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Royi
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Does Circular Convolution correspondCorrespond to Periodically Expanded Linear Convolution?

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Does Circular Convolution correspond to Periodically Expanded Linear Convolution?

I have a question whether circular convolution and periodically expanded linear convolution corresponds in following case or why it does not?

Think about a signal $x[t]$ and a signal $y[t]$ both of length $N$. We expand the singal $x[t]$ periodically to a signal $x'[t]=[x[t],x[t]]$ with length $2N$. We zeropadd the signal $y[t]$ to a signal $y'[t] = [y[t],0]$ to obtain the same length $2N$.

My question is does the circular convolution result $(x[t] \star y[t] )_{mod_N}$, correspond to the bins $[N...2N]$ in the linear convolution result $x'[t] * y'[t]$?

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