How can I plot an impulse (sech(x)) consisting of 2002 points, where last 1001 point are zeros?

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Anna_P
Anna_P 2025-6-24
评论： Mathieu NOE 2025-6-26
So, I've got 2 sech(x) impulses, 1-st consisting of 1001 points, and 2-nd, consisting of 2002 points. For the 2-nd one I need to set last (right) 1001 points as zeros. How can I do that?
Thank you!

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Mathieu NOE
Mathieu NOE 2025-6-24
Ran in:
hello
if you have a recent release (Since R2023b) you can use paddata : here we pad the four first non zero values (your first sech array) with here 2 zeroes
A = [1; 3; 5; 7];
B = paddata(A,6)
B = 6×1
1 3 5 7 0 0
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Sam Chak
Sam Chak 2025-6-24
Ran in:
Hi @Anna
Mathieu has shown you how to do that in MATLAB. This is the standard approach in MATLAB computing. However, if you are looking for a math function to include in your thesis or journal paper, you might consider solving the following puzzle:
What input to the hyperbolic secant function will yield when and output zero otherwise?
ub = 10; % upper bound
x = linspace(-ub, ub, 2001); % domain
figure(1)
plot(x, sech(x)), grid on
xlabel('x'), ylabel('sech(x)')
title('Standard Hyperbolic Secant function')
ylim([-0.2, 1.2])
From the plot, since we know that converges to zero at , or for , we can design an intermediate function for the input to the hyperbolic secant such that produces the desired output values within the domain. One approach is to use the signum function to create a step at such that for .
f = x + ub/2*sign(x) + ub/2;
y = sech(f);
figure(2)
subplot(211)
plot(x, f), grid on
xlabel('x'), ylabel('f(x)')
title('Intermediate function, f(x)')
subplot(212)
plot(x, y), grid on
xlabel('x'), ylabel('y')
title('Desired Output')
ylim([-0.2, 1.2])
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Sam Chak
Sam Chak 2025-6-25
Ran in:
Hi @Anna_P
@Mathieu NOE indeed has a point. My proposed approach does not give an absolute zero. If you require absolute zero for , then you should consider using this alternative approach, which also reflects my mathematical interpretation of the MATLAB indexing trick:
where is the Heaviside step function.
Note: You can imagine that acts like a lowpass filter but allows all signals pass for . For your info, "Lowpass" is an engineering term, typically used in E&E Engineering and Audio Engineering.
ub = 10; % upper bound
x = linspace(-ub, ub, 2001); % domain
f1 = 1 - heaviside(x); % function 1: Unit Step down
f2 = sech(x); % function 2: Hyperbolic Secant
y = f1.*f2;
subplot(211)
plot(x, f1), grid on
xlabel('x')
title('Unit Step down function (Heaviside)')
ylim([-0.2, 1.2])
subplot(212)
plot(x, y), grid on
xlabel('x')
title('Semi-Hyperbolic Secant function')
ylim([-0.2, 1.2])
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