by Jan Meier
I remember well the time when the first CD-players came on the market with specifications no other system could match. Over the years, however, both the quality-standard of my equipment and my demands on sound reproduction grew and I got more and more irritated. Although the CD outperforms the record (IMHO) by miles, I often noticed an edginess and harshness that was unnatural to my ears. It appears that I had been infected by digitalitis.
Recently I professionally got involved in the various aspects of digital recording of biomedical signals, and I started to understand that the CD is not as perfect a medium as manufacturers always claimed. Digital recording introduces a number of anomalies. Digitalitis is caused by the relatively low sampling rate of CDs, such that high frequency signals are recorded with poor resolution. The Analoguer circuit described in this article corrects this harshness of CD sound by attenuating frequencies above 15kHz with a signal processing technique called windowing. It can also be used to “tame” edgy analogue recordings.
The major anomaly of the CD is introduced by the relatively low sampling frequency of 44 kHz. Although this sampling frequency allows us to record signals up to 22 kHz the upper frequencies are not very well presented. Figure 1 compares the sampling of a 2.5 kHz and of a 21 kHz waveform. After sampling of the original signals I connected the consecutive measurement-points by straight lines. The image-signal of the 1 kHz signals thus constructed equals the original signal pretty well.
The image of the 21 kHz signal, however, continuously varies in amplitude; it “wobbles”. This phenomenon can be seen with all the higher frequencies above 15 kHz and is an inherent property of the system. Although such high frequencies hardly can be heard by most people (myself, I don’t hear anything above 15.5 kHz) the continuously varying amplitudes in combination with non-linearities of our reproduction system and our ears introduce lower frequency by-products that might well be discernible.
In a recording session, before a digital image of an analog audio-signal (microphone-signal, analog master-tape, …) is made, all the frequency components above 22 kHz are electronically removed with a sharp low-pass filter – a so-called brick-wall filter. Without this filtering higher frequency signals would be represented as low frequency signals and “distort” the sound. Figure 2 shows the sampling of a 41.5 kHz waveform and how its resulting image represents a 2.5 kHz signal. This effect is called aliasing.
The removal of these high frequencies results in another anomaly of the CD. Figure 3a demonstrates how a square wave signal of 2 kHz is composed of an infinite series of sinus-waves with frequencies of 2, 6, 10, 14, 18, 22, 26 …. kHz.. However, if all the components above 22 kHz are removed, the resulting waveform is no longer square, but shows a high frequency ringing. In signal-analysis, it is called the Gibbs phenomenon.
This phenomenon might not be a major problem as long as a continuous signal is used, but the ringing also shows with short pulses, as demonstrated in figure 4. What you can see from the picture is, that in the image of the pulse there is already a signal present before the pulse actually starts and that there is also signal left after the end of the pulse. The so-called pulse response has deteriorated considerably.
To minimize wobbling and to improve the pulse response in many (biomedical as well as other) applications not a brick-wall filter (as with CD) is used but a filter that gradually attenuates the amplitude of the higher frequencies. The second part of figure 3 shows the image of the square wave after such filtering. Ringing in the image has almost disappeared. However, the price that is paid is a less sharp transition between the two discrete signal levels.
The technique of such frequency dependent attenuation of the input signals is called windowing and, with proper filter settings, is able to eliminate ringing completely. Unfortunately, with audio-signals sampled at 44 kHz (as with the CD) these windowing settings would require strong attenuation of the signals between 5 kHz and 15 kHz and thus would affect the treble most negatively.
However, by only reducing the frequencies above 15 kHz, wobbling and ringing can already strongly be reduced without effecting the signals inside the audio-band. This is what the digital filters of the CD-players by WADIA (and some of the systems of T+A and Sony) do in the digital domain and the Digital Antidote by Taddeo in the analogue domain. Both reduce the signals in the upper frequency-band in order to improve pulse-response.
Unfortunately, I don’t have the money to buy myself a WADIA (or better said, I’m not willing to spend so much on a CD-player) and at the time when I decided to attack digitalitis I didn’t know about the Digital Antidote yet. So I had to make my own solution.
In order to achieve this goal, I needed a relatively steep low-pass filter. Standard solutions can be found in every text-book on electronics but for audio-applications standard solutions have one major drawback; they change the phase at the higher frequencies and our ear is very sensitive to phase-changes (so I’m told). I therefore decided to build a filter that does not introduce any phase changes over the audio-band. Not surprisingly (as I found out later) the solution I came up with resembles that of the Digital Antidote (well, the wheel was also invented more than once). Only the technical implementation differs.
