fft of two functions multiplied together

Hi, I was wondering if anyone could help with a question i have. Im trying to find the value of two functions, say f and g but am trying to do so in fourier space, e.g FFT(f*g) but when i take Ifft the answer is not the same as f*g which i figured it should be, does anyone know why? I have included my test code. Thanks

N=128;
x=((0:N-1)/N)*2*pi;

 dx=2*pi/N;

 u=sin(x);
 v=cos(x);

 u_hat=fft(u);
 v_hat=fft(v);

 ans_hat=((u_hat).*(v_hat));

 ans=real(ifftn(ans_hat));

 compare=u.*v;

Answer 1

[Matt J]

but am trying to do so in fourier space, e.g FFT(f*g) but when i take Ifft the answer is not the same as f*g

In Fourier space, FFT(f*g) is equivalent to the cyclic convolution of FFT(f) and FFT(g). You haven't done any convolution, but simply the plain element-wise product.