Meaning of Rect and Train of Rect Spectra

1. What is rect in Fourier transform?
2. What is rect and sinc?
3. What is a rectangular pulse signal?
4. What is a periodic pulse train?

What is rect in Fourier transform?

The rectangular function is a function that produces a rectangular-shaped pulse with a width of (where in the unit function) centered at t = 0. The rectangular function pulse also has a height of 1. Fourier transform.

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 a periodic pulse train?

A periodic impulse train consists of impulses (delta functions) uniformly spaced T₀ seconds apart. An application of a periodic impulse train is in the ideal sampling process. Using (3.28), an even periodic impulse train, as shown in Figure 3.21b, can be analytically expressed as follows: (3.31)