Aliasing is the inability to distinguish different continuous frequencies from sampled values. The identity above says that frequencies separated by an integer multiple of the sampling rate give identical samples of a complex Fourier mode. For real cosines, changing the sign of a frequency also gives the same waveform, explaining the -versus- example at rate . The Nyquist–Shannon sampling theorem prevents this ambiguity within its specified class of bandlimited functions. Before sampling, unwanted higher frequencies must be suppressed if they would violate that assumption; once two waveforms give the same samples, those samples cannot identify which was present.
Aliasing is a phenomenon that occurs in various fields, such as signal processing, computer graphics, and audio processing, when a signal is sampled or represented in a way that leads to misrepresentation or distortion of the original information. 1. **Signal Processing**: In the context of digital signal processing, aliasing occurs when a continuous signal is sampled at a rate that is insufficient to capture its full range of frequencies.
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