I am studying Discrete Fourier Transform currently and I have a doubt in that. Consider two sequences {1,2,3,4} and {0,1,0,0}. When I convolve them linearly, I get this {0,1,2,3,4,0,0}. However, if I take the 4 pt DFTs of {1,2,3,4} and {0,1,0,0} and then multiply them, and after that if I take IDFT of the result, I get this {4, 1, 2, 3}.
$$DFT({1,2,3,4}) = {10, -2+2j, -2, -2-2j}$$ $$DFT({0,1,0,0}) = {1, -j, -1, j}$$
Element wise product = $${10, 2+2j, 2, 2-2j}$$ $$IDFT({10, 2+2j, 2, 2-2j}) = {4, 1, 2, 3}$$
I know that the output of linear convolution here would need atleast 7 elements and I am calculating the 4 pt. DFT/IDFT which of course would not be enough. But what inference should I take from this. The result of IDFT looks somewhat like circular convolution but it is not exactly the result that you would get even after circular convolution.