In signal processing, oversampling is the process of sampling a signal with a sampling
frequency significantly higher than the Nyquist rate.
Theoretically a bandwidth-limited signal can be perfectly reconstructed if sampled above
the Nyquist rate, which is twice the highest frequency in the signal.
Oversampling improves resolution, reduces noise and helps avoid aliasing and phase distortion
by relaxing anti-aliasing filter performance requirements.
A signal is said to be oversampled by a factor of N if it is sampled at N times the Nyquist
rate.
Motivation There are three main reasons for performing
oversampling: Anti-aliasing
Oversampling can make it easier to realize analog anti-aliasing filters.
Without oversampling, it is very difficult to implement filters with the sharp cutoff
necessary to maximize use of the available bandwidth without exceeding the Nyquist limit.
By increasing the bandwidth of the sampled signal, design constraints for the anti-aliasing
filter may be relaxed.
Once sampled, the signal can be digitally filtered and downsampled to the desired sampling
frequency.
In modern integrated circuit technology, digital filters are easier to implement than comparable
analog filters.
Resolution In practice, oversampling is implemented in
order to achieve cheaper higher-resolution A/D and D/A conversion.
For instance, to implement a 24-bit converter, it is sufficient to use a 20-bit converter
that can run at 256 times the target sampling rate.
Combining 256 consecutive 20-bit samples can increase the signal-to-noise ratio at the
voltage level by a factor of 16, adding 4 bits to the resolution and producing a single
sample with 24-bit resolution.
The number of samples required to get bits of additional data precision is
To get the mean sample scaled up to an integer with additional bits, the sum of samples is
divided by :
This averaging is only possible if the signal contains equally distributed noise which is
enough to be observed by the A/D converter.
If not, in the case of a stationary input signal, all samples would have the same value
and the resulting average would be identical to this value; so in this case, oversampling
would have made no improvement.
This is an interesting counter-intuitive example where adding some dithering noise to the input
signal can improve the final result because the dither noise allows oversampling to work
to improve resolution.
In many practical applications, a small increase in noise is well worth a substantial increase
in measurement resolution.
In practice, the dithering noise can often be placed outside the frequency range of interest
to the measurement, so that this noise can be subsequently filtered out in the digital
domain--resulting in a final measurement with both higher resolution and lower noise.
Noise If multiple samples are taken of the same
quantity with uncorrelated noise added to each sample, then averaging N samples reduces
the noise power by a factor of 1/N. If, for example, we oversample by a factor of 4, the
signal-to-noise ratio in terms of power improves by factor of 4 which corresponds to a factor
of 2 improvement in terms of voltage.
Certain kinds of A/D converters known as delta-sigma converters produce disproportionately more
quantization noise in the upper portion of their output spectrum.
By running these converters at some multiple of the target sampling rate, and low-pass
filtering the oversampled signal down to half the target sampling rate, a final result with
less noise can be obtained.
Delta-sigma converters use a technique called noise shaping to move the quantization noise
to the higher frequencies.
Example For example, consider a signal with a bandwidth
or highest frequency of B = 100 Hz.
The sampling theorem states that sampling frequency would have to be greater than 200
Hz.
Sampling at four times that rate requires a sampling frequency of 800 Hz.
This gives the anti-aliasing filter a transition band of 300 Hz − B = − 100 Hz = 300 Hz)
instead of 0 Hz if the sampling frequency was 200 Hz.
Achieving an anti-aliasing filter with 0 Hz transition band is unrealistic whereas an
anti-aliasing filter with a transition band of 300 Hz is not difficult to create.
Oversampling in reconstruction The term oversampling is also used to denote
a process used in the reconstruction phase of digital-to-analog conversion, in which
an intermediate high sampling rate is used between the digital input and the analogue
output.
Here, samples are interpolated in the digital domain to add additional samples in between,
thereby converting the data to a higher sample rate, which is a form of upsampling.
When the resulting higher-rate samples are converted to analog, a less complex/expensive
analog low pass filter is required to remove the high-frequency content, which will consist
of reflected images of the real signal created by the zero-order hold of the digital-to-analog
converter.
Essentially, this is a way to shift some of the complexity of the filtering into the digital
domain and achieves the same benefit as oversampling in analog-to-digital conversion.
See also Upsampling
Undersampling Oversampling and undersampling in data analysis
Oversampled binary image sensor Notes
References
Further reading John Watkinson.
The Art of Digital Audio.
ISBN 0-240-51320-7.