näytteenottoteoreeman

The sampling theorem, known in Finnish as näytteenottoteoreema, is a fundamental principle in digital signal processing. It establishes the conditions under which a continuous-time signal can be perfectly reconstructed from its discrete samples. The theorem states that if a signal has a bandwidth of B Hertz, it can be represented without loss of information by its samples taken at a rate of at least 2B samples per second. This minimum sampling rate is known as the Nyquist rate.

If the sampling rate is below the Nyquist rate, a phenomenon called aliasing occurs. Aliasing causes higher frequencies in the original signal to be misrepresented as lower frequencies in the sampled signal, leading to distortion and an irreversible loss of information. Therefore, to avoid aliasing and ensure accurate reconstruction, the sampling frequency must be strictly greater than twice the highest frequency component present in the signal.

The practical implementation of the sampling theorem involves an anti-aliasing filter, which is an analog low-pass filter applied to the continuous-time signal before sampling. This filter removes any frequency components above half the sampling rate, ensuring that the subsequent sampling process adheres to the theorem's requirements. The näytteenottoteoreema is crucial for converting analog signals into digital formats for storage, transmission, and processing in numerous applications, including audio, video, and telecommunications.