Fixing Filtering Problems with 16x Oversampling

Earlier, filters were shown to remove the unwanted frequencies to prevent aliasing. With a 44.1 kHz sampling rate, and a desired perfect signal representation up to 20kHz, we have to have a filter that attenuates from 0dB (at 20kHz) to >90dB over a 2kHz range (half of 44.1 kHz is 22.05kHz - this is the largest frequency we can admit without aliasing.) This is possible for a filter, but one artifact of filter design is that a steep grade of attenuation is always accompanied by a phase shift in the signal frequencies in the cutoff frequency region. This phase shift starts as soon as the filtering slope becomes steep. The phase shift in the signal frequencies that lie just before the cut-off frequency and pass through the filter distorts the signal in a detectable way, since these frequencies are not being listened to in isolation, but with the rest of the signal. Making a filter that is acceptable is not the ideal solution, because it is not cheap, and because the components have to be precise. Analog components have properties that change as they age, making the filter unreliable with age.

An alternative is immediately obvious. If the range of frequencies over which the filter cut off the signal were increased, the phase shift would be less dramatic and would occur at undetectable levels. The filter could drift more with age without affecting the music quality, since the listener could not hear the upper end of the range, anyway. The filter can also be made more cheaply, since it would not have to have such a steep slope over its filtering range. So, the solution seems to be to sample the signal more often, allowing higher frequencies to be received accurately, and providing the ability to use a cheaper filter. Unfortunately, a higher sampling rate has two negative drawbacks, as mentioned earlier. Sampling more often means more data to store to represent the same signal. It also means having more data to process the retrieve the same signal. Therefore, an alternative method is sought.

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Last modified: Wed Nov 17 21:39:18 CST 1999