$($Difficulty: $***)$ Consider the length $-N$ signal

$x[n]=cos(2\frac{L}{M}n)$

where $M$ and $L$ are integer parameter with $M=NLy[n]=x[(n-D)modN]Y[k]=x[k]||x|{|}_{2}NMx[k]0n$

Consider the circularly shifted signal $y[n]=x[(n-D)modN].In$ the Fourier domain, since the $DFT$ operator $is$ shift invariant, $itisY[k]=x[k].$

$In$ general, $it$ will $be$ easier $to$ compute the norm $of$ the signal $||x|{|}_{2}in$ the Fourier domain, using the Parseval's identity.

For every choice $ofN$ and $M,$ the $DFTx[k]$ has two elements different from zero$\mathrm{.}2L,$ the signal has exactly $L$ periods for $0n$

Consider the circularly shifted signal $y[n]=x[(n-D)modN].In$ the Fourier domain, since the $DFT$ operator $is$ shift invariant, $itisY[k]=x[k].$

$In$ general, $it$ will $be$ easier $to$ compute the norm $of$ the signal $||x|{|}_{2}in$ the Fourier domain, using the Parseval's identity.

For every choice $ofN$ and $M,$ the $DFTx[k]$ has two elements different from zero$\mathrm{.}0.$

Choose the correct statements among the choices below.

$IfM=N$ and $2L,$ the signal has exactly $L$ periods for $0n$

Consider the circularly shifted signal $y[n]=x[(n-D)modN].In$ the Fourier domain, since the $DFT$ operator $is$ shift invariant, $itisY[k]=x[k].$

$In$ general, $it$ will $be$ easier $to$ compute the norm $of$ the signal $||x|{|}_{2}in$ the Fourier domain, using the Parseval's identity.

For every choice $ofN$ and $M,$ the $DFTx[k]$ has two elements different from zero.