QUESTION 5 (a) Describe the method of cyclic redundancy checking (CRC) for error detection. Illustrate the method by calculating the checksum for the data sequence 100 110 using the generating polynomial x 3 + x + 1. [8 Marks] (b) Prove that error patterns, represented by the polynomial E(x), which are multiples of the generating polynomial G(x) are undetected by the CRC [5 Marks] method (c) A commonly used method to improve signal-to-noise ratio at the receiver is to use a matched filter. For NRZ transmission, a useful implementation of a suitable matched filter is the "integrate and dump" detector With the aid of diagrams, explain the operation of such an "integrate and dump" matched filter for a signal using Bipolar NRZ coding. Your diagrams should include (i) the components of the receiver; typical output of the integrator component Your answer should also include a brief mathematical description of the [8 Marks] operation of the integrator stage. (ii) Do you consider such a matched filter would operate successfully in the face of non-Gaussian noise sometimes experienced in a telecommunications channel (e.g. impulse noise or crosstalk)? Explain [4 Marks] your answer carefully UFMFS7-15-3 Page 5 of 9