New answers tagged fourier
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The standard (conventional) definition of DFT (1D or 2D) is not unitary.
See for example the 1D standard (conventional) DFT pair as:
$$ X[k] = \sum_{n=0}^{N-1} x[n] e^{-j \frac{2\pi}{N} n k } $$
and
$$ x[n] = \frac{1}{N} \sum_{k=0}^{N-1} X[k] e^{j \frac{2\pi}{N} k n} $$
DFT is not unitary due to the fact that the forward and backward transforms are not ...
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The product $x(t)y(t)$ of two periodic signals with fundamental periods $T_x$ and $T_y$ is not a periodic signal unless $T_x$ and $T_y$ are rational multiples of one another; that is, $T_x = aT_y$ where $a$ is a rational number. Thus, except when such a relationship holds, $x(t)y(t)$ does not have a Fourier series.
When $T_x$ is a rational multiple of $T_y$,...
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