suggestion for the integrating the gaussian function

Can someone help me with how to integrate the following Gaussian function over x whose range is [0 16]. The problem occurs when I try to shift the signal over time t which ranges t = (-1000:2:1000)*1e^-9 and t0 = 100e-12;

bt = 2*exp(-0.5*((t-((2*x)/(2e^8)))/t0).^2)*attn

I tried with quad and trapezoid. I am getting errors related to numerical integration. Any help is appreciated.

thanks

[Sean de Wolski]

What errors? Please report the full text of the error message or any unexpected results.

[Neels]

thanks for the response. the following is my code, i am trying to mimic the propagation of light in optical fiber.x refers to the distance. I want the signal to attenuate gradually till the particular time x at the same time i want the signal to be shifted to mimic the delay in the propagation.

clc

clear all

global Po C m t0 taum dtau tunit tau vgroup alpham attn L N

% declared global to try with quad, but it was showing errors

Po= 4; % [mW] initial peak power of signal source

C = 0; % Chirping Parameter

m = 1; % Super Gaussian parameter (m=1 ==> Gaussian)

t0 = 100e-12; %[sec] 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; %

% fs = 1/(dtau*tunit);

at = sqrt(Po)*exp(-0.5*(1+i*C)*(tau/t0).^(2*m)) % Input field in the time domain

subplot(2,2,1);

plot(tau,at);

title('input wave');

for x=0:16

%bt = sqrt(Po)*exp(-0.5*((tau*x)/t0).^2)*attn

bt = sqrt(Po)*exp(-0.5*((t-((2*x)/vgroup))/t0).^2)*attn

subplot(2,2,2)

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

end

end

l=trapz(x,bt);

subplot(2,2,3);

plot(t,l,'-rx');

[anu chauhan]

also i am working with same problem kindly help me

Answer 1

[Daniel Shub]

I don't really understand the question. Your Gaussian function seems to depend on two variables (t and x). The t makes me think you want a 1D Gaussian. For the parameters you have given your sample rate on t is not high enough. If you plot bt, you just get a spike. Of course your parameters could be off since "1e^-9" and 2e^8 are not valid MATLAB syntax.

Once you figure out what you are trying to integrate and get your parameters correct, I would suggest

doc normcdf

or

 doc erf

to do the integration. I believe they are optimized for intgrating a Gaussian.

[Neels]

thanks for the response. the following is my code, i am trying to mimic the propagation of light in optical fiber.x refers to the distance. I want the signal to attenuate gradually till the particular time x at the same time i want the signal to be shifted to mimic the delay in the propagation.

clc

clear all

global Po C m t0 taum dtau tunit tau vgroup alpham attn L N

% declared global to try with quad, but it was showing errors

Po= 4; % [mW] initial peak power of signal source

C = 0; % Chirping Parameter

m = 1; % Super Gaussian parameter (m=1 ==> Gaussian)

t0 = 100e-12; %[sec] 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; %

% fs = 1/(dtau*tunit);

at = sqrt(Po)*exp(-0.5*(1+i*C)*(tau/t0).^(2*m)) % Input field in the time domain

subplot(2,2,1);

plot(tau,at);

title('input wave');

for x=0:16

%bt = sqrt(Po)*exp(-0.5*((tau*x)/t0).^2)*attn

bt = sqrt(Po)*exp(-0.5*((t-((2*x)/vgroup))/t0).^2)*attn

subplot(2,2,2)

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

end

end

l=trapz(x,bt);

subplot(2,2,3);

plot(t,l,'-rx');

[Daniel Shub]

Your code is still not valid. The variable t is undefined and there is an extra "end" statement. The for loop also does not do anything, since you keep over writing bt. The function trapz is going to have problems since x is a scalar (equal to 16). Try simplifying your code by deleting everything that is not part of the problem. For example, I am guessing everything up to the for loop (and possibly the for loop) could be deleted and the definition of bt could be redefined without the variables Po, vroup, t0 and atten.

[Neels]

yes mate,I agree with you. I was experimenting with the code the t should be tau. sorry for that. I am trying to shift the Gaussian pulse and attenuate it. I have trimmed the code below.

global Po C m t0 taum dtau tunit tau vgroup alpham attn L N

Po= 4; % [mW] initial peak power of signal source

C = 0; % Chirping Parameter

m = 1; % Super Gaussian parameter (m=1 ==> Gaussian)

t0 = 100e-12; %[sec] initial pulse width

vgroup= 2e8;

taum = 10000;

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

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

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

at = sqrt(Po)*exp(-0.5*(1+i*C)*(tau/t0).^(2*m))

subplot(2,2,1);

plot(tau,at);

title('input wave');

for x=0:16

bt = sqrt(Po)*exp(-0.5*((tau-((2*x)/vgroup))/t0).^2)*exp(3.84)

subplot(2,2,2)

end

l=trapz(x,bt);

subplot(2,2,3);

plot(t,l,'-rx');