A signal x[n] is sampled in discrete time as shown in Figure P7.46. hr[n] is an ideal
Chapter 7, Problem 7.46(choose chapter or problem)
A signal x[n] is sampled in discrete time as shown in Figure P7.46. hr[n] is an ideal lowpass filter with frequency response lwl < ~ ~ < lwl < 1T From eqs. (7.46) and (7.47), the filter output is expressible as x,[n] = k"!t;~ x[kN]h,[n- kN] = k'!toc x[kN]N;, si:~~(~ ~~~)where We = 2n"/N. Show that independent of whether the sequence x[n] is sampled above or below the Nyquist rate, Xr[mN] = x[mN], where m is any positive or negative integer.
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