Rectangular Pulse Train and Sinc Function

1. What is rect and sinc?
2. What is a rectangular pulse signal?
3. What is the autocorrelation of a rectangular pulse?
4. What is the Fourier transform of a rectangular pulse?

What is rect and sinc?

The rect function has been introduced by Woodward in as an ideal cutout operator, together with the sinc function as an ideal interpolation operator, and their counter operations which are sampling (comb operator) and replicating (rep operator), respectively.

What is a rectangular pulse signal?

A signal that produces a rectangular shaped pulse with a width of τ (where 𝜏 = 1 for the unit rectangular function) centred at 𝑡 = 0 is known as rectangular signal. The rectangular signal pulse also has a height of 1. Mathematically, the unit rectangular signal is defined as, ∏(tτ)=1for|t|≤(τ2) 0otherwise.

What is the autocorrelation of a rectangular pulse?

Explanation: The auto-correlation function is the method of correlating the various instants of the signal with itself and that of a rectangular pulse of duration T is a triangular pulse of duration 2T.

What is the Fourier transform of a rectangular pulse?

The Fourier transform of the rectangular pulse is real and its spectrum, a sinc function, is unbounded. This is equivalent to an upsampled pulse-train of upsampling factor L.