Fourier Transform of e^jkt, not giving an answer

This is the code

syms t w K
S=exp(K*j*t)
F = fourier(S,t);
disp(F)

This is the output

F =fourier(exp(Y*t5*1i), t5, t)

It dose not seem to do anything at all for this one.

I was able to use it for sine and cosine, just not for exp()

Answer 1

[Walter Roberson]

The fourier transform of that function does not converge.

You need to take abs(t)

syms t w K
S=exp(K*j*abs(t))
F = fourier(S,t);
disp(char(F))

(K*2i)/(K^2 - t^2)

[Paul]

Hi Walter,

The transform variable should (probably) be w, not t.

Also, I'm surprised at the result. S only has a Fourier transform if Re(1j*K) < 0. I'm surprised that the SMT returned a solution absent that assumption (I'm not even sure that can be specified via assumptions.)

syms t w
S = exp(2*1j*abs(t))
F = fourier(S,w)
disp(char(F))  % no transform for K = 2

fourier(exp(abs(t)*2i), t, w)

Now that I think about it, I wonder if fourier has other cases where it makes an implicit assumption.

Answer 2

[Paul]

Need to specify that K is real. Also, if only using two arguments to fourier the second argument is the transform variable, so should be w. I prefer using the three argument form to be clear what the function variable is and what the transform variable is.

syms t w K real
S=exp(K*j*t)
F = fourier(S,t,w)
disp(char(F))

2*pi*dirac(K - w)

Answers still not rendering symbolic output @Tushal Desai