Software for performing pickup analysis with a recording interface.

[Joe Gwinn]

Also the DEW line radars also discovered the ionosphere (by accident, incoherent backscatter).

That would be a previous generation. The current generation operates in the UHF region and uses circular polarization to handle Faraday rotation of the radar signal by the Ionosphere. The ionosphere isn't quite uniform, so one gets scintillation effects, just like viewing a star at night by unaided eye.

See for instance Eli Brookner's cover page article in Volume 252, Issue 2 (February 1985) of Scientific American.

Mars is different because it rotates faster. That is what causes the overspreading. Venus, for example rotates much slower, as does Mercury.
You are ignoring what I said about codes in responding to your statement about code105.

Ahh. Rotation speed. Mercury and Venus rotate such that the same side always faces the Sun, while planets from Earth outward are not forced to face the Sun.

Which statement did I ignore?

Windowing: the six(x)/x is only a significant problem when there are narrow spectral lines.

The effect of spectral leakage may not be obvious to the eye unless there are narrow spectral lines, but I would not bet that the ear cannot hear the leakage.

coherent integration: The cross spectral analysis used here takes the product computed between the ffts of the two inputs. It might be possible to use a combination of coherent and incoherent integration, but I do not think that the added complexity is worth the trouble.

Well, as always, it depends on the sequence length. With coherent integration, the SNR grows directly with the total number of samples, while for incoherent integration, it grows with the square root of sample size. With a large sample, the improvement is substantial.

[Mike Sulzer]

That would be a previous generation. The current generation operates in the UHF region and uses circular polarization to handle Faraday rotation of the radar signal by the Ionosphere. The ionosphere isn't quite uniform, so one gets scintillation effects, just like viewing a star at night by unaided eye.

The previous generation was UHF also. We still use those klystrons at 430 MHz. The incoherent backscatter from the ionosphere shows up as an increase in the noise level at the relevant ranges, although the bandwidth of this nosie-like signal is a lot less than the maximum bandwidth of the radar.

[Mike Sulzer]

The effect of spectral leakage may not be obvious to the eye unless there are narrow spectral lines, but I would not bet that the ear cannot hear the leakage.



Well, as always, it depends on the sequence length. With coherent integration, the SNR grows directly with the total number of samples, while for incoherent integration, it grows with the square root of sample size. With a large sample, the improvement is substantial.

How can the ear hear sin(x)/x leakage? The hearing system does not consist of square window ffts. It consists of fairly broad filters; the outputs are analyzed in time. More than one filter must respond to the same frequency, so there is some "leakage", undoubtedly used to good advantage in the processing.

The cross spectral analysis system used in this device in effect does coherent integration when used with a deterministic signal plus noise as is the case with code105. Consider the frequency response measurement just posted yesterday. One signal is the current sample, the reference; it has very high SNR because it is just a measurement of the high level signal used to drive the coil which excites the pickup. We can ignore the noise here compared to the other signal, which is induced in the pickup coil. It is weaker and so is more affected by noise. The processing takes the ffts of both signals, and then the complex conjugate of the fft of the reference signal is multiplied into that of the second signal. That signal has a phase which is the sum of that of the reference signal and that introduced by the pickup, and so multiplication by the conjugate removes the part due to the reference, leaving that of the pickup. When the next shot comes along, the signal adds coherently with the signal in the previous, but the noise is not coherent. You cannot do better than that, as is evident when the accumulation is done, and you take the magnitude squared to get the power. Of course, since the reference was multipled into the signal, we must also divide by its square (in the frequency domain, when the accumulation is complete) in order to remove its frequency variations. But the reference is high SNR, so it does not really matter whether the determination of its self-spectrum is coherently summed or not. Thus the process used when the signal is coherent can be the same as when a noise like signal is used, and it does them both as well as you need do.

[Joe Gwinn]

The previous generation was UHF also. We still use those klystrons at 430 MHz. The incoherent backscatter from the ionosphere shows up as an increase in the noise level at the relevant ranges, although the bandwidth of this noise-like signal is a lot less than the maximum bandwidth of the radar.

So, it's scatter from various UHF TV stations swamping echos from the planets?

This has not been a problem with the early-warning radars, probably because the echos of interest are far stronger than those from other planets.

[Joe Gwinn]

How can the ear hear sin(x)/x leakage? The hearing system does not consist of square window ffts. It consists of fairly broad filters; the outputs are analyzed in time. More than one filter must respond to the same frequency, so there is some "leakage", undoubtedly used to good advantage in the processing.

The effect of any leakage is to change the spectrum, and as we have found out, the ear is very good at telling spectra apart.

The cross spectral analysis system used in this device in effect does coherent integration when used with a deterministic signal plus noise as is the case with code105. Consider the frequency response measurement just posted yesterday. One signal is the current sample, the reference; it has very high SNR because it is just a measurement of the high level signal used to drive the coil which excites the pickup. We can ignore the noise here compared to the other signal, which is induced in the pickup coil. It is weaker and so is more affected by noise.

Given that we can make the drive very strong, I'd guess that the SNR of the induced signal is or can be pretty high as well, to the point that this is not limiting measurement accuracy.

Data point: When I was measuring impulse response functions directly, I used 10 microsecond pulses of at least 10 volts peak (into 50 ohms), the max the generator could provide. The per-shot induced signals were quite clean looking, and I would average 512 responses together, to largely cancel out noise in the scope front end. The scope was triggered directly from the generator via a dedicated sync path.

