Interpolation by the FFT revisited-an experimental investigation

TLDR: The experiments show that, with no input windowing, the accuracy of interpolation is almost independent of sinusoidal wavelength very close to the Nyquist limit, and small-kernal convolution methods, such as linear interpolation and cubic convolution, perform badly at wavelengths anywhere near the Nyqvist limit.

Abstract: A numerical investigation into the accuracy of interpolation by, fast Fourier transform (FFT), using a sinusoidal test signal, is described. The method is precisely defined, including a previously unnoticed detail which makes a significant difference to the accuracy of the result. The experiments show that, with no input windowing, the accuracy of interpolation is almost independent of sinusoidal wavelength very close to the Nyquist limit. The resulting RMS error is inversely proportional to input sequence length and is very low for sequence lengths likely to be encountered in practice. As wavelength passes through the Nyquist limit, there is a sudden increase in error, as is expected from sampling theory. If the sequence ends are windowed by short, cosine half-bells, accuracy is further improved at longer wavelengths. In comparison, small-kernal convolution methods, such as linear interpolation and cubic convolution, perform badly at wavelengths anywhere near the Nyquist limit. >