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 6/24/2019, 14h50 … )

Continue reading A Basic Limitation in Stereo FM Reproduction

LG Tone Infinim HBS-910 Bluetooth Headphones

In This earlier posting, I had written that my LG Tonepro HBS-750 Bluetooth Headphones had permanently failed. Today, I received the HBS-910 headphones that are meant to replace those. And as I’ve written before, it is important to me, to benefit from the high-quality sound, that both sets of headphones offer.

I’m breaking in the new ones, as I’m writing this.

There exists a design-philosophy today, according to which music-playback is supposed to boost the bass and attenuate the highest frequencies – the ones higher than 10kHz – so that the listener will get the subjective impression that the sound is ‘louder’, and so that the listener will reduce the actual signal-level, to preserve their hearing better than it was done a few decades ago.

  1. The lowest-frequency (default) setting on the equalizer of the headphones does both of those things.
  2. The next setting stops boosting the bass.
  3. The third setting, stops attenuating the treble.

Overall, I get the impression that the highest frequencies which the HBS-910 can reproduce, extend higher, than what the HBS-750 was able to reproduce.

Continue reading LG Tone Infinim HBS-910 Bluetooth Headphones

About the Amplitudes of a Discrete Differential

One of the concepts which exist in digital signal processing, is that the difference between two consecutive input samples (in the time-domain) can simply be output, thus resulting in a differential of some sort, even though the samples of data do not represent a continuous function. There is a fact which must be observed to occur at (F = N / 2) – i.e. when the frequency is half the Nyquist Frequency, of (h / 2) , if (h) is the sampling frequency.

The input signal could be aligned with the samples, to give a sequence of [s0 … s3] equal to

0, +1, 0, -1

This set of (s) is equivalent to a sine-wave at (F = N / 2) . Its discrete differentiation [h0 … h3] would be

+1, +1, -1, -1

At first glance we might think, that this output stream has the same amplitude as the input stream. But the problem becomes that the output stream is by same token, not aligned with the samples. There is an implicit peak in amplitudes between (h0) and (h1) which is greater than (+1) , and an implicit peak between (h2) and (h3) more negative than (-1) . Any adequate filtering of this stream, belonging to a D/A conversion, will reproduce a sine-wave with a peak amplitude greater than (1).

(Edit 03/23/2017 : )

In this case we can see, that samples h0 and h1 of the output stream, would be phase-shifted 45⁰ with respect to the zero crossings and to the peak amplitude, that would exist exactly between h0 and h1. Therefore, the amplitude of h0 and h1 will be the sine-function of 45⁰ with respect to this peak value, and the actual peak would be (the square root of 2) times the values of h0 and h1.

(Erratum 11/28/2017 —

And so a logical question which anybody might want an answer to would be, ‘Below what frequency does the gain cross unity gain?’ And the answer to that question is, somewhat obscurely, at (N/3) . This is a darned low frequency in practice. If the sampling rate was 44.1kHz, this is achieved somewhere around 7 kHz, and music, for which that sampling rate was devised, easily contains sound energy above that frequency.

Hence the sequences which result would be:

s = [ +1, +1/2, -1/2, -1, -1/2, +1/2 ]

h = [ +1/2, -1/2, -1, -1/2, +1/2, +1 ]

What follows is also a reason for which by itself, DPCM offers poor performance in compressing signals. It usually needs to be combined with other methods of data-reduction, thus possibly resulting in the lossy ADPCM. And another approach which uses ADPCM, is aptX, the last of which is a proprietary codec, which minimizes the loss of quality that might otherwise stem from using ADPCM.

I believe this observation is also relevant to This Earlier Posting of mine, which implied a High-Pass Filter with a cutoff frequency of 500 Hz, that would be part of a Band-Pass Filter. My goal was to obtain a gain of at most 0.5 , over the entire interval, and to simplify the Math.

— End of Erratum. )

(Posting shortened here on 11/28/2017 . )



aptX Handles Polyphonic Sound Surprisingly Well.

Right now, as I am typing this, I am listening to Beethovens 9th Symphony on my real “LG Tone Pro HBS-750″ Bluetooth Headphones. The quality of sound is dramatically better, than what the fake HBS-730s had produced, simply because those were fake.

This recording of Beethoven is stored on my phone, as a series of FLAC files, and Android Lollipop devices are well-able to play back FLAC files. I did this, in order to test the fake headphones at first, because I was not sure whether their poor performance then was due to some interaction of aptX, with MP3 or OGG compression, rather than due to the implementation of aptX I was getting. Playing back a FLAC file is equivalent to playing back a raw audio file.

From what I read, aptX not only splits the uncompressed spectrum into 4 sub-bands, but then quantizes each sub-band. The 4 sub-bands are approximately from 0 to 5.5 kHz, from 5.5 to 11 kHz, from 11 kHz to 16.5 kHz, and finally from 16.5 kHz to 22 kHz. These sub-bands are then compressed using ADPCM, which allocates 8,4,2,2 bits to each.

This implies, that the first sub-band contains the bass and the mid-range, and that what I would call ‘melodic treble’ sounds, do not extend beyond sub-band 2, since treble notes with fundamental frequencies higher than 11 kHz are not usually played. And sub-bands 3 and 4 simply add texture to the sound. This means, that to allocate fewer bits of precision to sub-bands 3 and 4 ‘makes sense’, since our natural way of interpreting sound, already sees less detail at those frequencies.

A question which I had raised earlier, was if the act of quantizing the sub-bands 3 and 4 greatly – down to 2 bits in fact – will damage the degree of polyphony that can be achieved.

And now that I possess true headphones I am finding, that the answer is No. The sub-bands 3 and 4, are still capable of being played back in a multi-spectral way, even though their differentials have been quantized that much.

(Edit 06/25/2016 : ) Instead of receiving a regular sequence of +1, 0 and -1 data-points, it is possible to receive an atactic sequence of them. The first thing that happens when decoding that, is an integration, which will already emphasize lower, original frequency components that have been deemphasized. After that, the degree with which the analog signal can be reconstructed is only as good, as the interpolation. And in practice, interpolation is often provided by means of a linear filter which has more than two coefficients. Having a longer sequence of coefficients, such as maybe 6 or 8, provides better interpolation, even in sub-bands 3 and 4, which we supposedly hear less-well.


I do find though, now that the entire signal is much more clear, that when I listen closely, the highest frequencies belonging to Beethovens 9th, seem to have slightly less resolution than they are truly supposed to have. But not as much less resolution, than I am used to hearing, due to poor headphones, or due to MP3 compression.

It is already a dramatic improvement over what my past told me, that today, Some Bluetooth Headphones can play back high-quality music, in addition to being usable for telephony.

Now, Beethoven died before he finished his 9th symphony, and later artists officially completed it, by adding the 5th movement, which is actually “Shiller’s Ode To Joy”. According to what I am hearing, that 5th movement is compromised more by the aptX compression than the first 4 were, that were actually written by Beethoven.

The reason seems to be the fact, that Shiller’s work is more operatic, and has choruses singing very high notes, which results in a lot of the signal energy being in the 2nd, 3rd and 4th sub-bands. So when I hear that movement, I can hear the quantization quite clearly.

It is usually not a preference of mine, to listen to this 5th movement, because I don’t find it to be authentic Beethoven. Right now I am listening to it, and observing this effect with some fascination.