shifting a gaussian pulse

I wish to shift(delay) a Gaussian pulse in time domain, plot the delayed signal and its Fourier transform over a particular length x(0:16). generally if we have a signal f(t) we shift the signal using f(t-k). For the following Gaussian pulse i tried the same but i get an error. Each contribution is appreciated

clc clear all

Po= 4; % [mW] initial peak power

C = 0; % Chirping Parameter

m = 1; % Super Gaussian parameter

t0 = 100e-12; %initial pulse width

vgroup= 2e8;

alpham=0.24;

attn=0.24;

taum = 10000;

dtau = 2*taum/2^12; %1.953

tunit= 1e-12; % make time unit in psec

tau = (-1000:dtau:(taum-dtau))*tunit;

x=0:16;

bt = sqrt(Po)*exp(-0.5*(1+1i*C)*((tau./t0-(2.*x./vgroup)).^2)).*exp(0.24.*x)% my shifted format

subplot(2,1,1)

plot(tau,bt,'-rx');

l=trapz(x,bt);

subplot(2,1,2);

plot(x,l,'-rx');

I get the following error

??? Error using ==> rdivide Matrix dimensions must agree.

Error in ==> shift at 28 bt = sqrt(Po)*exp(-0.5*(1+1i*C)*((tau./t0-(2.*x./vgroup)).^2)).*exp(0.24.*x)% my shifted format

Answer 1

[David Young]

tau has 2252 elements but x has 17 elements, so you can't build expressions that try to combine them with elementwise operations. If you give x a scalar value, the computation succeeds (though the call to trapz fails).

Can you explain what you're aiming to do with x?

[Neels]

Actually i am trying to model the propagation of Gaussian pulse through an optical fiber. if we assume the Gaussian pulse f(t), after traveling a short distance the pulse gets delayed by a factor (2*x/group_velocity). Then finally i integrate the Gaussian pulse over the entire length of the fiber 0 to 16. i have my length as 16 because

l= t*group velocity = 80ns * 2*10^8 =16