Delta-sigma Modulation - Oversampling

Oversampling

Let's consider a signal at frequency and a sampling frequency of much higher than Nyquist rate (see fig. 5). ΔΣ modulation is based on the technique of oversampling to reduce the noise in the band of interest (green), which also avoids the use of high-precision analog circuits for the anti-aliasing filter. The quantization noise is the same both in a Nyquist converter (in yellow) and in an oversampling converter (in blue), but it is distributed over a larger spectrum. In ΔΣ-converters, noise is further reduced at low frequencies, which is the band where the signal of interest is, and it is increased at the higher frequencies, where it can be filtered. This technique is known as noise shaping.

For a first order delta sigma modulator, the noise is shaped by a filter with transfer function . Assuming that the sampling frequency, the quantization noise in the desired signal bandwidth can be approximated as:

.

Similarly for a second order delta sigma modulator, the noise is shaped by a filter with transfer function . The in-band quantization noise can be approximated as:

.

In general, for a -order ΔΣ-modulator, the variance of the in-band quantization noise:

.

When the sampling frequency is doubled, the signal to quantization noise is improved by for a -order ΔΣ-modulator. The higher the oversampling ratio, the higher the signal-to-noise ratio and the higher the resolution in bits.

Another key aspect given by oversampling is the speed/resolution tradeoff. In fact, the decimation filter put after the modulator not only filters the whole sampled signal in the band of interest (cutting the noise at higher frequencies), but also reduces the frequency of the signal increasing its resolution. This is obtained by a sort of averaging of the higher data rate bitstream.