NAIM NDX - User Manual - page 4
Copyright Naim Audio 2010
Page 4 of 8
closely enough matched to the incoming data rate. To
cope with this eventuality we have also implemented, as a
backup, an asynchronous sample rate converter (ASRC)
that will accept any sample rate from 32kHz –10% to
192kHz +10%.
Oversampling and analogue filtering
When an analogue signal is converted to digital form it
is no longer continuously variable: it is now a discrete
representation of the original. This means that the signal
amplitude is only known at certain, regularly spaced
discrete time intervals determined by the sample rate.
For CD the sample rate is 44.1kHz (44,100 samples
per second) and therefore the time interval between
each sample is 22.7μs (microseconds). To recreate the
analogue signal, the DAC chip holds each sample value
until the next arrives, resulting in a staircase waveform
rather than the smooth, continuous original. An example
is shown below.
Looking at the staircase signal in the analogue time domain,
as below, it may not look too bad. But if we look instead at
the frequency spectrum of this signal (below right) we see
that instead of containing just the single frequency of the
original analogue signal, the staircase waveform contains
a lot more due to its sharp high frequency steps.
If the analogue signal is a 1kHz sine wave (below right),
then the frequency spectrum of the staircase equivalent will
also display a peak at 1kHz. But it additionally has peaks
at every multiple of the sample rate plus or minus 1kHz
(ie 47 and 49kHz, 95 and 97kHz, 143 and 145kHz, etc).
In order for the DAC output to be as close as possible to
the analogue original, these extra frequency components
have to be removed by filtering out everything above half
the sample rate. Then only those frequency components
that were present in the original signal are left.
This requires a very steep low-pass filter. Achieving
adequate performance using an analogue filter is
extremely difficult. It requires the use of costly, high-
precision components, and even then the filter
performance may change with temperature, loading, etc.
One way of relaxing the constraints on the analogue filter
is to increase the frequency space between the audible
band (up to 22.05kHz at 44.1kHz sample rate) and the
first of the unwanted frequency components. One popular
method of achieving this is called oversampling and is
described below. By oversampling we can use a relatively
simple analogue filter to remove the remaining high
frequency components that the DAC introduces
.
To increase the sample rate we have to insert additional
samples between the original samples. If we want to
double the sample rate then we need to insert one extra
sample between each two original samples, if we want to
quadruple the sample rate then we need to insert three
extra samples between each two original samples, and
so on. But what sample values do we put there? If we
oversample by a factor of two we could perform linear
interpolation, so that each additional sample has a value
half way between that of the original samples on either side
– but that simplistic approach will create a lot of unwanted
frequency components. In fact, linear interpolation is just
a very basic low-pass filter. We can do better than that!
1kHz sine wave (green trace) and the staircase equivalent
generated by a DAC chip (red trace). Sample rate is 48kHz
Spectral analysis of the original signal (green trace) and the
unprocessed DAC output (red trace).
Note that the peak in the green trace at 1kHz overlays an
equivalent peak in the red trace. Sample rate is 48kHz