In Figure P8.43, x[n] is a finite-length sequence of length 1024.The sequence R[k] is ob...

In Figure P8.43, x[n] is a finite-length sequence of length 1024.The sequence R[k] is obtained by taking the 1024-point DFT of x[n] and compressing the result by 2.

(a) Choose the most accurate statement for r[n], the 512-point inverse DFT of R[k]. Justify your choice in a few concise sentences.

(b) The sequence Y [k] is obtained by expanding R[k] by 2. Choose the most accurate statement for y[n], the 1024-point inverse DFT of Y [k]. Justify your choice in a few concise sentences.