(New page: =Lecture Blog, ECE438, Fall 2010, Prof. Boutin= Please do not edit this page. If you want to add/remove something, just copy the code on a new page and edit only that new page. -pm ---...)
 
 
(2 intermediate revisions by the same user not shown)
Line 1: Line 1:
−
=Lecture Blog, [[ECE438]], Fall 2010, Prof. Boutin=
+
=Lecture Blog, [[ECE438]], Fall 2010, [[user:mboutin|Prof. Boutin]]=
 
Please do not edit this page. If you want to add/remove something, just copy the code on a new page and edit only that new page. -pm
 
Please do not edit this page. If you want to add/remove something, just copy the code on a new page and edit only that new page. -pm
 
----
 
----
 
[[Lecture1ECE438F10|Lecture 1]]
 
[[Lecture1ECE438F10|Lecture 1]]
−
{{:Lecture1ECE438F10|Lecture 1}}
+
{{:Lecture1ECE438F10}}
 
----
 
----
−
[[Lecture2ECE438F10|2]]
 
 
----
 
----
−
[[Lecture3ECE438F10|3]]
+
[[Lecture2ECE438F10|Lecture 2]]
 +
{{:Lecture2ECE438F10}}
 
----
 
----
−
[[Lecture4ECE438F10|4]]  
+
[[Lecture3ECE438F10|Lecture 3]]
 +
{{:Lecture3ECE438F10}}
 
----
 
----
−
[[Lecture5ECE438F10|5]]
 
 
----
 
----
−
[[Lecture6ECE438F10|6]]  
+
[[Lecture4ECE438F10|Lecture 4]]  
 +
{{:Lecture4ECE438F10}}
 
----
 
----
−
[[Lecture7ECE438F10|7]]
 
 
----
 
----
−
[[Lecture8ECE438F10|8]]  
+
[[Lecture5ECE438F10|Lecture 5]]
 +
{{:Lecture5ECE438F10}}
 
----
 
----
−
[[Lecture9ECE438F10|9]]
 
 
----
 
----
−
[[Lecture10ECE438F10|10]]  
+
[[Lecture6ECE438F10|Lecture 6]]  
 +
{{:Lecture6ECE438F10}}
 
----
 
----
−
[[Lecture11ECE438F10|11]]
 
 
----
 
----
−
[[Lecture12ECE438F10|12]]  
+
[[Lecture7ECE438F10|Lecture 7]]  
 +
{{:Lecture7ECE438F10}}
 
----
 
----
−
[[Lecture13ECE438F10|13]]
 
 
----
 
----
−
[[Lecture14ECE438F10|14]]  
+
[[Lecture8ECE438F10|Lecture 8]]
 +
{{:Lecture8ECE438F10}}
 
----
 
----
−
[[Lecture15ECE438F10|15]]
 
 
----
 
----
−
[[Lecture16ECE438F10|16]]  
+
[[Lecture9ECE438F10|Lecture 9]]
 +
{{:Lecture9ECE438F10}}
 
----
 
----
−
[[Lecture17ECE438F10|17]]
 
 
----
 
----
−
[[Lecture18ECE438F10|18]]  
+
[[Lecture10ECE438F10|Lecture 10]]  
 +
{{:Lecture10ECE438F10}}
 
----
 
----
−
[[Lecture19ECE438F10|19]]
 
 
----
 
----
−
[[Lecture20ECE438F10|20]]  
+
[[Lecture11ECE438F10|Lecture 11]]
 +
{{:Lecture11ECE438F10}}
 
----
 
----
−
[[Lecture21ECE438F10|21]]
 
 
----
 
----
−
[[Lecture22ECE438F10|22]]  
+
[[Lecture12ECE438F10|Lecture 12]]  
 +
{{:Lecture12ECE438F10}}
 
----
 
----
−
[[Lecture23ECE438F10|23]]
 
 
----
 
----
−
[[Lecture24ECE438F10|24]]  
+
[[Lecture13ECE438F10|Lecture 13]]  
 +
{{:Lecture13ECE438F10}}
 
----
 
----
−
[[Lecture25ECE438F10|25]]
 
 
----
 
----
−
[[Lecture26ECE438F10|26]]  
+
[[Lecture14ECE438F10|Lecture 14]]  
 +
{{:Lecture14ECE438F10}}
 
----
 
----
−
[[Lecture27ECE438F10|27]]
 
 
----
 
----
−
[[Lecture28ECE438F10|28]]  
+
[[Lecture15ECE438F10|Lecture 15]]  
 +
{{:Lecture15ECE438F10}}
 
----
 
----
−
[[Lecture29ECE438F10|29]]
 
 
----
 
----
−
[[Lecture30ECE438F10|30]]  
+
[[Lecture16ECE438F10|Lecture 16]]  
 +
{{:Lecture16ECE438F10}}
 
----
 
----
−
[[Lecture31ECE438F10|31]]
 
 
----
 
----
−
[[Lecture32ECE438F10|32]]  
+
[[Lecture17ECE438F10|Lecture 17]]  
 +
{{:Lecture17ECE438F10}}
 
----
 
----
−
[[Lecture33ECE438F10|33]]
 
 
----
 
----
−
[[Lecture34ECE438F10|34]]  
+
[[Lecture18ECE438F10|Lecture 18]]  
 +
{{:Lecture18ECE438F10}}
 
----
 
----
−
[[Lecture35ECE438F10|35]]
 
 
----
 
----
−
[[Lecture36ECE438F10|36]]  
+
[[Lecture19ECE438F10|Lecture 19]]  
 +
{{:Lecture19ECE438F10}}
 
