How to generate a vector of a shifted impulse function?

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.

Answer 1

[Star Strider]

‘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.

.

[FW]

Thank you, no wonder I could not see it in a plot. How should we convert the infinity to 1 or any other scaled version of unity?

[Star Strider]

My pleasure!

Try this (following on my previous code):

d(nzdidx) = 1;

figure
stem(x, d, 'LineWidth',1)
grid

Note that this is no longer a true impulse function, although defining it with a width of 1 as well would at least satisfy the requirement that it integrates to 1.

.

[FW]

Thanks, I am wondering why Heaviside is not differentiating to a height of 1, instead I get 0.5 and 0.5 instead.

[Star Strider]

As always, my pleasure!

I am not certain what you are doing.

Try this:

syms x 
h = heaviside(x - 1)
dh = diff(h)

to get:

dh =
dirac(x - 1)

(I am using R2020a, although I doube that there would be any version differences.)

.

[FW]

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.

[Star Strider]

As always, my pleasure!

As for upgrading to R2020a, see the Release Notes to see if it would be of any benefit to you. (Note that Update 4 is current.)