the Trap Sum is inaccurate. I.e., if the curve is concave-up, then the Midpoint will tend to underestimate the area under it, while the Trap Sum will tend to overestimate. And in general, with integration, consistent under- or over-estimation, is more problematic, than random under- or over-estimation would be.

But casual inspection of the link above will reveal, that this is not the only way to weight the three data-points. In effect, it’s also possible to place a weight of 1/2 on the Midpoint, plus a weight of 1/2 on the Trap Sum.

And so a logical question to ask would be, ‘Which method of summation is best?’

The answer has to do, mainly, with whether the stream of data-points is ‘critically sampled’ or not. When I was taking ‘Cal 2′, the Professor drew curves, which were gradual, and the frequencies of which, if the data-points did form a stream, would have been below half the Nyquist Frequency. With those curves, the Midpoint was visibly more-accurate, than the Trap Function.

But one parameter for how Electrical Engineers have been designing circuits more recently, not only states that an analog signal is to be sampled in the time domain, but that the stream of samples which results will be critically sampled. This means considerable signal-energy, all the way up to the Nyquist Frequency. What will result is effectively, that all 3 data-points will be as if random, with great variance between even those 3.

Under those conditions, there is a slight advantage to computing the average, between the Midpoint, and the Trap Sum.

(Update 12/08/2018, 20h25 : )

I’ve just prepared a small ‘wxMaxima’ work-sheet, to demonstrate the accuracy of the 2/3 + 1/3 method, applied to a sine-wave at 1/2 Nyquist Frequency:

Worksheet

(Update 12/09/2018, 12h35 : )

Continue reading An observation about computing the Simpson’s Sum, as a numerical approximation of an Integral.

A Gap in My Understanding of Surround-Sound Filled: Separate Surround Channel when Compressed

In This earlier posting of mine, I had written about certain concepts in surround-sound, which were based on Pro Logic and the analog days. But I had gone on to write, that in the case of the AC3 or the AAC audio CODEC, the actual surround channel could be encoded separately, from the stereo. The purpose in doing so would have been, that if decoded on the appropriate hardware, the surround channel could be sent directly to the rear speakers – thus giving 6-channel output.

While writing what I just linked to above, I had not yet realized, that either channel of the compressed stream, could contain phase information conserved. This had caused me some confusion. Now that I realize, that the phase information could be correct, and not based on the sampling windows themselves, a conclusion comes to mind:

Such a separate, compressed surround-channel, would already be 90⁰ phase-shifted with respect to the panned stereo. And what this means could be, that if the software recognizes that only 2 output channels are to be decoded, the CODEC might just mix the surround channel directly into the stereo. The resulting stereo would then also be prepped, for Pro Logic decoding.

Dirk