Example[edit]
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 ((fs/2) − B = (800 Hz/2) − 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.
Reconstruction[edit]
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 analog output. Here, digital interpolation is used to add additional samples between recorded samples, thereby converting the data to a higher sample rate, a form of upsampling. When the resulting higher-rate samples are converted to analog, a less complex and less expensive analog reconstruction filter is required. Essentially, this is a way to shift some of the complexity of reconstruction from analog to the digital domain. Oversampling in the ADC can achieve some of the same benefits as using a higher sample rate at the DAC.