A Basic Limitation in Stereo FM Reproduction

One of the concepts which exist in modern, high-definition sound, is that Human Sound perception can take place between 20 Hz and 20kHz, even though those endpoints are somewhat arbitrary. Some people cannot hear frequencies as high as 20kHz, especially older people, or anybody who just does not have good hearing. Healthy, young children and teenagers can typically hear that entire frequency range.

But, way back when FM radio was invented, sound engineers had flawed data about what frequencies Humans can hear. It was given to them as data to work with that Humans can only hear frequencies from 30Hz to 15kHz. And so, even though Their communications authorities had the ability to assign frequencies somewhat arbitrarily, they did so in a way that was based on such data. (:1)

For that reason, the playback of FM Stereo today, using household receivers, is still limited to an audio frequency range from 30Hz to 15kHz. Even very expensive receivers will not be able to reproduce sound, that was once part of the modulated input, outside this frequency range, although other reference points can be applied, to try to gauge how good the sound quality is.

There is one artifact of this initial standard which was sometimes apparent in early receivers. Stereo FM has a pilot frequency at 19kHz, which a receiver needs to lock an internal oscillator to, but in such a way that the internal oscillator runs at 38kHz, but such that this internal oscillator can be used to demodulate the stereo part of the sound. Because the pilot signal which is actually part of the broadcast signal is ‘only’ at 19kHz, this gives an additional reason to cut off the audible signal at ‘only’ 15Khz; the pilot is not meant to be heard. But, way back in the 1970s and earlier, Electrical Engineers did not have the type of low-pass filters available to them which they do now, that are also known as ‘brick-wall filters’, or filters that attenuate frequencies above the cutoff frequency very suddenly. Instead, equipment designed to be manufactured in the 1970s and earlier, would only use low-pass filters with gradual ‘roll-off’ curves, to attenuate the higher frequencies progressively more, above the cutoff frequency by an increasing distance, but in a way that was gentle. And in fact, even today the result seems to be, that gentler roll-off of the higher frequencies, results in better sound, when the quality is measured in other ways than just the frequency range, such as, when sound quality is measured for how good the temporal resolution, of very short pulses, of high-frequency sound is.

Generally, very sharp spectral resolution results in worse temporal resolution, and this is a negative side effect of some examples of modern sound technology.

But then sometimes, when listeners with high-end receivers in the 1970s and before, who had very good hearing, were tuned in to an FM Stereo Signal, they could actually hear some residual amount of the 19kHz pilot signal, which was never a part of the original broadcast audio. That was sometimes still audible, just because the low-pass filter that defined 15kHz as the upper cut-off frequency, was admitting the 19kHz component to a partial degree.

One technical accomplishment that has been possible since the 1970s however, in consumer electronics, was an analog ‘notch filter’, which seemed to suppress one exact frequency – or almost so – and such a notch filter could be calibrated to suppress 19kHz specifically.

Modern electronics makes possible such things as analog low-pass filters with a more-sudden frequency-cut-off, digital filters, etc. So it’s improbable today, that even listeners whose hearing would be good enough, would still be receiving this 19kHz sound-component to their headphones. In fact, the sound today is likely to seem ‘washed out’, simply because of too many transistors being fit on one chip. And when I just bought an AM/FM Radio in recent days, I did not even try the included ear-buds at first, because I have better headphones. When I did try the included ear-buds, their sound-quality was worse than that, when using my own, valued headphones. I’d say the included ear-buds did not seem to reproduce frequencies above 10kHz at all. My noise-cancelling headphones clearly continue to do so.

One claim which should be approached with extreme skepticism would be, that the sound which a listener seemed to be getting from an FM Tuner, was as good as sound that he was also obtaining from his Vinyl Turntable. AFAIK, the only way in which this would be possible would be, if he was using an extremely poor turntable to begin with.