The processing takes the ffts of both signals, and then the complex conjugate of the fft of the reference signal is multiplied into that of the second signal. That signal has a phase which is the sum of that of the reference signal and that introduced by the pickup, and so multiplication by the conjugate removes the part due to the reference, leaving that of the pickup.

Yes.

When the next shot comes along, the signal adds coherently with the signal in the previous, but the noise is not coherent. You cannot do better than that, as is evident when the accumulation is done, and you take the magnitude squared to get the power. Of course, since the reference was multiplied into the signal, we must also divide by its square (in the frequency domain, when the accumulation is complete) in order to remove its frequency variations. But the reference is high SNR, so it does not really matter whether the determination of its self-spectrum is coherently summed or not. Thus the process used when the signal is coherent can be the same as when a noise like signal is used, and it does them both as well as you need do.

I'm not sure I follow this part. If you sum shots in the complex domain, and only compute power once, at the end, you have coherent integration. If the power is computed before summation over the shots, you have incoherent integration.

[Mike Sulzer]

So, it's scatter from various UHF TV stations swamping echos from the planets?

This has not been a problem with the early-warning radars, probably because the echos of interest are far stronger than those from other planets.

All I am saying is that the DEW line radars unexpectedly saw incoherent scatter from the ionosphere. No, the 2.38 MHz planetary rad does not get interference from tv stations.

[Mike Sulzer]

I'm not sure I follow this part. If you sum shots in the complex domain, and only compute power once, at the end, you have coherent integration. If the power is computed before summation over the shots, you have incoherent integration.

Yes, if you use a signal such as code105 it is coherent integration, although I did not look at it that way at first. But if you use random noise as the exciting signal, it is not coherent integration because the signal is not coherent

[Joe Gwinn]

All I am saying is that the DEW line radars unexpectedly saw incoherent scatter from the ionosphere. No, the 2.38 MHz planetary radar does not get interference from tv stations.

What is the 430 MHz for, then?

[Joe Gwinn]

Yes, if you use a signal such as code105 it is coherent integration, although I did not look at it that way at first. But if you use random noise as the exciting signal, it is not coherent integration because the signal is not coherent

If you are dividing the induced signal by the drive signal, why does it matter if the drive signal is random versus pseudorandom (which includes code105)?

[Mike Sulzer]

If you are dividing the induced signal by the drive signal, why does it matter if the drive signal is random versus pseudorandom (which includes code105)?

The random signal is different on each shot; code105 is the same on each shot. When using a random (noise like) signal you have to accumulate incoherently so that the spectrum of each sample, which is spikey, is added too the others and approaches the sample of the process. When using the same waveform on each shot, such as code105, you just have to reduce the additive noise. If, when using a noise like signal, you divided through on each shot, you would emphasize the random noise at frequencies where the sample has a low amplitude.

[Joe Gwinn]

The random signal is different on each shot; code105 is the same on each shot. When using a random (noise like) signal you have to accumulate incoherently so that the spectrum of each sample, which is spikey, is added too the others and approaches the sample of the process. When using the same waveform on each shot, such as code105, you just have to reduce the additive noise. If, when using a noise like signal, you divided through on each shot, you would emphasize the random noise at frequencies where the sample has a low amplitude.

Except that you are dividing through by the high-SNR drive signal, and the high-amplitude areas are more important than the low-amplitude areas, so does this matter in practice?

By the way, what is the test circuit?

[Mike Sulzer]

Except that you are dividing through by the high-SNR drive signal, and the high-amplitude areas are more important than the low-amplitude areas, so does this matter in practice?

By the way, what is the test circuit?

It is the noise in the signal the numerator that gets blown up when you divide by a small number.

I will draw the circuit when I get time.

[Joe Gwinn]

Broadband Impedance Spectroscopy as a model for Pickup Measurement

Sanchez 2012 Basics of broadband impedance spectroscopy 0957-0233_23_10_105501.pdf

I stumbled upon a relevant article on impedance spectroscopy. We are doing something very close to that. Interestingly, their best test signal is a collection of sine waves with randomized phases, although coarse random noise is almost as good for impedance spectroscopy, which is doing things like measure sugar concentration in water or blood. For guitar pickups, the ranking of various test signals may differ from that in the article.

[Mike Sulzer]

[ATTACH]27820[/ATTACH]

I stumbled upon a relevant article on impedance spectroscopy. We are doing something very close to that. Interestingly, their best test signal is a collection of sine waves with randomized phases, although coarse random noise is almost as good for impedance spectroscopy, which is doing things like measure sugar concentration in water or blood. For guitar pickups, the ranking of various test signals may differ from that in the article.

Very interesting! The randomized multi-sine looks very much like Gaussian random noise, as it should, but since it is a finite nymber of discrete sine waves, it is like repeating the same random noise over and over. That does look like a good technique; you can make a flatter spectrum than, say, code105, but the waveform has less average power per unit time because of its dynamic range. Might be worth a try after fully analyzing what we have.

[Mike Sulzer]

Some more on how to use this and what it does

This drawing (Connections.pdf) shows the hardware connections needed to measure the pickup frequency response. It is pretty simple.

Joe Gwinn brought up an interesting question as to how much integration is necessary when using code105. This figure (sbbr300_1code105.pdf) shows two measurements, 300 shots underneath 1 shot. You really cannot see much difference. However, if you look more closely at the lower frequencies (sbbr300_1code105lf.pdf), Then you can see differences, and depending upon what you are doing, you might want the more accurate measurement. If I were measuring a bass pickup, I would use a coil that pumps out more flux and also integrate longer. There is no point in having much uncertainty at frequencies that matter.

Next is more on the performance when random noise is used.