The course webpage contains links to the syllabus, past tripos questions, lecture notes and the learning guide.

Please make sure that your work reaches my inbox at least 24 hours before the supervision, either by email or paper-based via the post box outside Student Administration in the William Gates Building.

## First Supervision [70]

1. 2003 Paper 8 Question 10 [20]
2. 2004 Paper 7 Question 8 Part (a) [12]
3. 2004 Paper 8 Question 10 Parts (a) and (b) [15]
4. 2005 Paper 8 Question 10 Part (a) [5]
5. 2006 Paper 7 Question 8 Parts (a), (b) and (d) [12]
6. Derive Fano’s Inequality. [6]

## Second Supervision [70]

1. 2002 Paper 9 Question 10 Part (b) [12]
2. 2005 Paper 7 Question 8 Parts (b) and (c) [7]
3. 2005 Paper 8 Question 10 Part (c): prove (i), do (ii) and explain (iii) [9]
4. 2006 Paper 8 Question 16 Parts (c) and (d) [9]
5. 2007 Paper 7 Question 8 Parts (b) and (c) [7]
6. 2008 Paper 9 Question 10 Part (b) + show that they are self-Fourier [8]
7. 2009 Paper 9 Question 9 Part (c) [5]
8. Show how to derive complex Fourier coefficients cn from ‘normal’ Fourier coefficients an and bn. Prove that your expressions for cn are correct by substituting in the expressions for an and bn. [8]
9. Prove the space/time shifting property of the Fourier transform. [5]

## Third Supervision [70]

1. 2002 Paper 7 Question 12 Parts (a) and (c) [14]
2. 2002 Paper 9 Question 10 Part (c) [4]
3. 2004 Paper 8 Question 10 Part (c) [5]
4. 2006 Paper 8 Question 16 Part (e) [5]
5. 2007 Paper 7 Question 8 Part (d) [3]
6. 2007 Paper 8 Question 7 Parts (c), (d) and (e) [10]
7. 2008 Paper 8 Question 9 Parts (b) and (c) [11]
8. 2009 Paper 9 Question 9 Part (d) [5]
9. Prove the shift property of the Discrete Fourier Transform (DFT). [4]
10. Explain how the Fast Fourier Transform (FFT) works. [9]