The advantages and disadvantages of digital and analog output filters in Compact Disc players
by David Ranada
ADVERTISEMENTS for many of the latest Compact Disc players extol their use of "digital filters" rather than the supposedly passe analog variety used in earlier designs. Is this puffery to be believed? Well, yes and no. Digital output filtering in a CD player can be considered desirable, but not necessarily for the reasons many of the ads would have you believe. To understand this state of affairs requires knowing why CD players need filters at all.
One of the two fundamental processes of digital audio recording is called sampling, the other is quantization. Sampling is the capturing or freezing of the amplitude of the audio signal at regular, very closely spaced intervals. Quantization is the conversion of each sample into a number via an electronic measurement process. In the CD system a sample of each audio channel is taken every 22.6757 millionths of a second.
Correctly performed by a digital-audio recorder, sampling does not alter the original signal in any way.
Sampling does, however, add to the original audio signal a great deal of extraneous high-frequency energy.
Suppose you wanted to make a digital recording of a musical work with a wide frequency range. The green area in Figure 1 below represents the music and contains all audio frequencies up to 20,000 Hz. The red areas show what would be added to the original signal by the sampling process. The original signal is untainted by sampling, and since the added energy is all above 20,000 Hz, it is ultrasonic and inaudible. The whole green-plus-red spectrum is encoded by a digital tape recorder, survives the mass-duplication process, and appears as the digital-audio data signal on a Compact Disc pressing.
You might think that because the added high frequencies are totally ultrasonic they pose no threat to sound quality and can be let out of a CD player unattenuated. But there are two very important reasons why they must be removed. First, if the ultrasonic products pass through the rest of the audio system, they can inter-modulate with themselves and with the audio signal to create audible distortion. Second, "loud" (high-amplitude) ultrasonic signals can easily burn out the tweeters in the loudspeakers.
Accordingly, one of the last circuits a recorded audio signal must pass through before it appears at a CD player's output jacks is a sharp-cutoff high-frequency filter. And I do mean sharp. Compared with a typical well-designed infrasonic filter in an amplifier, which would have a rolloff rate of 12 to 18 dB per octave below 20 Hz, these high-cut CD output filters drop precipitously. In order to attenuate ultrasonics fully while preserving the entire audio range, the filters have roll-off rates ranging from about 60 dB to more than 100 dB per octave above 20,000 Hz. (Lexical aside: There is no single accepted term for these filters, even among engineers. They have been called "output-smoothing," "de-sampling," "reconstruction," "output-lowpass," and just plain "output" filters. The last term is the most general one and is therefore used here. Anti-aliasing filters, though similar in action, are different in function and are found only in digital-audio recorders, not playback units.)
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Sampling adds ultrasonic energy, as shown in the red areas of Figure 1, top. and the difference between the red pulses and the green wave form in Figure 2(a). bottom left. Digital filters remove ultra sonics by a process of interpolation, as in Figure 2(b). right.
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Output Filter Requirements
In order to maintain the audible integrity of the recorded 16-bit digital audio signal, a signal that in theory can have an absolutely flat frequency response and a 96-dB dynamic range, a CD player's output filters must have very high performance. Among the criteria suggested in engineering papers are: (1) stopband attenuation (the amount by which the ultrasonic information above 20,000 Hz is reduced) of at least 50 dB; (2) flat passband frequency response (design goals of better than ±0.1 dB from 0 to 20,000 Hz are often mentioned); and (3) distortion and noise below that contained in a perfectly recorded 16-bit signal (implying less than 0.001 percent distortion and a dynamic range of greater than 96 dB).
The traditional method of building an electronic filter is the "analog" way. In the old days-before digital computers and even before transistors--a sharp-cutoff filter was made out of just resistors, capacitors, and inductors (coils). Loudspeaker crossovers are still made this way. More modern analog filters, like those used in many CD players, use integrated-circuit operational amplifiers in special circuit configurations to replace the bulky and expensive inductors. Analog out put filters must operate on analog audio signals containing the extra ultrasonic energy, so they have to be placed just after the digital-to-analog converter (D/A or DAC) stage of a CD player, the section where the recorded numbers are reconverted into a continuously varying voltage.
