Fig 1: The top 2 graphs depict Fourier transforms of 2 different functions that produce the same results when sampled at a particular rate. The baseband function is sampled faster than its Nyquist rate, and the bandpass function is undersampled, effectively converting it to baseband. The lower graphs indicate how identical spectral results are created by the aliases of the sampling process.Plot of sample rates (y axis) versus the upper edge frequency (x axis) for a band of width 1; grays areas are combinations that are "allowed" in the sense that no two frequencies in the band alias to same frequency. The darker gray areas correspond to undersampling with the maximum value of n in the equations of this section.
When one undersamples a bandpass signal, the samples are indistinguishable from the samples of a low-frequency alias of the high-frequency signal. Such sampling is also known as bandpass sampling, harmonic sampling, IF sampling, and direct IF-to-digital conversion.[1]