Reconstruction using sinc

1. What is the role of sinc function in reconstruction of a signal from samples?
2. How do you reconstruct a sampled signal?
3. What is the sinc function used for?
4. How does sinc interpolation work?

What is the role of sinc function in reconstruction of a signal from samples?

From the above expression, we see that the perfect recovery of the continuous-time signal requires that we employ an infinite number of samples. More specifically, to recover the value of the signal at a time instant t, we center a sinc function at each sample and then add all such sinc functions.

How do you reconstruct a sampled signal?

The reconstruction process consists of replacing each sample by a sinc function, centered at the time of the sample and scaled by the sample value x(nT) times 2f_c/ f_s and adding all the functions so created. Suppose the signal is sampled at exactly Nyquist rate f_s= 2f_m, Then f_m= f_s/2 = f_s- f_m and F_m= 1/2 = 1- F_m.

What is the sinc function used for?

The normalized sinc function is the Fourier transform of the rectangular function with no scaling. It is used in the concept of reconstructing a continuous bandlimited signal from uniformly spaced samples of that signal.

How does sinc interpolation work?

The well known and commonly used digital signal processing method for discrete sinc-interpolation is 'zero padding'. It is implemented by padding the signal discrete Fourier transform (DFT) spectrum with an appropriate number of zeros and performing the inverse transformation of the padded spectrum.