Digital Filtering
The output-filtering requirements of a CD player can be met in another way, however, precisely because the audio signal is available as a series of numbers. Digital filters operate on the recorded numbers representing the audio signal; they are examples of special-purpose digital computers. A digital filter's output is a series of binary numbers with a precisely defined mathematical relationship to the numbers entering the filter's input.
Since both the input and output of a digital filter are numerical, the filter must be in the circuit before the D/A converter.
How does a computer filter an audio signal? That's fairly easy to explain with the aid of Figure 2. The sampling of a waveform (green) produces a regular series of pulses (red) at spaces determined by the sampling period. The difference in shape between the green trace and the red trace in Figure 2(a) is the extraneous ultrasonic information depicted in red back in Figure 1 (rule of thumb: the more angular a waveform appears, the greater its high-frequency content). In an analog-filter player, the output of the DAC will look like the red trace in Figure 2(a). To oversimplify it somewhat, an analog filter removes the ultrasonic information by connecting the tips of the pulses. The filter is designed to "move" slower than the pulses so that the output waveform gets smoothed out.
A digital filter, however, operates on the numbers representing the pulses in Figure 2(a) before they are sent to the DAC. The number series is sampled by the digital filter circuit at a rate two or four times the original digital-audio sampling rate. You'll recall that sampling involves freezing the signal at regular intervals.
But between the pulses in Figure 2(a) there is no signal to freeze. Therefore, a digital filter calculates from the original number series what the signal should be at those intermediate points. It removes the extraneous high-frequency information by interpolation, that is, by calculating and inserting additional pulses between the ones already encoded. The result, as in Figure 2(b), is a digital signal that more closely approximates the original analog signal.
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Figure top, shows how an analog filter rings after an impulse hits it,
whereas a digital filter, shown in the second photo, 3(b), rings both before
and after the same impulse. The difference between the two types of filters
is less notice able with the 1-kHz square wave in the bottom two photos.
The upper one, Figure 4(a), shows an analog filter; the lower one, Figure 4(b). a digital filter.
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But doesn't this "resampling" or "oversampling" itself add high-frequency energy? After all, the wave form is still a series of pulses, albeit more closely spaced ones. That's exactly right. What a digital filter does is to reduce the amount of ultrasonic information immediately above the audio band while increasing the amount of ultrasonics in other locations above the band. When a digitally filtered, resampled signal is fed to a DAC, the converter's output must still undergo some analog filtering. But this filtering need not have as steep a rolloff as the digital filter (or an analog-only output filter) because there is now less ultrasonic energy to filter out between 20,000 and 44,100 Hz. A simpler 18- or 36-dB-per-octave analog filter can be used in the final stage.
Analog vs. Digital
So it seems that using a digital filter still requires using an analog filter for the final output stage; two filters are required where one will actually do. What, then, are the advantages of digital filters that make them a desirable feature in a CD player? There are several important advantages, mostly stemming from the monolithic character of a digital filter, which consists of a single integrated-circuit chip, as opposed to the dozen or more interconnected parts required in an analog filter.
First of all, it's easier for manufacturers to obtain high-quality performance from a digital filter than from an analog one. Analog output filters require closely matched, high-quality, precisely assembled components to achieve a flat audio-frequency response with low distortion and noise. But a digital filter will work "perfectly" if it works at all. Its characteristics depend solely on the set of calculations it is designed to per form and the degree of numerical precision with which they are executed (the "quality" of these attributes can vary from design to design). Moreover, those characteristics will not change with time or temperature, since changing them would require altering the circuits in the semiconductor chip itself. This makes digital filters more reliable than analog ones, any of whose parts can eventually fail, taking the filter with it.
