Consider the signal aet with the Fourier transform X ju Cons

Consider the signal ae(t) with the Fourier transform X (ju): Consider the signal tc(t) with the Fourier transform Xc(jw We 0, else.

Solution

According to sampling theorem, we can completely recover the signal from its samples only when sampling period is less than or equal to nyquist period.

(iv) T=T_Nyquist

This condition satisfies the sampling theorem, so we can recover x_c(t) compltely from x[n].

(vi) T=2T_Nyquist means T>T_Nyquist

This condition not satisfies the sampling theorem, so we cannot recover x_c(t) compltely from x[n].

(vii)  T=(T_Nyquist)/2 means T<T_Nyquist

This condition satisfies the sampling theorem, so we can recover x_c(t) compltely from x[n].