Author_Institution :
Dept. of Electr. Eng., New South Wales Univ., Canberra, ACT, Australia
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
Keywords :
fast Fourier transforms; interpolation; FFT; Nyquist limit; RMS error; fast Fourier transform; input sequence length; interpolation; sampling theory; sinusoidal test signal; sinusoidal wavelength; Concurrent computing; Convolution; Digital filters; Digital signal processing; Discrete Fourier transforms; Fast Fourier transforms; Frequency; Interpolation; Sampling methods; Testing;