Equation for impulse train

1. What is impulse train function?
2. What is the Fourier transform of an impulse train?
3. What is periodic impulse train?
4. What is impulse train sampling?

What is impulse train function?

Impulse trains are trains of action potentials spaced over time, with varying time intervals between them. The brain thus includes a massively parallel impulse train generator and processor. Simultaneously generated impulse trains can have patterns that are a function of the activity of ensembles of neurons.

What is the Fourier transform of an impulse train?

Therefore, the Fourier transform of the periodic impulse train has an impulse at the frequency of each Fourier series component and the area of the impulse equals the Fourier series coefficient. ⇐⇒ X(f) = XT (f) × S(f).

What is periodic impulse 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)

What is impulse train sampling?

One type of sampling that satisfies the Sampling Theorem is called impulse-train sampling. This type of sampling is achieved by the use of a periodic impulse train multiplied by a continuous time signal, $ x(t) $.