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UPSAMPLING

The word "upsampling" was brought to the vocabulary of high-end digital audio by a few companies to describe a digital process that they suggest is unique, and requires a different term from one already in use, "oversampling". This has created confusion in the market, and generated sales for these companies because they were offering something "new".

So what is upsampling and how is it different from oversampling? To answer these questions it is important to understand the basics and evolution of digital audio. Please see figure 1.

Figure 1 (click on image to open larger view in a separate window)

Analog to digital conversion involves taking measurements of a signal’s amplitude and converting them to digital numbers. In any digital conversion, it is necessary to sample the analog waveform at twice the highest desired frequency. This basic rule is called the Nyquist Theorem and the sampling frequency is called the Nyquist Frequency. If one wants a frequency response of 20Hz - 20KHz, it is necessary to sample the analog waveform at least 40,000 times per second. In practice, 44.1KHz was chosen for compatibility with early video systems which were converted to digital audio use.

Mathematical Mirages
In the process of digital to analogue conversion, it is necessary to remove all frequencies above the highest desired frequency, in this case 20KHz. This is because the mathematics of digital signal processing creates higher-frequency multiples of the audible-range signal (from 0 - 22.050KHz). The first duplicate signal is cast into the range of 22.050KHz - 44.1KHz. There are additional duplicates, or "images" in each sequential 22.050KHz step above 44.1KHz. If these duplicates are not removed, they will interact with the desired range of 0Hz - 20KHz, creating intermodulation distortion. This non-musical distortion can be extremely unpleasant to listen to. It can also cause great harm to tweeters in loudspeakers, as they respond to ultrasonic signals.

Digital information appearing in the supersonic range from 22.050KHz - 44.1KHz is called an "image" because it is a duplicate of the lower, audible range. The part of a digital-to-analog converter that removes the image is called, appropriately enough, the "anti-imaging filter". It is also known as the "reconstruction filter".

Figure 2

As you can see in figure 2, the earliest CD players extracted data from the CD at a rate of 44.1KHz / 16 bits. This data was then sent directly to the digital-to-analog converter. As stated earlier, it is necessary to remove all frequencies above the desired (audible) frequency range. This was done with a very complex analog filter called a "brick wall". It simply chopped off all signals at 20 kHz, causing severe phase shift. Such a steep filter causes easily measurable – and horribly audible – destructive effects to the analog signal. This drastic filter was largely responsible for the harsh and irritating sound from early CD players.

Figure 3

In 1983 the first Phillips CD player was a 4x "oversampling" player. Around 1986, most other CD player manufacturers used oversampling techniques to ameliorate the negative effects of the brick wall analog filter (see figure 3). In oversampling, the digital data extracted from the CD at 44.1KHz is passed through a "digital filter", a device that performs a mathematical process on the data. In a 2-times oversampled system, the digital filter would be fed 44.1KHz data and it would output 88.2KHz data. In a 4-times oversampled system, the digital filter would be fed 44.1KHz data and it would output 176.4KHz data. This process is called "interpolation", which means to estimate the value of an intermediate point between two known data points on a curve. It effectively creates more data points to represent the analog waveform, although the new data points can not be exactly the same as if the waveform was originally sampled at 88.2KHz.

There is confusion in many consumers’ minds about the power of interpolation (upsampling or oversampling) to create data. It is not possible to create more accurate information than is already in the digitally sampled signal. Creating data points in between adjacent ones does not give a signal equivalent to an 88.2kHz or 96kHz digital recording, just as blowing up a photograph does not increase its detail.

The desired effect of oversampling is an alteration of the supersonic frequency spectrum. The first image, which occupied a range of 22,050Hz - 44,100Hz, has moved out to the range 66,150 - 88,200.

The 88.2KHz digital audio data is then sent to the digital-to-analog converter. After the conversion, the most significant benefit of oversampling becomes apparent. The very steep "brick wall" analog filter that was required to remove all frequencies above 20Khz is no longer required. A much gentler analog filter can be used, because only the frequencies above 44.1KHz (where the first image resides) must be removed. The filter will generate less phase shift and other negative effects on the analog signals in the 20KHz range. See figure 4 for a comparison of early CD player phase shift to current CD players.

Figure 4

Figure 5

Oversampling can be done at higher multiplication factors, and usually is (figure 5). It is common to find 4x, 8x, 16x and even higher amounts of oversampling, allowing successively gentler analog filters. Of course, the digital-to-analog converters themselves must be able to accurately handle the higher effective sampling rates. This puts limitations on the use of oversampling.

A very few companies use split or two-part filters. One filter does 2x oversampling, then another filter does 4 x oversampling. Some of those companies refer to this way of filtering the signal as an included "upsampler." This is the same as the two-stage and three-stage oversampling Theta does, without any extra links, boxes, and the additional jitter, noise, and expense these create.

Theta's Prime was a 2-stage oversampler; the "Generation" series and Basic III are 3-stage.

As stated previously, oversampling is a mathematical process applied to the digital audio data and is commonly called a "digital filter". This process can physically be done a number of different ways. In CD players, it is commonly done in an "IC" (integrated circuit) based digital filter. It may or may not be integrated with the digital-to-analog converter chip. It can also be done in a "DSP" or digital signal processor. (These are specialized computers that can be used for many different tasks, such as motion control, voice recognition and video processing.) Theta’s products most often rely on DSP processing, as, for one thing, it allows us to program DSPs with our own software; to create and refine our own processing algorithms. Most companies don’t do this, resorting to pre-programmed, "off the shelf" circuits.