What has happened however, is that audibility curves have been accepted – since the 1980s – that state the upper limit of Human hearing as 20kHz, and that all manner of audio equipment designed since then takes this into consideration. This would include Audio CD Players, some forms of compressed sound, etc. What some people will claim in a way that strikes me as credible however, is that the frequency-response of the HQ turntables was as good, as that of Audio CDs was. And the main reason I’ll believe that is the fact that Quadraphonic LPs were sold at some point, which had a sub-carrier for each stereo channel, that differentiated that stereo channel front-to-back. This sub-carrier was actually phase-modulated. But in order for Quadraphonic LPs to have worked at all, their actual frequency response need to go as high as  40kHz. And phase-modulation was chosen because this form of modulation is particularly immune to the various types of distortion which an LP would insert, when playing back frequencies as high as 40kHz.

About Digital FM:

(Updated 7/3/2019, 22h15 … )

There is a basic false interpretation which exists, of what exactly ‘Digital FM’ is supposed to mean. What is widely available is a kind of tuning system that has been named ‘Digital’, the only purpose of which is to stabilize and determine the received frequencies, using partially digital technologies. This set of technologies actually uses an accurate quartz crystal as a reference frequency, as well as a counter, that divides the frequency of a Voltage-Controlled Oscillator – a ‘VCO’ – by whatever number it has been assigned to count to. This counter is digital and produces a pulse each time it resets. The resulting train of pulses is phase-discriminated with the reference frequency, resulting in a lower-frequency voltage which is made to complete a feedback loop and to control the frequency of the VCO. (:5)

The result is that the VCO will run at a frequency which is the reference frequency multiplied, by whatever number the frequency divider counts to. This result is exact. This strategy is also what gets referred to as a “Phase-Locked Loop” – a PLL – even though other types of Phase-Locked Loops are possible in Electronics. (:4)

When the RF input to such a tuner is mixed with the VCO frequency – thus “heterodyned” – the objective is an Intermediate Frequency which is predictable, and which is then selected before demodulation.

But, the RF stages, the mixer, the IF stages, and the demodulator are still Analog with this technology. And thus, this technology still counts as ‘Analog AM or FM’.

However, a technology is possible which is referred to as Digital Audio Broadcasting, and this is what I’d actually refer to as ‘Digital Radio’ instead then.

(As of 6/22/2019 … )

One of the facts which I’m aware of is, that ‘Digital Radio’ exists. What this simply does is to encode a digital stream, and then, to count on lossy compression on that stream, to make up for the fact that it has not been assigned as many radio frequencies as the broadcasting of Analog FM has been allotted.

A fundamental property of lossy sound compression is, that the audio frequency range can be as wide as anybody could wish for, but that the sound reproduction is compromised in other ways, which are too complex to write about in this posting. Elsewhere in this blog, I posted about that. (:2)

For all I know, the form of lossy compression assigned for use in Digital Radio could harm sound quality less, than first-generation MP3 compression did. My main skepticism towards Digital Radio stems from the observation that other forms of dissemination now exist, such as subscription-based, digital streaming services, as well as personal music libraries to which listeners have added their own content. Since most of these frameworks already offer lossy, compressed sound, I do not see what advantage Digital Radio would bring, and this in itself could have a negative impact on eventual, commercial success. Its adoption would require that broadcasters make significant investments into equipment, and that listeners do so as well. But, listeners have already invested their precious money into MP3 Players, High-Definition Digital Audio Players, smart-phones with HQ sound chips, (Digital) Satellite Radio Receivers etc. They would not see much of a reason to go beyond Analog FM then as well.


 

1:)

Engineers at the time did not refer to such “Technical Information” as data. But nevertheless, some of it represented false information, that was used to design electronic devices, and that generated more false information, much as flawed data would do today.


 

2:)

I have encountered people who do not believe in the existence of ‘lossy compression’. Those people believe in “Lossless Compression”, but also believe that “Its opposite is MP3 Compression.” This is similar to saying that the opposite of ‘a Diesel Engine’ is ‘a Lincoln Cadillac’. One term specifies a category of objects, and the other is a specific brand name.

