CONCLUSIONS

I have presented an efficient algorithm for interpolating irregularly sampled, one dimensional data. This algorithm can also be used to compute the discrete Fourier transform of irregularly sampled data. Examples show that, if the given data samples are not aliased and are of finite length, the algorithm gives satisfactory results. Two potential problems are not addressed in this paper. The first one is the truncation effects at the beginning and ending points of the interpolated signal. Because the signal is modeled with its Fourier series expansion, it behaves periodically. The ending point of one period of the signal is connected with the starting point of the next period. Any discontinuity at the juncture cannot be modeled by a finite number of frequencies. This problem results in interpolation errors near the beginning and ending points of the signal. This problem can be partially solved by padding free samples at the end of the signal to be interpolated. The second problem is related to noises and bad samples. To prevent isolated noisy samples from affecting far away interpolated samples, Hale (1980) suggested that a local interpolation operator should be used. The operator defined in equation (2) contains periodic functions; hence it is a global operator. It is not obvious how one can localize this operator. Nevertheless, the output of the algorithm is insensitive to random noises outside of the signal band.