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black_hole
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What does the square of a Dirac delta function look like? Is the approximate graph the same as that of the delta function?
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black_hole said:Is the approximate graph the same as that of the delta function?
black_hole said:What does the square of a Dirac delta function look like?
rbj said:often this question comes up in an electrical engineering class when one is faced with convolving an impulse [itex] \delta(t) [/itex] with another impulse. i.e. what would happen if you had a linear, time-invariant system with impulse response [itex] h(t) = \delta(t) [/itex] and you input to that system [itex] x(t) = \delta(t) [/itex]. obviously, the output should be [itex] y(t) = \delta(t) [/itex], but how do you get that from the convolution integral?
Mute said:Of course, this is a physicist's way of looking at the issue, so there are some gaps in the formality and rigor, and mathematicians should feel free to shore it up (or tear it down, as the case may be) with the appropriate rigor.
A Dirac delta function, also known as the Dirac delta distribution, is a mathematical function that represents a point mass or impulse at a specific point. It is often used to model a single event or a point source in physics and engineering.
A Dirac delta function is defined as a function that is zero everywhere except at a single point, where it is infinite. It is represented mathematically as δ(x) and has the following properties: δ(x) = 0 for all x ≠ 0 and ∫δ(x)dx = 1.
The Dirac delta function is often used in physics to simplify mathematical calculations and model physical phenomena such as point charges, impulses, and point masses. It also plays a crucial role in the theory of distributions and is used to define various mathematical concepts in quantum mechanics and signal processing.
No, a Dirac delta function cannot be graphed in the traditional sense as it represents a point mass and not a continuous function. However, it can be represented as a spike at the specific point where it is non-zero on a graph with a very high peak and zero width.
In engineering, the Dirac delta function is often used in signal processing to model impulses in a system. It is also used in control theory to represent the effect of a sudden change in a system, such as a step input. Additionally, it is used in circuit analysis to model ideal voltage and current sources.