A Practical Application, that calls for A Uniform Phase-Shift: SSB Modulation

A concept that exists in radio-communications, which is derived from amplitude-modulation, and which is further derived from balanced modulation, is single-sideband modulation. And even back in the 1970s, this concept existed. Its earliest implementations required that a low-frequency signal be passed to a balanced modulator, which in turn would have the effect of producing an upper sideband (the USB) as well as an inverted lower sideband (the LSB), but zero carrier-energy. Next, the brute-force approach to achieving SSB entailed, using a radio-frequency filter to separate either the USB or the LSB.

The mere encumbrance of such high-frequency filters, especially if this method is to be used at RF frequencies higher than the frequencies, of the old ‘CB Radio’ sets, sent Engineers looking for a better approach to obtaining SSB modulation and demodulation.

And one approach that existed since the onset of SSB, was actually to operate two balanced modulators, in a scheme where one balanced modulator would modulate the original LF signal. The second balanced modulator would be fed an LF signal which had been phase-delayed 90⁰, as well as a carrier, which had either been given a +90⁰ or a -90⁰ phase-shift, with respect to whatever the first balanced modulator was being fed.

The concept that was being exploited here, is that in the USB, where the frequencies add, the phase-shifts also add, while in the LSB, where the frequencies subtract, the phase-shifts also subtract. Thus, when the outputs of the two modulators were mixed, one side-band would be in-phase, while the other would be 180⁰ out-of-phase. If the carrier had been given a +90⁰ phase-shift, then the LSB would end up 180⁰ out-of-phase – and cancel, while if the carrier had been given a -90⁰ phase-shift, the USB would end up 180⁰ out-of-phase – and cancel.

This idea hinges on one ability: To phase-shift an audio-frequency signal, spanning several octaves, so that a uniform phase-shift results, but also so that the amplitude of the derived signal be consistent over the required frequency-band. The audio signal could be filtered to reduce the number of octaves that need to be phase-shifted, but then it would need to be filtered to achieve a constrained frequency-range, before being used twice.

And so a question can arise, as to how this was achieved historically, given analog filters.

My best guess would be, that a stage which was used, involved a high-pass and a low-pass filter that acted in parallel, and which would have the same corner-frequency, the outputs of which were subtracted – with the high-pass filter negative, for -90⁰ . At the corner-frequency, the phase-shifts would have been +/- 45⁰. This stage would achieve approximately uniform amplitude-response, as well as achieving its ideal phase-shift of -90⁰ at the one center-frequency. However, this would also imply that the stage reaches -180⁰ (full inversion) at higher frequencies, because there, the high-pass component that takes over, is still being subtracted !

( … ? … )

What can in fact be done, is that a multi-band signal can be fed to a bank of 2nd-order band-pass filters, spaced 1 octave apart. The fact that the original signal can be reconstructed from their output, derives partially from the fact that at one center-frequency, an attenuated version is also passed through one-filter-up, with a phase-shift of +90⁰ , and a matching attenuated version of that signal also passed through one-filter-down, with a phase-shift of -90⁰. This means that the two vestigial signals that pass through the adjacent filters are at +/- 180⁰ with respect to each other, and cancel out, at the present center-frequency.

If the output from each band-pass filter was phase-shifted, this would need to take place in a way not frequency-dependent. And so it might seem to make sense to put an integrator at the output of each bp-filter, the time-constant of which is to achieve unit gain, that the center-frequency of that band. But what I also know, is that doing so will deform the actual frequency-response of the amplitudes, coming from the one band. What I do not know, is whether this blends well with the other bands.

If this was even to produce a semi-uniform -45⁰ shift, then the next thing to do, would be to subtract the original input-signal from the combined output.

(Edit 11/30/2017 :

It’s important to note, that the type of filter I’m contemplating does not fully achieve a phase-shift of +/- 90⁰ , at +/- 1 octave. This is just a simplification which I use to help me understand filters. According to my most recent calculation, this type only achieves a phase-shift of +/- 74⁰ , when the signal is +/- 1 octave from its center-frequency. )

Now, my main thought recently has been, if and how this problem could be solved digitally. The application could still exist, that many SSB signals are to be packed into some very high, microwave frequency-band, and that the type of filter which will not work, would be a filter that separates one audible-frequency sideband, out of the range of such high frequencies.

And as my earlier posting might suggest, the main problem I’d see, is that the discretized versions of the low-pass and high-pass filters that are available to digital technology in real-time, become unpredictable both in their frequency-response, and in their phase-shifts, close to the Nyquist Frequency. And hypothetically, the only solution that I could see to that problem would be, that the audio-frequency band would need to be oversampled first, at least 2x, so that the discretized filters become well-behaved enough, to be used in such a context. Then, the corner-frequencies of each, will actually be at 1/2 Nyquist Frequency and lower, where their behavior will start to become acceptable.

