## Exam A update | |

Dear students, following a successful appeal of one of you concerning the solution of question II) b), we have reviewed the case for all students and have increased the grades accordingly. The issue is that we tolerated sub-optimal results (with good justification), although an optimal one could be found but we did not enforce it, but we did not mention this explicitly in the solution. The solution provided to the exam has also been further detailed to respond to the underlying imprecision. Thank you for pointing this out to us and we deeply apologise to all those concerned. Best regards, The course staff |

פורסם ב- 20/2/2020, 14:53:46 Created on 20/2/2020, 14:53:46 Создано 20/2/2020, 14:53:46 تم النشر ب- 20/2/2020, 14:53:46 |

## Exam A grades and solution online | |

Dear students, the grades for exam A and a scan of your exam is now available online. You will also find the exam and its solution in the material section in the exam folder. Your final grade will soon appear on this site. It is computed as defined in the "General Info" tab. Best regards, The course staff |

פורסם ב- 16/2/2020, 18:55:49 Created on 16/2/2020, 18:55:49 Создано 16/2/2020, 18:55:49 تم النشر ب- 16/2/2020, 18:55:49 |

## Open material definition: 1 piece of paper | |

Dear students, after a lengthy consultation, it has been decided that you will be allowed only 1 A4 piece of paper for the exam with handwritten notes only. That means both sides of an A4 piece of paper. You can write whatever you want on it. You cannot print on it though. We recommend that you design such a sheet by finding the core material (in the slides, tutorials, and homeworks) and putting there formulae that are essential and that allow you to find everything else very quickly. You should also know how to get such formulae on your own in case you are faced with a similar yet different problem that requires you to adapt the proof. Note that such a paper is not necessary to complete the exams. Good luck! Best regards, The course staff |

פורסם ב- 3/2/2020, 11:18:48 Created on 3/2/2020, 11:18:48 Создано 3/2/2020, 11:18:48 تم النشر ب- 3/2/2020, 11:18:48 |

## Grades and feedback HW4 | |

Dear students, the grades for HW4 are out, check the grades sections. The grade that is in the first sheet of the comments is the grade before factorisation. Feedback for each submission can be found on the original page of the homework next to the submission link. Best regards, The course staff |

פורסם ב- 30/1/2020, 13:23:35 Created on 30/1/2020, 13:23:35 Создано 30/1/2020, 13:23:35 تم النشر ب- 30/1/2020, 13:23:35 |

## Grades and feedback HW3 | |

Dear students, the grades for HW3 are out, check the grades sections. The grade that is in the first sheet of the comments is the grade before factorisation. Feedback for each submission can be found on the original page of the homework next to the submission link. Best regards, The course staff |

פורסם ב- 29/1/2020, 16:24:19 Created on 29/1/2020, 16:24:19 Создано 29/1/2020, 16:24:19 تم النشر ب- 29/1/2020, 16:24:19 |