The higher frequencies are removed by adding a small frequency independent time-delay, Tdelay, to the audio signal and adding this delayed signal to the original input signal. After division by a factor of 2, we have the average of the input and the delayed signals. For low-frequency signals this small delay has little effect and the average (output) signal nearly equals the original input signal. For higher frequencies, however, the delayed and the original signals are no longer in phase and the amplitude of the average signal is much lower than that of the original input. This is demonstrated in figure 5.
It can be easily shown that the ratio of the amplitudes of the average (output) and of the input signal is given by:
- A(f) = cos ( pi*f*T
The amplification factor stays close to 1 over a long frequency range and next drops to zero relatively fast.
The total delay of the output signal (as referenced to the input signal) is Tdelay/2 and is frequency-independent. Thus no phase-shifts are present between the various frequency components in the output signal.
A block-diagram of the required circuit is shown in figure 6. First the input signal is buffered. Next the signal is time-delayed and in a third step both input and delayed signals are added (and buffered) by an adder.
The buffer and the adder are relatively easy to build using opamps. Standard solutions can be found in any textbook. However, since inverting adders are intrinsically more stable then non-inverting adders (one of the inputs of the opamp is directly connected to ground which minimizes problems with DC-drift) I decided to use both an inverting buffer and an inverting buffer. The output signal thus is non-inverted (figure 7).
Calculations showed that the delay-circuitry (called an “all-pass filter”) should be able to delay the input signal up to (approximately) 18 microseconds over the complete frequency band from 0 to 22 kHz. There exist solutions that achieve such a delay using a single opamp. The Digital Antidote (US Patent No. 5436882) for example uses such an approach.
These systems, so-called second-order, all-pass filters, use the intrinsic system-resonances at higher frequencies to broaden their bandwidth. To use resonances, however, in my understanding also implies an impairment of the pulse-response. I never did, however, a thorough analysis and testing of these circuits for my application.
I decided to use first order all-pass filters instead. These filters are only able to delay the signal up to 10 microseconds (over the band-width required) and therefore two of these circuitries have to be placed in series to achieve the required overall delay of 18 microseconds. The price that we have to pay is that two opamps are to be used instead of one.
A basic first order all-pass filter is shown in figure 8. Simple mathematics show that this filter has a gain factor:
- A(f) = ( R – 1/(2*pi*f*C ) / ( R + 1/(2*pi*f*C )
The absolute gain is 1 for all frequencies but there is a frequency-dependent phase shift that results in a constant time-delay at the lower frequencies of 2RC. Placing two equal filters in series the time shift Tdelay becomes 4RC.
By interchanging the resistor and the capacitor, each all-pass filter not only delays the signal but also inverts it. A signal inversion is unwanted, but this is automatically corrected using two filters in series. The advantage of interchanging these components is, that the non-inverting input of each opamp is DC-coupled to ground which (again) increases stability and minimizes problems with DC-shifts.
At frequencies far beyond the audio range, the phase shift of the delayed signal is maximally 360 degrees, which means that the input and the delayed signals are in-phase again. This implies that these very high frequencies are not attenuated by the system. However, although there are no audio signals in this range, most CD-players produce various high-frequency “noise”-components (quantisation noise, RF-interferences from the microprocessors in the system, etc.) that are not heard but still make life hard for our amplifiers. To eliminate these components I placed capacitors in parallel to the feedback resistors of both the buffer and the adder. This results in an additional second order low-pass filtering with a filter-frequency of 72 kHz, which is beyond the audio range, and therefore has no effect on the sound.
As for the exact delay time we have to compromise. A larger delay not only results in a stronger reduction of the anomalies but also in a stronger reduction of the bandwidth at the higher frequencies. A trade-off has to be made and the optimal value might well depend on your ears, your equipment, and your taste. I therefore decided to make the filter settings variable. The time delay can be changed with a switch that changes the resistances in the delay line. Five different settings are provided.
The complete schematics of the filter are shown in figures 9a and 9b. The opamps used are the LM6171 from National Semiconductor. By additionally connecting the output of each opamp via a resistance to one of the power-rails the output stage of each amp is forced into class A functionality. The power supply has a ground loop breaker, so the audio inputs and outputs MUST have floating grounds – their grounds cannot be directly connected to the enclosure. (See A Precision Preamplifier-Power Amplifier System with Natural Crossfeed Processing for more discussion about biasing opamps to function in class A and ground-breakers in power supplies).
The frequency characteristics of the various filter settings are shown in figure 10. Setting 1 only attenuates the very high frequencies and can be used to reduce the anomalies of systems with a high sampling rate (DVD-Audio or SACD). The other settings are meant for CD, DAT, minidisc, DCC, etc.
