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Questions and Answers
What does the term $a_i$ represent in the expression $h(τ) = ∑ aᵢδ(τ - τᵢ)$?
What does the term $a_i$ represent in the expression $h(τ) = ∑ aᵢδ(τ - τᵢ)$?
- Values of $τ$ at which the delta function is centered
- The coefficients associated with each delta function (correct)
- A constant value unrelated to the summation
- The total number of terms in the summation
What role does the delta function $δ(τ - τ_i)$ play in the expression?
What role does the delta function $δ(τ - τ_i)$ play in the expression?
- To represent continuous data over $τ$
- To sum all the terms over a continuous range
- To exponentially decay values at certain points
- To provide a way to pick values at discrete points (correct)
If $τ_i$ are distinct values, what happens to $h(τ)$ as the number of terms in the summation increases?
If $τ_i$ are distinct values, what happens to $h(τ)$ as the number of terms in the summation increases?
- It converges to a uniform distribution
- It remains constant regardless of $τ$
- It will show an increasing density of points (correct)
- It becomes a piecewise function with more discontinuities
Which of the following statements is true about the expression $h(τ)$?
Which of the following statements is true about the expression $h(τ)$?
In which scenarios would the expression $h(τ)$ equal zero?
In which scenarios would the expression $h(τ)$ equal zero?
Flashcards
Impulse Train
Impulse Train
A mathematical function that represents a series of impulses, each with a specific weight and location on the time axis.
Dirac Delta Function
Dirac Delta Function
The individual impulses that make up the impulse train, each represented by a Dirac delta function.
Impulse Location
Impulse Location
The location of each impulse in the impulse train, represented by the variable 'τᵢ'.
Impulse Weight
Impulse Weight
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Impulse Train Function
Impulse Train Function
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Study Notes
Function h(τ)
- h(τ) is defined as a summation
- The summation is over all values of i
- Each term in the summation is a_iδ(τ - τᵢ)
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Description
Explore the function h(τ) defined as a summation over values of i. Understand each term in the summation, specifically how a_i and δ(τ - τᵢ) interact within the function. This quiz will test your comprehension of the concepts involved in this mathematical function.
