# Questions tagged [dirac-delta-impulse]

The Dirac delta impulse is a mathematical idealization which is used in the theory of DSP, e.g., for the description and analysis of sampling, impulse responses, Fourier transform of pure tones, etc.

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### Fourier Transform of impulse train proof in Julius O Smith's textbook

$\DeclareMathOperator{\sinc}{sinc}\DeclareMathOperator{\asinc}{asinc}$I'm trying to follow the proof of the Fourier Transform for an Impulse train given in Julius Smith's textbook. I come across the ...
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### Product of Doublet and Arbitrary Function

We know that the product of the delta function and another function samples the latter function. That is, $$\delta(t-\tau)f(t)=\delta(t-\tau)f(\tau)$$ Does the doublet function retain this same ...
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### How can I get rid of this unexpected minus sign on my inverse Fourier transform of two impulse functions?

I'm trying to find the inverse Fourier transform of two impulse functions, which correspond to the Fourier transform of the function $h(t)=A\sin(2πf_0t)$. The Fourier transform of the above sine ...
62k views

### What is the first derivative of Dirac delta function?

Could you please help me in a simple way, what is the first derivative of a Dirac delta function? I found this answer: The informal answer is a positive Delta function immediately followed by a ...
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### What is the Effect of Multiplying a Function by the Unit Impulse Function in the Frequency Domain?

I know about the the shifting property of the impulse function in the time domain as can be seen in equation $(1)$. $$\int_{-\infty}^{\infty} f(x)\delta(x - a)dx = f(a)\tag{1}$$ But what is the ...
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### Time scaling and shifting of delta function

Learning signals and systems. Solving time scaling and shifting problems. For the question $$x(t) = u(2t - 1)$$ First we shift by 1 to the right side and then we do time scaling , i.e divide by 2 ...
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### How is $\delta(at+b)=\frac{1}{|a|}\delta(t+b/a)$?

This result has been used in the second last line of the pic. I don't know why it's true. Both functions are zero for $t$ not equal to $-b/a$. But at $t=-b/a$, a scaling factor $1/|a|$ has been ... 721 views

### Confusion in deriving formula for fourier tansform of impulse train

I was trying to derive fourier transform for impulse train : I know how to solve for this using using properties of fourier transform. But now I wanted to use a brute force approach to it so I did ...
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### Inverse Fourier Transform Dirac impulse with scaled argument

Currently, I am dealing with the sampling problems and I don't understand how to calculate inverse Fourier transform of a scaling impulse function $\textrm{IFT}\{\delta(\Omega T)\} = ?$, $T$ is ...
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### Help regarding property of unit impulse function

We know that using properties of unit impulse function it can be shown that $$\int_{t_1}^{t_2} x(t) \delta^{(n)}(t-t_0) dt=(-1)^nx^{(n)}(t_0),\quad t_1<t_0<t_2$$ (source: Continuous and ...
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### Unit Impulse : Bounded or Unbounded?

As the title suggests, I have a confusion here. In a Systems text I am going through, it mentions of the Unit Impulse as an unbounded signal. Yes, the unit impulse "height" is unbounded, but the "...
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### Fourier transform of dirac comb with function: The scaling factor

Multiplication in the time domain corresponds to convolution in the frequency domain: $$f(t) \cdot x(t) \iff F(j \omega) * X( j \omega) \tag*{No scaling factor}$$ I know the fourier transform of ...