Sinc interpolation

The Whittaker–Shannon interpolation formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real numbers.

1. How does sinc interpolation work?
2. What is interpolation in sampling?
3. What is sinc in math?
4. What is the formula for the perfect reconstruction interpolator?

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.

What is interpolation in sampling?

In the domain of digital signal processing, the term interpolation refers to the process of converting a sampled digital signal (such as a sampled audio signal) to that of a higher sampling rate (Upsampling) using various digital filtering techniques (for example, convolution with a frequency-limited impulse signal).

What is sinc in math?

The sinc function , also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms. The full name of the function is "sine cardinal," but it is commonly referred to by its abbreviation, "sinc." There are two definitions in common use.

What is the formula for the perfect reconstruction interpolator?

x(t)=∞∑n=−∞xs(n)sinc(t/Ts−n). This perfect reconstruction formula is known as the Whittaker-Shannon interpolation formula and is sometimes also called the cardinal series.