## WARNING: DFT, normalisation, and other troubles | |

Dear students, after checking homework 4 (and 3) we have noticed that many of you have not correctly understood the subtlety mentioned in the last tutorial and that was confusing in the previous homework. Depending on the normalisation convention for the (DFT) matrix, the formula can change: 1)i) (\lambda_0,...,\lambda_{n-1})^T= \sqrt{n} (DFT)^* (h_0,h_{n-1},...,h_1)^T if (DFT)^* is unitary, that is we a 1/\sqrt{n} normalisation. ii) (\lambda_0,...,\lambda_{n-1})^T= (DFT)^* (h_0,h_{n-1},...,h_1)^T if (DFT)^* is NOT unitary, and defined without any normalisation, that is it is a matrix of complex exponentials. iii) (\lambda_0,...,\lambda_{n-1})^T= n(DFT)^* (h_0,h_{n-1},...,h_1)^T if (DFT)^* is NOT unitary, and defined without the normalisation of 1/n. 2)i) (DFT)z = (DFT)x.*(DFT)y if z = conv(x,y), if DFT is defined without normalisation ii) (DFT)z = \sqrt{n}(DFT)x.*(DFT)y if z = conv(x,y), if DFT is defined as unitary ETC We apologise for the confusion in the previous homework as we were using inconsistent conventions and this is our bad. We did not penalise any of you for this in homework 3 but we did (a tiny bit) in homework 4 as we did tell you and insist on this in the last tutorial. 3) Be careful in the ordering of your eigenvalues of the (DFT) and (DFT)^* matrices. If (\lambda_0,\lambda_1,...,\lambda_{n-1}) are the ordered eigenvalues while diagonalising with (DFT), then (\lambda_0,\lambda_{n-1},...,\lambda_1) are the ordered eigenvalues while diagonalising with (DFT)^*. The source of the confusion for most of you comes from seeing that the roots of the unity are the eigenvalues of the J matrix defined in HW3. While this is true, you must be careful to what eigenvectors they correspond. The eigenvectors can be chosen to be the columns of the (DFT) matrix, and it happens that these are also the columns of the (DFT)^* matrix (up to a factor if we do not use the unitary convention) with a flipped order (except the first one). A good trick to memorise the right order is that exp(-i(2*\pi/n)k) is associated to the k-th column of (DFT)^* a column of complex exponentials with a + inside the exponent, while exp(+i(2*\pi/n)k) is associated to the k-th column of (DFT) a column of complex exponential with a - inside the exponent. You need the the opposite sign in order to compensate the shift. 4) When we ask you to prove or consider diagonalisation by (DFT)^*, you must write: A = (DFT)^*Diag (DFT) or equivalently Diag = (DFT)A(DFT)^* (we recommend learning the first equation) When we ask you to prove or consider diagonalisation by (DFT), you must write : A = (DFT)Diag (DFT)^* or equivalently Diag = (DFT)^*A(DFT). Please pay attention to the position of the matrices. Your solution might be correct, as it is equivalent to being diagonalised by (DFT) or (DFT)^*, however the ordering of the eigenvalues differs. Thus if you are asked diagonalisation by (DFT)^* and solely prove diagonalisation by (DFT) you have not answered the question. Please be careful. 5) It is not sufficient for the matrix to be circulant for its PCA matrix to be the (DFT) or (DFT)^* matrix. Indeed, the PCA matrix will be the (DFT) or the (DFT)^* matrix up to a reordering of the columns in the order of the eigenvalues. We did not penalise this mistake in the last homework. Beware for the exam. 6) When you claim that a matrix is diagonalised by (DFT)^* then it has to be circulant, then your reasoning is true but lacks half of it and to be circulant is also a sufficient condition. Please work by equivalence by saying "if and only if " and you are sure to be perfectly accurate and not forget half of the cases and lose points unfortunately. 7) In real life, when working with (DFT), please be careful. Try and guess what the convention of the authors are. If you are using code, read the documentation to be careful. You will find for instance that matlab does not use the unitary definition for the fourier transform, but the unormalised version for the fourier transform and 1/n normalisation for the inverse etc. Please beware. 8) The previous TA of this course was a human and as a human did some mistakes sometimes. Thus in the solutions to previous years exams you might find some mistakes following the previous points. Find them, understand them, and you will master the topic better than a TA! We wish you a happy exam period. All the best, The course staff |

פורסם ב- 28/1/2020, 21:58:29 Created on 28/1/2020, 21:58:29 Создано 28/1/2020, 21:58:29 تم النشر ب- 28/1/2020, 21:58:29 |

## Update HW4 | |

Dear students, we have updated HW4 to add an assumption we had previously omitted in Exercise 2. We added the line: "We further assume that M and (L1,L2) are independent random variables." Good luck! Best regards, The course staff |

פורסם ב- 13/1/2020, 19:26:56 Created on 13/1/2020, 19:26:56 Создано 13/1/2020, 19:26:56 تم النشر ب- 13/1/2020, 19:26:56 |

## Grades and feedback HW2 | |

Dear students, the grades for HW2 are out, check the grades sections. The grade that is in the first sheet of the comments is the grade before factorisation. Feedback for each submission can be found on the original page of the homework next to the submission link. Best regards, The course staff |

פורסם ב- 12/1/2020, 12:42:19 Created on 12/1/2020, 12:42:19 Создано 12/1/2020, 12:42:19 تم النشر ب- 12/1/2020, 12:42:19 |

## Grades and feedback HW1 | |

Dear students, grades for HW1 have been generously updated to take into account the fact that all of you, even those with the lowest grades, clearly invested a significant amount of time for the homework and overall seem to understand most of the material. We hope this will help you for your other studies. Best regards, The course staff |

פורסם ב- 8/1/2020, 15:58:13 Created on 8/1/2020, 15:58:13 Создано 8/1/2020, 15:58:13 تم النشر ب- 8/1/2020, 15:58:13 |

## Grades and feedback HW1 | |

Dear students, the grades for HW1 are out, check the grades sections. Feedback for each submission can be found on the original page of the homework next to the submission link. Best regards, The course staff |

פורסם ב- 7/1/2020, 16:42:12 Created on 7/1/2020, 16:42:12 Создано 7/1/2020, 16:42:12 تم النشر ب- 7/1/2020, 16:42:12 |

## Homework 4 | |

Dear students, The final problem set is published on the course website. The due date is January 25th at 23:59. Good luck!! Best regards, The course staff |

פורסם ב- 7/1/2020, 10:54:16 Created on 7/1/2020, 10:54:16 Создано 7/1/2020, 10:54:16 تم النشر ب- 7/1/2020, 10:54:16 |

## תרגיל בית 3 Homework 3 Homework 3 Homework 3 | |

Dear students, The third problem set is published on the course website. The due date is January 6th at 23:59. It should clearly include your entire solution both the theoretical part and the Matlab part with code. Have fun and good luck:) Best regards, The course staff |

