When Will ‘Oversampling and Decimation’ Work?

Normally, a signal contains some noise. This noise very often has the characteristic of Gaussian noise, more commonly known as white noise or thermal noise, recognized by the wide frequency spectrum and by the fact that the total energy is equally divided over the entire frequency range. In these cases, the method of ‘oversampling and decimation’ will work if the amplitude of the noise is sufficient to toggle the LSB of the ADC conversion.

In other cases, it might be necessary to add an artificial noise signal to the input signal. This method is referred to as dithering. The waveform of this noise may be Gaussian noise, but a periodical waveform will also work. What frequency this noise signal may have depends on the sampling frequency. A rule of thumb is: ”When adding m samples, the noise signals period may not exceed the period of m samples”. The amplitude of the noise may be at least 1 LSB. When adding artificial noise to a signal, it is important to remember that noise has a mean value of zero; insufficient oversampling therefore may cause an offset, as shown in the following figure.

Figure 1. Offset Caused by Insufficient Sampling

The stippled line illustrates the averaged value of the saw-tooth signal. The sampling shown in figure (a) above will cause a negative offset, while the sampling in (b) will cause a positive offset. In figure (c), the sampling is sufficient, and offset is avoided. To create an artificial noise signal, one of the AVR® counters can be used. Since the counter and the ADC are using the same clock source, this gives the possibility of synchronizing the noise and the sampling frequencies to avoid offset.