Regardless of method, digital filters have many characteristics that determine quality.

Figure 6

So far, we have discussed CD players exclusively. What about the separate digital-to-analog converters so prevalent in high-end audio (figure 6)? Functionally, these do the same tasks as that already done inside a CD player, but often at a much higher quality.

The 44.1KHz / 16 bit data extracted from the disc is sent over a digital audio link, usually SPDIF (Sony / Phillips Digital Interface Format). The separate digital-to-analog converter takes in the digital audio data, performs some amount of oversampling (usually 4x to 16x) and then sends the data to the digital-to-analog converter devices themselves. The reconstruction filter is then applied to the analog signal, which is then output through a buffer.

Higher quality can be obtained from a separate digital-to-analog converter because of the benefits of isolating the CD transport mechanism and the sensitive clocking, processing and conversion sections. Of course, any quality differences are subject to parts quality and design / implementation. Just because the DAC is separate doesn't necessarily mean it is better.

(Surround processors usually handle the digital signal no better, and sometimes worse, than the average CD player. Surround processors' D/A conversion appears to aim at a lowest common denominator, using off-the-shelf chips for these critical transformations. There are exceptions, and of course Theta is among them, but they are rare.)

Figure 7

So what is upsampling then? Upsampling is a term some companies use to describe oversampling when it is done between the CD transport and the separate DAC (figure 6). Another implementation is to perform the 1x - 2x digital filter inside of the CD player, then send the 88.2KHz data across the digital link. Processing-wise and functionally, it is oversampling, although some "upsamplers" also perform a task called sample rate conversion (converting a 44.1KHz signal to 48KHz, for example). That task is usually used in professional audio and serves no useful purpose in consumer audio except for home recording.

It has been conjectured that some benefit might be had from sending a high sample rate over the SPDIF link, but no proof has been offered. The question naturally arises as to what benefit upsampling provides and at what cost. The answer is that it is simply a matter of the quality of the oversampler inside the separate digital-to-analog converter. If the oversampling digital filter in the separate "upsampler" is superior to the digital filter in the DAC, sonic benefits will be realized. The converse is also true: if the oversampling digital filter in the upsampler is of lower quality than in the separate DAC, a reduction in quality will occur.

In order to use a separate "upsampler", the DAC must be able to accept higher sampling rates than the standard 44.1KHz / 48KHz. Normally it would need to accept at least 96KHz.

The cost of some of the "upsamplers" in the market would leave one to question their value. One unit, which sells for $6,000, uses two Motorola 56002 processors for the oversampling filter. The Theta DS Pro Gen V which sells for $5,500 uses three Motorola 24-bit DSP processors (identical to the 56002, horsepower-wise) and contains a full differential balanced digital to analog conversion stage with discrete transistor based analog circuitry.

Any device inserted into the SPDIF link can affect the signal. The rationale of "oversampling"– and its limitations – have been addressed. But there is another way the signal can be affected. It is called jitter (figure 8). Jitter is a term used to describe timing errors in a digital system. It has various sonic attributes depending on the type of jitter, but generally speaking the less jitter the better the system will sound. This has been thoroughly described in the press. Devices designed specifically to remove jitter come from various companies, such as the Digital Time Lens from Genesis and the Timebase Linque Conditioner from Theta Digital. It would be undesirable for any device inserted in the SPDIF datastream to increase jitter.

A measurement of the $6,000 outboard Upsampler revealed the following:

Picoseconds of measured jitter

Figure 8

Source component: Theta Digital David II
Receiving component: Theta Digital Casa Nova
Jitter measured on pin 11 of industry-standard Crystal Semiconductor CS8414 (word clock)
Measured using a Stanford Research SR620 Universal Time Interval Counter with Hewlet-Packard 3 foot 10x probe. All connections AES/EBU.

Due to the large amount of jitter revealed, further testing was performed.

All of the above measurements were done again, using RCA coaxial type connections. The jitter measurement still increased slightly in most cases, but was not nearly as poor as with the AES/EBU connections. The waveform also appeared much cleaner on an oscilloscope.

Source component: Theta Digital Carmen
Receiving component: Theta Digital Casa Nova
Jitter measured on pin 11 of industry-standard Crystal Semiconductor CS8414 (word clock)
Measured using a Stanford Research SR620 Universal Time Interval Counter with Hewlet-Packard 3 foot 10x probe.
All connections SPDIF RCA coaxial

These measurements reveal poor to unacceptable jitter performance.

The device will improve a poor transport with a large amount of jitter but will degrade the performance of a superior transport.

SUMMARY
In systems with high quality digital components, "upsampling", especially in the sense of outboard, additional devices should be regarded with a great degree of caution.

It would appear to be beneficial to include the functions of the "upsampler" within the DAC unit, where it is normally referred to as oversampling, and achieves the same benefits without requiring additional and potentially deleterious links for the signal to pass through.

While an upsampling device may help a poor DAC with a poor filter, it will degrade the performance of a superior DAC. Even then, because of potential jitter introduced by the addition of extra digital links into the system, it is undoubtedly best to include oversampling functions in the DAC’s digital filter rather than an outboard filter.