פורסם ב- 17/12/2019, 10:20:28 Created on 17/12/2019, 10:20:28 Создано 17/12/2019, 10:20:28 تم النشر ب- 17/12/2019, 10:20:28 |

## HW2 Question 4 | |

Dear students, This question is updated, note the new function and the range. Thank you for the feedbacks. Best regards, The course staff |

פורסם ב- 8/12/2019, 12:46:06 Created on 8/12/2019, 12:46:06 Создано 8/12/2019, 12:46:06 تم النشر ب- 8/12/2019, 12:46:06 |

## Lecture and tutorial in the upcoming week | |

Dear students, Please note the following updates regarding the lecture and tutorial times in the upcoming week: On Sunday, a tutorial will replace the lecture (at 10:30 in Taub 5). On Wednesday, a two-hour lecture will replace the tutorial (at 10:30 in Taub 5). Best regards, The course staff |

פורסם ב- 7/12/2019, 22:49:42 Created on 7/12/2019, 22:49:42 Создано 7/12/2019, 22:49:42 تم النشر ب- 7/12/2019, 22:49:42 |

## תרגיל בית 2 Homework 2 Homework 2 Homework 2 | |

Dear students, The second problem set is published on the course website. The due date is December 14th at 23:59. Please recall that the submission is electronic via the course website. It should include your entire solution both the theoretical part and the Matlab part with code. Have fun and good luck! Best regards, The course staff |

עדכון אחרון ב- 27/11/2019, 12:21:26 Last updated on 27/11/2019, 12:21:26 Последняя модификация 27/11/2019, 12:21:26 تمت الحتلنة الأخيرة ب- 27/11/2019, 12:21:26 |

## Homework 1 update | |

Dear students, Regarding question 2b, it's permitted to solve the questions by Matlab instead of purely handy. Please write the initialization and each step's representation numbers and decision numbers explicitly. Regarding question 3, Taylor's expansion is not assumed here (we didn't have large N). You need to derive the optimal coefficients respect to the derivatives, plug in the optimal coefficients, and find the MSE. Good luck! Best regards, The course staff |

עדכון אחרון ב- 17/11/2019, 15:40:48 Last updated on 17/11/2019, 15:40:48 Последняя модификация 17/11/2019, 15:40:48 تمت الحتلنة الأخيرة ب- 17/11/2019, 15:40:48 |

## New Office Hours | |

Dear students, please note that a slot for office hours with Tom has been added after the tutorials on Wednesday 12:30-13:30, in Taub 412. Extra emergency office hours with Tom can also be scheduled by email at uthomas.dagesatcs.technion.ac.il. Note that Tom will be unavailable for two weeks starting from the 24/11. Good luck with the homework, we strongly advise to start working on it ASAP, Best regards, The course staff |

פורסם ב- 14/11/2019, 12:49:36 Created on 14/11/2019, 12:49:36 Создано 14/11/2019, 12:49:36 تم النشر ب- 14/11/2019, 12:49:36 |

## תרגיל בית 1 Homework 1 Homework 1 Homework 1 | |

Dear students, The first problem set is published on the course website. The due date is November 25th at 23:59. Please note that the submission is in pairs and is electronic via the course website. It should include your entire solution both the theoretical part and the Matlab part with code. Have fun and good luck! Best regards, The course staff |

פורסם ב- 10/11/2019, 09:17:53 Created on 10/11/2019, 09:17:53 Создано 10/11/2019, 09:17:53 تم النشر ب- 10/11/2019, 09:17:53 |

## Lecture and tutorial this week and in the upcoming week | |

Dear students, On this Wednesday (06/11), a lecture will replace the tutorial at 10:30-12:30 at Taub 5. Next Sunday (10/11), the lecture will be held as usual (10:30-13:30 at Taub 5) and there will be a supplementary tutorial at 17:30-19:30 at Taub 4. Best regards, The course staff |

פורסם ב- 4/11/2019, 13:29:04 Created on 4/11/2019, 13:29:04 Создано 4/11/2019, 13:29:04 تم النشر ب- 4/11/2019, 13:29:04 |

## Welcome to 236200! | |

Dear Students, Welcome to the "Signal, Image, and Data Processing" course (236200). The first tutorial will be held on Wednesday at 10:30-12:30 and the first lecture will be given on next Sunday at 10:30-13:30. The lecture slides, tutorial slides, tutorial MATLAB code will be updated to the course website. The homework assignments will be published on it as well, so be sure to check the course website regularly (an announcement will be published with every homework assignment). Feel free to contact us, our contact details are available on the course website. We hope you'll have an enjoyable and interesting semester. Good luck! Course Staff |

עדכון אחרון ב- 20/10/2019, 21:12:29 Last updated on 20/10/2019, 21:12:29 Последняя модификация 20/10/2019, 21:12:29 تمت الحتلنة الأخيرة ب- 20/10/2019, 21:12:29 |