In signal processing, oversampling is the process of sampling a signal at a sampling frequency significantly higher than the Nyquist rate. Theoretically, a bandwidth-limited signal can be perfectly reconstructed if sampled at the Nyquist rate or above it. The Nyquist rate is defined as twice the bandwidth of the signal. Oversampling is capable of improving resolution and signal-to-noise ratio, and can be helpful in avoiding 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: to improve anti-aliasing performance, to increase resolution and to reduce noise. 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 sampling system, 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, the digital filter associated with this downsampling is easier to implement than a comparable analog filter required by a non-oversampled system. Resolution In practice, oversampling is implemented in order to reduce cost and improve performance of an analog-to-digital converter (ADC) or digital-to-analog converter (DAC). When oversampling by a factor of N, the dynamic range also increases a factor of N because there are N times as many possible values for the sum. However, the signal-to-noise ratio (SNR) increases by , because summing up uncorrelated noise increases its amplitude by , while summing up a coherent signal increases its average by N. As a result, the SNR increases by . 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 SNR by a factor of 16, effectively 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 effective if the signal contains sufficient uncorrelated noise