How to generate a vector of a shifted impulse function?

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FW 2020-7-27

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评论： Star Strider 2020-7-27

Hello, Suppose we have a time vector x=0:0.1: 50. I would like to have a delta function at a non-zero position, say at 25 with unit height (or any other scaled version of it).

MATLAB has a function d = dirac(x)

It generates dirac at x=0. If we write, d=dirac(x-25), it does not shift the impulse function like the H=heaviside(t-25) translates the heaviside function at 25.

I tried differentiating the translated heaviside function but I get 0.5 0.5 at the desired location instead of 1 at 25, no matter what the sampling frequency is.

Is there are a better way to do

(a) Generate a vector unit delta at a non-zero position

(b) Differentiate translated Heaviside and get a shifted delta at the desired position.

Thanks.

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Star Strider 2020-7-27

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‘If we write, d=dirac(x-25), it does not shift the impulse function like the H=heaviside(t-25) translates the heaviside function at 25.’

It does, actually.

Consider:

x = 0:0.1:50;
d = dirac(x - 25);
nzdidx = find(d>0)                              % Index
dnzd = d(nzdidx)                                % Value

producing:

nzdidx =
   251
dnzd =
             Inf

So it will not appear on the plot, since it has infinite amplitude and 0 width, integrating to an area of 1.

Strider, I was trying to demonstrate the effect of convolution of a Lorentzian with a shifted delta to a person. I was stumped as to how one can generate a displaced delta vector in MATLAB. Thanks for your assistance. I have MATLAB 2019b. I can download 2020 but I don't think it is worth changing.