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Upsampling vs. Oversampling for Digital Audio - page 2

By Nauman Uppal

Jitter

Jitter is basically a timing error that is caused by inaccuracies of a system clock relative to the data stream. In an ADC for example, jitter will cause the sampling of the analog waveform either too early or too late relative to the previous sample. This error will cause the sample's level to be incorrect. Logically, a signal that is high frequency and high amplitude will be more likely to be affected by jitter than one that is lower frequency and smaller amplitude. One major claim that the proponents of upsampling, or sample rate conversion claim is reduction of the effects of this jitter. It is very important to note that the increase in rate itself is not responsible for the reduction in jitter. In fact, the jitter that is caused by the inaccurate ADC clock can not be removed completely since it is already present in our digital samples. However by upsampling to another rate and using a clock that is asynchronous to our original, the incorrectly sampled data can be somewhat corrected. Basically what we achieve is a 'spreading out' of the effects caused by sampling jitter over a wider spectrum. Jitter appears in our system by increasing the noise floor on our audio spectrum. By going through this rate increase, we basically spread out this jitter over more samples, interpolate, and then filter once again. One popular ASIC that does such a function is the AD1896 produced by Analog Devices. Another important point to note is that if not implemented correctly, this whole process of upsampling can actually yield poorer results. Also, with the use of an accurate clock relative to our input data's frequency, we can greatly reduce the effects of jitter at the head end. The amount of jitter that is really audible is something that is debated religiously and the psychoacoustics behind that is beyond the scope of this.

Oversampling DACs and Bits
Oversampling is widely used in the DAC. The effects of oversampling at the DAC are advantageous to the design of the analog reconstruction filter that must be built, as we have seen previously. By having a high sample rate out of our DAC we can use a very simple, gentle analog filter to reconstruct our analog filter. This is important since we will be able to design an analog filter that is not only cheap hardware wise, but also has a nice linear phase response over the passband.

Another reason for oversampling is to reduce the effects of quantization noise. By oversampling, we can spread any quantization noise over a larger bandwidth while keeping our signal of interest in the same band. Our filter will serve to cut out the out-of-band quantization noise while keeping our original signal and thereby increasing our SNR. For each factor of four that we oversample by, we gain 6dB of noise lowering. 6dB represents approximately one bit of information. By oversampling, we can theoretically drop one bit for every 4x increase in sample rate.

The question of number of bits is another thing to consider. Does carrying extra bits increase the amount of information in our signal? Unfortunately, once we have sampled our signal, nothing can be done to increase the amount of information we have to work with. What carrying more bits does is that it prevents the loss of information. DSP algorithms and filters require additions, multiplications, and other math functions. If we are able to carry more bits in the results of these operations, we lose less information by chopping off fewer bits. Every truncation of a result will add noise to our signal. But now we can see that by balancing the number of bits we carry in our computations and by the amount we oversample, we can reduce the effect of this truncation in word length. One thing to note is that many products claim 24-bit word lengths, but yet only process internally at 20 bits.

What Does This All Mean - Will it Sound Better?
So the question remains whether upsampling or oversampling actually make music sound 'better'. How much do we need? We have seen the main motivation behind oversampling and how it allows us to use simpler digital and analog filters as well as helping us with quantization noise. The effects of upsampling are greatly debated. While it is true that upsampling does help us in attenuating the amount of jitter caused by sampling errors and an inaccurate clock, whether this jitter is audible or not is a point of contention. There is no doubt that wide bit words and super-high sampling rates that are touted by the latest products are largely marketing. Oversampling has been around for a very long time and has been used extensively in audio products to not only improve sound quality through 'better' filtering but to make these same products much cheaper. Upsampling, on the other hand, is relatively newer and debated greatly. The effects of upsampling are no doubt overstated. By carefully designing the sampler, ADC, digital processing path, and oversampling DAC, the upsampling and asynchronous rate transfer can, in my opinion, be avoided.

The Purists Point of View
There are basically two points of view regarding this upsampling an oversampling. The audio 'purists' want no additional processing on their signal and want whatever comes in from the source to come out as analog. They talk about zero oversampling DACs and such that are completely filter free both in the analog and digital domain. That is one extreme that some may argue is the purest since it avoids any digital artifacts and it's quality relies on human perception by arguing that the human ear in itself acts as a brickwall filter after 20 kHz. Whenever we get into debates of human perception, the math and theory go out the window. Does it sound better without all the digital processing and filtering even with the image of the signal sitting just past fs/2? The energy past 22.05kHz is still present and you are still sending it to the speaker's tweeter. How will the tweeter react to such out-of-band frequencies that are present? Furthermore, sending such a signal that is not limited in bandwidth could cause stability problems with wide-bandwidth amplifiers that have a high unity-gain crossing. The overall system's signal-to-noise- ratio will be adversely affected as well. The DAC will also introduce frequency spurs all over the place. If we don't filter them at all, what will their presence do to the sound? It's a complicated problem and such a minimalist approach could introduce more non-linearities and negative effects, more so than the digital processing ever would.

About the Author
Nauman Uppal received his Bachelors Degree in Electrical Engineering from the University of Maryland College Park in 1998 and went on to complete a Masters Degree in 2000 at the University of Maryland. His focus in graduate school was in communications and signal processing. Naumans work experience includes 2.5 years working as an ASIC designer for PMC-Sierra plus some work for Nortel Networks while he was in school. He has held his current position for 1.5 years and is working on designing digital communication systems using FPGAs. Click here more info on Nauman's background.

 

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