Sampling and reconstruction of time-limited signals using sum-of-sincs kernel

We address the problem of sampling and reconstruction of time-limited signals. Finite-energy, time-limited signals can be represented using time-limited orthogonal Fourier basis functions, and a finite linear combination can approximate a signal with the assumption that most of the signal energy is concentrated in a certain frequency band. The expansion coefficients in this approximation are uniform samples of the frequency spectrum. As time-limited signals are not bandlimited, we propose the use of finite-duration sum-of-sincs sampling kernel, which annihilates the effect of aliasing at desired frequency locations with a suitable choice of the sampling frequency. This method does not require inner product operations for each coefficient in the expansion. An expression for the approximation error is derived. Experiments are performed on both simulated and natural time-limited signals and compared with widely used Shannon-Nyquist sampling and reconstruction method. The reconstruction error using the proposed method is smaller by 2 - 20 dB compared with the Shannon-Nyquist method.