MP3 compression is only one type, which is not lossless. Some other compression-formats which have this in common include: OGG Vorbis, AC3, and AAC compression, that are used in .OGG, MPEG-2 and .MP4 Files respectively. And as a distinction from .MP4 Files that are meant to encode video, .M4A Files exist which only include the sound (AAC-compressed).

The key to understanding these forms of compression lies in the fact that Although they do not lose any data, when decoding, they also fail to reproduce the sound-waves that were first encoded. As seen on an oscilloscope, the sound waves that result from decompressing an .MP3 File, will not match the waves that were first compressed. This is where those are all ‘lossy’. They lose information by first converting it into an exact spectral representation instead of the time-domain sample-sequence, which is done with some form of Fourier Transform – usually a Discrete Cosine Transform – and then, those schemes quantize the resulting coefficients. This means that any specific frequency coefficient, that was once exact, ends up having an integer value, with only a very small range of integers, let’s say from (0) to (±10). When the transform is inverted, the original sound-waves do not result.

Alternatively, some forms of lossy compression, such as GSM, depend on Linear Predictive Coding, but substitute pseudo-random noise for the residual when decoding. This tends to be too low in quality for music, but gets used for digital voice transmission, and can result in very low bit-rates.


 

A completely different type of strategy which exists, is to compute a Linear Predictive Coding for a given block of input samples, to record that, but also to record the exact residual. Because the residual will usually have a lower amplitude than the original signal (but not always), its number of bits can be made smaller than those for the original sequence of samples, for some blocks, and lossless compression results. And a brand of that frequently used, is .FLAC .


 

(Update 5/22/2019, 22h20 : )

I should acknowledge that a type of lossy compression exists, which differs from those dependent on the almighty Discrete Cosine Transform. That would be ADPCM. This is a form of compression which damages the sound less, than frequency-based formats, If, as the WiKi suggests, it is preceded by a subdivision of the spectrum of audio frequencies, into sub-bands. This allows fewer bits to be used to encode higher-frequency sub-bands, than were allotted to encode the main sub-band, that Human hearing perceives well.

ADPCM has been confused by some people in the past, with lossless compression, and one reason why could be the fact that it will reproduce waveforms on an oscilloscope, that roughly match those which were first encoded. However, the fact should also be pointed out that, because Human hearing is based more-strongly on frequencies than it is on the waveform of sounds, forms of compression are possible that do preserve waveforms, but that sound awful. The simple precedence of DPCM, not ADPCM, demonstrated this.

Either way the strategy is to encode the ‘step’, or the discrete differential, between the current sample and the previous sample (conceptually :3), instead of just encoding the current sample. This differential can be assigned a certain number of bits fewer than those of the general audio format. Yet, if the signal has a high-frequency transient, then pure DPCM will clip that transient and produce dulled sound, because the theoretical maximum of the difference, between two consecutive sample-values, would actually need to have one bit more than the sample format.

ADPCM makes up for that with an active loop, either in hardware or in software, that will determine a quantization step greater than (1), as soon as this happens, so that the decoding can apply this same parameter as the scale factor, and keep reproducing sound that includes the sudden changes in sample-value.

(Edit 6/23/2019, 22h40 :

Digital Audio Broadcasting actually uses MPEG-1 Layer 2 compression.

)

I know that it can’t be lossless because lossless cannot guarantee any compression better than 1:1, and Digital Radio will require some fixed degree of compression that is greater than 1:1.

But, if Digital Radio was thought out very well (In My Opinion), then it would adopt such a variant of ADPCM because that format allows for a true, fixed bit-rate, while also offering listeners potential sound quality exceeding what the frequency-based methods would offer. And it would then also offer listeners ‘a different experience’, from what MP3, M4A, OGG, etc., already offer.

3:)

A necessary refinement of ADPCM or DPCM is, instead of computing the difference between the current sample and the previous, the encoder runs a local model of what the decoder will decode. Then, the encoder computes the difference between the current input sample, the what the local model predicts the decoder to have decoded as the previous sample.

