Detecting aliased frequency components in discrete Fourier transforms

In digital signal analysis, frequency components in a signal that are higher than the Nyquist sampling frequency will appear in the frequency spectrum at a lower (incorrect) frequency. This aliasing problem is a consequence of the properties of the Discrete Fourier Transform (DFT) and it is usually avoided by the use of anti-aliasing filters. These are low-pass analogue filters that block frequencies higher the Nyquist sampling frequency. This paper presents a method for detecting aliased components in a frequency spectrum when anti-aliasing filters are not in use. Essentially this is done by sampling the data at two or more different rates and comparing the resultant DFTs. Under certain conditions, this technique allows signals to be transformed into the frequency domain without the need for anti-aliasing filters that are not only expensive, but can introduce phase shifts into the data. It also has application when signals are over-sampled so that anti-aliasing filters may be implemented digitally.