MATLAB: I’m trying to integrate, but I get an “undefined function” error.

continuous time fourier seriesMATLABnumerical integration

This is my code:

syms ao an bn t
t = 0 : 0.1 : 2*pi;
x = sin(pi*t);
T = 2;
n = -10 : 1 : 10;
wo = (2*pi)/T;
ao = (1/T)*int(x, t)
an = (2/T)*int((x*cos(n*wo*t)), t)
bn = (2/T)*int((x*sin(n*wo*t)), t)
plot(ao, t, an, t, bn, t)
grid on
xaxis('t')
yaxis('x(t)')
Title('Coefficients of CTFS')

And this is the error I'm getting:

Best Answer

int does not accept numerical inputs, because it performs symbolic integration - so you have to define a numerical vector for t also - here t_num. This has to be the same size like an, and bn are to plot the results:

syms ao an bn t
x = sin(pi*t);
T = 2;
n = -10 : 1 : 10;
t_num = linspace(0,2*pi,numel(n));
wo = (2*pi)/T;
ao = (1/T)*int(x, 0, 2*pi)
an = (2/T)*int((x*cos(n*wo*t)), 0, 2*pi)
bn = (2/T)*int((x*sin(n*wo*t)), 0, 2*pi)
plot(ao, t_num, an, t_num, bn, t_num)
grid on
xlabel('t')
ylabel('x(t)')
title('Coefficients of CTFS')

Related Solutions

MATLAB: Can someone please help me to figure out whats wrong with the fourier series code

You need to do array multiplication here:

q1 = an*cos(n*wo*t)'
q2 = bn*sin(n*wo*t)'
q1 =
0
q2 =
- (2*sin(pi*conj(t)))/pi - (2*sin(3*pi*conj(t)))/(3*pi) - (2*sin(5*pi*conj(t)))/(5*pi)

Note the transpose (') operator. Since this is your assignment, I leave the rest to you.

However, using symsum is probably not the way you want to go, since that function is intended to provide analytic summations of symbolic expressions, not the sort of summation you’re doing here. The solution seems simpler than that to me.

MATLAB: Undefined function ‘int’ for input arguments of type ‘char’.

You have

syms n t ;

which is equivalent to

n = sym('n');
t = sym('t');

which make connections between those variables in the MATLAB workspace and symbolic variables with those names inside the symbolic engine.

You have

n=50;                      
t=linspace(-5,5,1000);

This breaks the connection between the variables in the MATLAB workspace and the variables in the symbolic engine, because you wrote over variables with the same names.

You have

     ao= (1/T).*(int('1',t,0,t));

You replaced t with a numeric variable, so this is

   int('1', NUMERIC_VECTOR, 0, NUMERIC_VECTOR)

None of the parameters are object-oriented objects, so the first parameter is used as the data type to search for a matching method. There is no method int for character vectors, so you get a failure.

If you had used

       ao= (1/T).*(int(sym('1'),t,0,t));

then since there was an object-oriented parameter, the int method for that object would be looked up and found, so symbolic int would be called. However, this case would be

int(SYMBOL, NUMERIC_VECTOR, 0, NUMERIC_VECTOR)

and symbolic int cannot have a numeric vector as it second argument.

So what you should have done is not re-used the variable 't' between the syms t and the t = linspace(...) . Use different variable names for the two, and use the appropriate variable names in the appropriate positions in the int() call.

If syms t was still in effect, then the call would be

int(CHARACTER_VECTOR, SYMBOL, 0, SYMBOL)

which would invoke symbolic int, which would automatically transform it to equivalent to

int(sym(CHARACTER_VECTOR), SYMBOL, 0, SYMBOL)

and do the integration. Perhaps

syms n t ;
n=50;                      
trange=linspace(-5,5,1000);          
T=max(trange);                       
wo=(2*pi)/T;                   
for k=1:n
    thist = trange(k);
    ao= (1/T).*(int('1',t,0,thist));
    an= (2/T).*(int('1*cos(n*wo*t)',t,0,thist))
    bn= (2/T).*(int('1*sin(n*wo*t)',t,0,thist))
    f(k) = ao+(an.*cos(k.*wo.*thist))+(bn.*sin(k.*wo.*thist));
end
figure(1);clf(1)
plot(t,f)
xlabel('Time')
ylabel('Amplitude')
title('Fourier sawtooth Trasnform')

Best Answer

Related Solutions

MATLAB: Can someone please help me to figure out whats wrong with the fourier series code

MATLAB: Undefined function ‘int’ for input arguments of type ‘char’.

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