With little effort I was also able to incorporate a bass-enhancement similar to the one implemented in the headphone amplifier. It electronically increases the lower frequencies to compensate for the natural decrease of bass-response that every acoustic driver has. The frequency characteristics of the bass-enhancement are shown in figure 11.
The Analoguer is placed inside a sturdy aluminum case and only parts of premium quality are used (a PC board with a 70 micrometer copper-layer, 1% metal-film resistors, polystyrol and polycarbonate film capacitors, LM6171 opamps, torroidal transformer, heavy-duty silver-plated switches, gold-plated jackets, etc.).
The filter is pretty straighforward to make but note that quick and dirty solutions using cheap parts and a non-optimal mechanical construction (bread-board, no shielding) tend to degrade sound quality. The gains might well be counterbalanced by the losses.
Setting the Analoguer
The optimal settings for removal of the higher frequencies depends on various factors such as the listening environment, the characteristics of your loudspeakers and, above all, your personal upper limit of hearing (which may vary from 14 to 20 kHz). Therefore the filter function of the Analoguer can be adjusted by the filter switch.
The filtering effect at the first position is very weak and is specially intended for SACD and DVD-A. Due to a higher sampling frequency, the anomalies in these systems are less pronounced and require less reduction of the higher frequencies.
It is recommended that you start listening with the right switch in its middle position and leave it there for several hours of listening. The effect of the Analoguer is subtle, and few people will notice an immediate effect. However, after a few hours you will notice that listening has become more relaxed and less strenuous. If after a while you find some of the upper frequencies missing, reduce the filter action by one step and again spend several hours of listening before you make any further adjustments. If, on the other hand, you don’t notice the absence of upper frequencies, increase the filter action by one step. Again, please wait before making further adjustments. The effect of the Analoguer is most readily heard and felt with music that has a large share of overtones. The female voice, as well as violins, oboes, etc. are well suited for finding your personal optimal settings.
Some headphones and smaller loudspeakers have a restricted bass response. To compensate for this natural loss of the lower frequencies, the Analoguer can electronically enhance the bas signals. The bass-enhancement should be used with care. The lowest frequencies are amplified by 10 dB and the power that your amplifier must deliver increases accordingly. If your music starts to sound harsh, please switch off the bass-enhancement or reduce the sound level immediately. The bass-enhancement switch has five positions. In the first position the enhancement is switched off.
For loudspeakers, The benefits of bass-enhancement strongly depends on the type of loudspeaker. Some speakers, especially bass-reflex systems, have a fast roll-off at lower frequencies that can not be properly compensated for by the Analoguer. Loudspeakers with a closed cabinet tend to roll-off more gently and generally will benefit more from the bass-enhancement. Enhancement of the lower frequencies may also increase colourations and make the sound muddy. Always be aware that sonically less can be more. With bass-heavy music at high sound levels distortion can be produced that will damage your loudspeakers.
In a direct A-B comparison, using medium filter settings and bass-heavy music no evident differences can be discerned. However, using music with a substantial share of upper frequencies (soprano, hobo, upper strings) one notices that the sounds gets less brittle and that the harshness at the treble has gone. The sound simply becomes more relaxed. I’m now able to listen to music at a much louder sound-level than I did before without getting annoyed. This, for me, is the best proof that I’m cured from digitalitis and that is just what the filter is supposed to do. Sound has a more analogue quality (in the best sense of the word) and that’s why I called this device “Analoguer”.
I want to emphasize that the effect of the filter is very subtle. Most people probably will hear the effect more noticeably with their headphones since these are normally more revealing. It will not make a Wadia out of your Samsung CD-player or make your $ 200,- HiFi sound like something state-of-the-art. If you use cheap equipment I strongly advice you to spent your money elsewhere before you build this filter. If, however, you’re an audiophile and if you have high-resolution equipment, then you might well consider building this filter.
For people that are interested to build their own filter I’m offering a DIY-kit for approximately $260 US. I know that it is cheaper to buy all the electronic parts by yourself, but please note that for the money you have a professional PC board added (with soldering mask, tinned soldering eyes, and all the holes drilled) as well as the aluminum case with a 4 mm (!) front- and a 2 mm back-plate with all the holes milled. It also should be noted though that, in order to bring this project to a good end, you need at least to have some basic soldering experience and as well as proper tools (soldering iron with a 0.4 ~ 0.5 mm pencil tip). Although construction is rather straight-forward (a component plan is added), this project is not intended for real novices. If you doubt your own skills please contact the author for the possibilities to obtain a finished device.
As always, have fun.
c. 2002 Jan Meier.