Recovering a signal after filtering A signal $x[n]$ is to be transmitted over a communication channel. The communication channel is described by an FIR filter of length $M$ such that the received signal
  is given by
  $$r[n]=\sum_{k=0}^{M-1} x[k]h[n-k]\text.$$
  
  The data are transmitted in blocks where each block contains N samples of a data
  stream $d[n]$, and in addition each transmitted block also contains a so-called cyclic
  prefix where the last values of the block are duplicated at the beginning of the
  block. Consider for example the first block of data ${d[0], d[1], . . . , d[N − 1]}$.
  
  The
  corresponding block to be transmitted with the cyclic prefix is
  ${x[n]}_{k=0}^{N+K-1}= {d[N − K], d[N − K + 1], . . . , d[N − 1], d[0], d[1], . . . , d[N − 1]}$
  $i.e. x[0] = d[N − K], x[1] = d[N − K + 1], . . ..$
  At the receiver end, the first $K$ values are discarded and the next $N$ values are saved in a buffer  ${y[n]}_{k=0}^{N+K-1}={r[K], r[K + 1], . . . , r[K + N − 1]}, i.e. y[0] = r[K], y[1] =r[K + 1], . . ..$
  a) Show that at the receiver end the original data stream d[n] can be recovered
  using the following algorithm if the cyclic prefix is sufficiently long.
  
  
  $Y [k] = FFT({y[n]})$
  $D'[k] = Y [k]/H[k]$
  $d'[n] = IFFT (D'[k])$
  
  
  Show all workings, and in particular determine the length $K$ of the cyclic prefix such
  that $d'[n] = d[n]$,$ n = 0, . . . , N − 1,$ and show exactly how $H[k]$ should be computed
  from $h[n]$.


To solve this question for the given info do we have to convert the sequence into odd and even sequence respectively and then arrive at the FFT or is there any alternative? I don't need the solution. A hint would be good to start.
don't need the solution. A hint would be good to start.


This is bog-standard cyclic-prefix OFDM, and that's really well-covered in literature.