 

(Edit 6/23/2019, 2h20 : )

There have existed two common forms of ADPCM that are ‘IMA ADPCM’ and ‘MS ADPCM’, which will compress the coding from 16 bits to 4. But this older form of the method is unsuitable for music and again, this is because the entire audible band is being encoded to that same number of bits. A delta with 4 bits of precision is sufficient for higher sub-bands, but not for midrange frequencies.

When it gets used, ‘IMA ADPCM’… is typically stored in .WAV container files.

A variant called ‘AptX’ subdivides the audio band evenly into 4 sub-bands, and encodes them with 8, 4, 2, 2 bits. It is suitable for music. However, AptX is also highly proprietary, and finds much use these days connecting Bluetooth headsets to phones, for use with music, where without, only telephone-quality sound was once possible. Phones that support AptX use a dedicated chip to perform the compression.


 

(Update 6/23/2019, 12h25 : )

One challenge which the designers of Digital Radio must have faced, would have been the inevitable trade-off, of needing a high number of bits per second, or otherwise, to accept sub-standard sound quality. If the candidate method was a form of ADPCM with a 16-bit sample format and multiple sub-bands, then designers could fall into a kind of mental trap, of considering only two sub-bands, but allotting 8 and 4 bits to them. And then the problem would be that the resulting bit-rate would be 3/8 of the uncompressed bit-rate, which would give good sound, but which might be a higher bit-rate than what the (Analog) Carrier can modulate.

A little more effort might reveal that using the Quadrature Mirror Filters to create 4 sub-bands, but then allotting them 8, 4, 4, 4 bits, would also result in good sound, as well as a bit rate which is 5/16 the uncompressed bit-rate, which is therefore almost as low as what AptX would achieve.


 

(Update 6/24/2019, 14h50 : )

4:)

What an Electrical Engineer may find is that he needs to have his local oscillator run at odd multiples of 100kHz, yet, that there are no crystals available that oscillate as low as at 100kHz. But, crystals are available that oscillate at ‘exactly’ 1MHz. Due to the scale of integration today, a second counter can be put on a chip that divides the raw frequency of such a crystal by 10, to arrive at the actual reference frequency. And because those circuits are in fact digital, putting more of them does not harm the quality of the eventual output.

In other words, methods exist to arrive at more interesting ratios, than simply, the frequency of the crystal multiplied by a certain integer. And then the resulting frequency is an exact ratio.

Just as it is with any feedback control system, the potential exists for a PLL to become unstable. In order to prevent instability, the range of targeted frequencies is limited, and the appropriate low-pass filter is applied to the voltage fed back, to control the VCO. However, if a reference frequency is chosen which is too low, then what follows is that the PLL will need to be too slow as well. Since a PLL could be useless that takes too long to lock in on any one frequency, this consideration eventually limits what can be achieved with a PLL.

And, the reader is unlikely to find a PLL, the highest target frequency of which is more than twice the lowest, in any one mode of operation.


 

(Updated 7/3/2019, 22h15 : )

5:)

The reader might have noticed that my proposed concept of a frequency divider would have as a main drawback, the generation of relatively short pulses, which in turn could present a challenge for phase-discrimination. But I can think of three ways of solving that problem:

  • Each pulse-train could be fed to a flip-flop, resulting in waves with 50% duration, but with half the original frequency. The two resulting waves could be sent to an XOR gate, and its output followed by a low-pass filter.
  • One pulse-train could be converted by a simple analog circuit to an approximate saw-wave, while the other could be sent to the gate of a MOSFET meant to act as a sample-and-hold circuit. Its output would be followed by a capacitor that completes the sample-and-hold circuit, then followed by a resistor, then followed by another capacitor that completes a low-pass filter.
  • Even though the counter always counts to 10 before resetting, only the MSB of the resulting 4-bit number may be monitored. This results in a wave with 20% duration, which can be converted into a much gentler saw-wave. There is no risk that the PLL would lock on to the ‘wrong’ side of such a saw-wave, as only one side will give a stable lock.

Dirk

 

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