Normalised Sinc Function

The normalised sinc function is a smooth oscillatory function that appears when you reconstruct a continuous signal from evenly spaced samples. The factor of π in the definition makes the zeros land exactly at every nonzero integer, which is especially convenient in digital signal processing because it matches the sampling grid. It works as an interpolation kernel because, under the sampling theorem, a band-limited signal can be rebuilt by summing shifted sinc functions weighted by the sample values.

Use this when you are modelling ideal band-limited interpolation, such as reconstructing a signal from samples in DSP, communications, or numerical signal analysis. It is also useful when analysing low-pass filters, Fourier transforms, and aliasing-related sampling results.

• Forgetting that this is the normalised form and using sin(x)/x instead of sin(πx)/(πx)
• Treating sinc(0) as undefined instead of using the limiting value 1
• Mixing up radians and degrees when evaluating the sine term