- #1

mm391

- 66

- 0

δ(t-1)

Can you also explain what the function represents?

Thanks

mm

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In summary, The function δ(t-1) represents an impulse at t=1, which has a rectangular pulse of area 1, with a very narrow width approaching 0.00 nanoseconds and a correspondingly high height approaching infinity. This function is useful for testing the impulse response of real-world systems. When computing the Laplace of the Dirac delta function, it is important to know that the integral of the function from 0 to t is equal to the value of the function at t.

- #1

mm391

- 66

- 0

δ(t-1)

Can you also explain what the function represents?

Thanks

mm

Engineering news on Phys.org

- #2

NascentOxygen

Staff Emeritus

Science Advisor

- 9,242

- 1,074

it represents a rectangular pulse of area = 1

the width of the impulse is very narrow, approaching 0.00 nanoseconds

which means its height is correspondingly high, tending to infinity.

In practice, a realistic approximation to the delta function is plenty good enough for testing the impulse response of real-world systems.

Sorry, I can't relate it to Laplace, I have forgotten the topic through disuse.

Try searching google.

- #3

Engineer_Phil

- 27

- 0

∫[f(t)*δ(t-ε)]dt from {0 to t} = f(ε) because δ(t-ε) = 0 everywhere except ε and ∫(δ) from {0 to ∞} =1.

The Laplace Transform is a mathematical operation that converts a function of time into a function of a complex variable. In Systems Control and Analysis, it is used to transform differential equations into algebraic equations, making it easier to analyze and control the behavior of a system.

The Laplace Transform allows for the analysis of complex systems with multiple inputs and outputs. It also simplifies the process of solving differential equations and evaluating stability and performance of a system.

Yes, Laplace Transform can be used for both continuous and discrete systems. For continuous systems, the Laplace Transform is represented by an integral, while for discrete systems it is represented by a summation.

Laplace Transform is closely related to frequency domain analysis. By taking the inverse Laplace Transform, the time-domain function can be converted back to the frequency domain, allowing for the analysis of a system's behavior at different frequencies.

While both Laplace Transform and Fourier Transform are used to convert functions between the time and frequency domains, the Laplace Transform also takes into account the initial conditions of a system. It is also more suitable for solving differential equations, while Fourier Transform is more commonly used for periodic signals.

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