Non-Uniform Fourier Transform: An Extension of Traditional Fourier Transform

In the signal processing domain, the Non-Uniform Fourier Transform represents an extension of the conventional Fourier Transform method. Its primary advantage lies in handling non-uniformly sampled data and computing spectral components at arbitrary frequency points. Unlike the standard FFT which requires equidistant sampling, the NUFFT algorithm utilizes interpolation schemes (such as Gaussian or Kaiser-Bessel kernels) to resample non-uniform data onto a regular grid, enabling more accurate frequency representation that better captures signal characteristics. This transform demonstrates particular effectiveness when processing nonlinear systems or non-stationary signals, as it accommodates irregular sampling patterns often encountered in real-world applications. Consequently, the Non-Uniform Fourier Transform finds widespread implementation in signal processing, image analysis, and audio processing domains, with common programming approaches involving precomputation of interpolation coefficients and optimized matrix-vector multiplications for computational efficiency.