The reality of modern technology could well be such, that the need for this technique no longer exists. For example, a Quadrature Mirror Filter could be used instead, to achieve a number of side-bands that is a power of two, the sense with which each side-band would either be inverted or not inverted could be made arbitrary, and instead of achieving 2^n sub-bands at once, the QMF could just as easily be optimized, to target one specific sub-band at a time.

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Testing the Focusrite Scarlett 2i2 external sound device, with my Samsung Tab S Tablet

I have tested, whether this external USB recording tool, works with my Samsung Galaxy Tab S Tablet, using a ‘StarTech.com’ OTG adapter. The results were resoundingly affirmative.

Scarlett 2i2 _1

In This Earlier Posting, I had tested the same USB Sound Card, with my Samsung Galaxy S6 Smart-Phone. At that time, an attempt also to use it with my Tab S tablet had failed. In order to get the Scarlett 2i2 to work with the Tab S, the following two conditions need to be fulfilled:

  1. The amount of current that the USB Slave Device may draw, needs to be reinforced, in principle, with a self-powered OTG adapter, or with a similar arrangement. The ‘StarTech.com’ is Not a self-powered OTG adapter, and with it, the Scarlett 2i2 is bound to draw too much current, for the likes of the Tab S. It was after all meant as an audio workstation workhorse, and not as a replacement for a simple USB Microphone.
  2. The Master / Host Device, the Tab S, needs to have the correct drivers.

Condition (1) is something I was able to fulfill for now, in a roundabout way. I bought a ‘j5create USB 3.0 4-Ports Mini HUB’, with the part number ‘JUH340′. This is a self-powered hub by default, with its own power cord, and has Type A USB connectors up-stream and down-stream. Granted, it has a special up-stream cable, that connects to the hub with a special connector, just so that the user does not get this socket confused with the down-stream sockets. But then, the far side of that cable has a standard Type A USB jack.

This USB jack can be plugged, into the far side of the OTG adapter. Since the hub is self-powered, the current requirements of the Scarlett 2i2 are met by it, and not by the OTG adapter, and thus not by the micro-USB port on the Tab S, the latter of which now faces a minimum current load.

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Testing the Focusrite Scarlett 2i2 external sound device, with my Samsung S6 Smart-Phone

I have tested, whether this external USB recording tool, works with my Samsung Galaxy S6 Smart-Phone, using an ‘StarTech.com’ OTG adapter. The results were mixed. In An Earlier Posting, I had tested whether this external USB Sound Card, works under Linux. And the answer to that question was a resounding Yes.

Scarlett 2i2 _1

When we plug an OTG adapter into a smart-phone or tablet, this puts the mobile device into Master / Host Mode, that would otherwise normally work in Slave Mode. Thus, we can then plug in a USB storage device, and hopefully have that recognized, while by default, we can only plug our mobile device into a computer, and have the computer recognize this mobile device, as the storage device.

But it is also plausible to connect other external devices to our mobile device, when using an OTG adapter. All this happens because the OTG adapter itself contains an additional chip, that gives it the ability to act as a USB Host. Whether such external devices will work or not, generally depends on two factors:

  1. Whether the micro-USB port on the mobile device can output enough current, to supply the external / Slave device, and
  2. Whether the mobile device possesses the drivers needed, for the USB device in question. Under Linux, this last question is more likely to be answered in the affirmative.

The OTG adapter I was using, uses its micro-USB side as the only power-supply. This means that if the connected device draws a full 500mA of supply current, we are pushing the limit, that is generally set for USB 2.0  PC ports.

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I just custom-compiled Ardour 5.3.0

I know an acquaintance, whose name I will protect, who uses “Garage Band” on his Mac, but who has a hard time imagining that there exist many, many different programs like it, for other platforms, and that there must exist such, in order for professional musicians also to have access to a great array of such tools.

Of greater relevance is the fact, that such software exists under Linux as well – not just on Macs or PCs – as well as under Android.

And there is one observation which I would like to add, about what form this takes if users and artists wish to do audio work using Free, Open-Source applications.

Typically, we can access applications that do most of the work that polished, commercial examples offer. But one area in which the free applications do lag behind, is in the availability of sample packs – aka loops – which some artists will use to construct songs.

If Linux developers were to offer those, they would probably also need to ask for money.

Further, Garage Band has it as a specific advantage, that if such loops are simply dropped into the project, this program has the tempo stored, with which that loop was playing by default, in addition to which all DAWs have the tempo of the project set and available. Garage Band will automatically time-stretch the loop, to adapt to the project tempo. Most of the DAW programs I know, do not do this automatically.

A common ability the open-source applications offer though, is to time-stretch the sample manually after importing it, which can be as easy as shift-clicking on one of the edges of the sample and dragging it.

In order for this to be intuitive, it is helpful if the sample has first been processed with a Beat Slicer, so that the exact size of the rectangle will also snap into place with the timing marks on the project view, and the sample-tempo will match the project-tempo.

Shuriken_Klystr_1

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