Digital filters are not a panacea, however. Because they do their calculations at very high speed, digital output filters can consume much more power than analog filters, possibly restricting their use in portable CD applications. But their primary disadvantage is that they have to be used with very fast digital-to-analog converters. Since the effective sampling rate is doubled or quadrupled by a digital filter, the DAC must operate at two or four times normal speed, which also requires more power. And since high-quality 16-bit converters are hard to make to begin with, fast 16-bit DAC's tend to be relatively expensive parts. On the other hand, that expense can be offset because the dig ital filters themselves can be made inexpensively, like most digital IC's, and they can even be incorporated within the structure of other CD-player chips. We may thus see digital filters used in even low-priced CD players because of their manufacturing advantages.
Phase Response
The most highly touted advantage of digital output filters is not their consistency, cheapness, or reliability, however, but their linear phase response, referring to the amount of time signals of different frequencies take to pass through the filter. If all audio frequencies take precisely the same time to pass through a filter, it has linear phase response.
Analog CD-player output filters are minimum-phase filters, meaning that they have the least amount of phase nonlinearity necessary to obtain the desired steep rolloff characteristic with an analog circuit. To attenuate ultrasonic frequencies requires delaying the high audio frequencies (ultrasonics are delayed "forever," which is how they get filtered out). High audio frequencies emerge later than low-frequency signals fed to the filter at the same time. When playing back an impulse-which contains all audible frequencies in perfect phase alignment-an analog filter will "ring" as the high frequencies near 20,000 Hz come out "late." The effect is shown in Figure 3(a); The input pulse shown below the filter's output represents a one-sample-on/all-others-off signal found on CD test records.
Digital filters ring also, but they do so in an interesting way, as shown in Figure 3(b). Digital-filter impulse responses are often considered "superior" to an analog filter's response since they appear to be more like the "original" impulse. There are three problems with this interpretation. First of all, the input pulse is not a realistic digital-audio signal, being an artificial test signal generated by computer and recorded directly onto a digital CD master tape. No real-world audio signal that has to go through the analog inputs of a digital recorder will ever result in a one-sample impulse on a CD.
Secondly, the ringing from a digital audio filter is unnatural-it starts too early. It's as if the filter knows what's coming before it gets there-which, in effect, is exactly what is happening during the filter's calculations. You've got a choice between a "causal" analog filter that rings after the impulse arrives and a "non-causal" digital filter with an output that starts ringing even before the impulse gets there.
Finally, use of an impulse signal exaggerates the differences between the filters' waveform responses. Using a slightly more relevant computer-generated 1,000 Hz square wave, as in Figure 4, shows a greater similarity between the two filters' outputs: they both ring.
The upshot of all this is that it has yet to be conclusively demonstrated that any of the differences in high-frequency phase response between analog and digital output filters are audible, audiophile opinions not withstanding. Carefully conducted tests reported in the Journal of the Audio Engineering Society show that listeners cannot detect the operation of either type of filter when impulses are being reproduced, even when several of the filters are connected in series! Earlier experiments showed that listeners could not detect the presence of steep-cutoff analog filters when the cutoff frequency is as high as 20,000 Hz, as in CD players.
And psychoacoustic tests have long established that humans are far less sensitive to high-frequency phase shifts than to low-frequency ones. Even human hearing acuity rolls off dramatically above 15,000 Hz, making the phase response at 20,000 Hz still less important.
What is important, and can be audible, are the slight ripples in audio-frequency response that both types of filter can produce. It is to make these effects apparent that STEREO REVIEW publishes high-resolution frequency-response curves in CD-player test reports rather than impulse-response photos. Whether a player uses analog or digital filters should be less important in choosing a player than its other characteristics. But if two players have identical features and error-correction/tracking ability, you can confidently prefer the one with the digital filters, especially if it has a flatter frequency response and adequate ultrasonic attenuation. It probably won't sound better (or worse) because of the digital filters, but the digital filters should be more reliable in the long run.
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Also see: The New Compact Disc Players (Jul. 1985)
Turntable Drive Systems (Jan. 1985)
Source: Stereo Review (USA magazine)