----
 
----
−
[[Lecture37ECE438F10|37]]
 
 
----
 
----
−
[[Lecture38ECE438F10|38]]  
+
[[Lecture20ECE438F10|Lecture 20]]  
 +
{{:Lecture20ECE438F10}}
 
----
 
----
−
[[Lecture39ECE438F10|39]]
 
 
----
 
----
−
[[Lecture40ECE438F10|40]]  
+
[[Lecture21ECE438F10|Lecture 21]]  
 +
{{:Lecture21ECE438F10}}
 
----
 
----
−
[[Lecture41ECE438F10|41]]
 
 
----
 
----
−
[[Lecture42ECE438F10|42]]  
+
[[Lecture22ECE438F10|Lecture 22]]  
 +
{{:Lecture22ECE438F10}}
 
----
 
----
−
[[Lecture43ECE438F10|43]]
 
 
----
 
----
−
[[Lecture44ECE438F10|44]]
+
[[Lecture23ECE438F10|Lecture 23]]
 +
{{:Lecture23ECE438F10}}
 +
----
 +
----
 +
[[Lecture24ECE438F10|Lecture 24]]
 +
{{:Lecture24ECE438F10}}
 +
----
 +
----
 +
[[Lecture25ECE438F10|Lecture 25]]
 +
{{:Lecture25ECE438F10}}
 +
----
 +
----
 +
[[Lecture26ECE438F10|Lecture 26]]
 +
{{:Lecture26ECE438F10}}
 +
----
 +
----
 +
[[Lecture27ECE438F10|Lecture 27]]
 +
{{:Lecture27ECE438F10}}
 +
----
 +
----
 +
[[Lecture28ECE438F10|Lecture 28]]
 +
{{:Lecture28ECE438F10}}
 +
----
 +
----
 +
[[Lecture29ECE438F10|Lecture 29]]
 +
{{:Lecture29ECE438F10}}
 +
----
 +
----
 +
[[Lecture30ECE438F10|Lecture 30]]
 +
{{:Lecture30ECE438F10}}
 +
----
 +
----
 +
[[Lecture31ECE438F10|Lecture 31]]
 +
{{:Lecture31ECE438F10}}
 +
----
 +
----
 +
[[Lecture32ECE438F10|Lecture 32]]
 +
{{:Lecture32ECE438F10}}
 +
----
 +
----
 +
[[Lecture33ECE438F10|Lecture 33]]
 +
{{:Lecture33ECE438F10}}
 +
----
 +
----
 +
[[Lecture34ECE438F10|Lecture 34]]
 +
{{:Lecture34ECE438F10}}
 +
----
 +
----
 +
[[Lecture35ECE438F10|Lecture 35]]
 +
{{:Lecture35ECE438F10}}
 +
----
 +
----
 +
[[Lecture36ECE438F10|Lecture 36]]
 +
{{:Lecture36ECE438F10}}
 +
----
 +
----
 +
[[Lecture37ECE438F10|Lecture 37]]
 +
{{:Lecture37ECE438F10}}
 +
----
 +
----
 +
[[Lecture38ECE438F10|Lecture 38]]
 +
{{:Lecture38ECE438F10}}
 +
----
 +
----
 +
[[Lecture39ECE438F10|Lecture 39]]
 +
{{:Lecture39ECE438F10}}
 +
----
 +
----
 +
[[Lecture40ECE438F10|Lecture 40]]
 +
{{:Lecture40ECE438F10}}
 +
----
 +
----
 +
[[Lecture41ECE438F10|Lecture 41]]
 +
{{:Lecture41ECE438F10}}
 +
----
 +
----
 +
[[Lecture42ECE438F10|Lecture 42]]
 +
{{:Lecture42ECE438F10}}
 +
----
 +
----
 +
[[Lecture43ECE438F10|Lecture 43]]
 +
{{:Lecture43ECE438F10}}
 +
----
 +
----
 +
[[Lecture44ECE438F10|Lecture 44]]
 +
{{:Lecture44ECE438F10}}
 +
----
 
----
 
----
 
Please do not edit this page. If you want to add/remove something, just copy the code on a new page and edit only that new page. -pm
 
Please do not edit this page. If you want to add/remove something, just copy the code on a new page and edit only that new page. -pm

Latest revision as of 04:40, 29 December 2010

Contents

Lecture Blog, ECE438, Fall 2010, Prof. Boutin

Please do not edit this page. If you want to add/remove something, just copy the code on a new page and edit only that new page. -pm

Lecture 1

Lecture 1 Blog, ECE438 Fall 2010, Prof. Boutin

Monday August 23, 2010 (Week 1) - See Course Outline.

In the first lecture, we covered the syllabus and gave a short introduction to Rhea. We then talked about what is "Digital Signal Processing". In particular, we discussed the two following applications:

The actual material covered was very similar the material of the first lecture of Fall 2009. Lecture notes for that lecture are here. (These would be a very good starting point in case you were thinking of typing the notes and sharing them on Rhea.)

Action items for students include

The main goal of this lecture was to clarify the course policies and get everybody excited about the subject!

Next: Lecture 2

Back to 2010 Fall ECE 438 Boutin

Lecture 2

Lecture 2 Blog, ECE438 Fall 2010, Prof. Boutin

Wendesday August 25, 2010 (Week 1) - See Course Outline.

In the second lecture, we introduced the CT Fourier transform in terms of frequency "f" and discussed its relationship with the frequency transform in terms of $ \omega $. The "rep" and "comb" functions were introduced. Some subtleties regarding the rescaling of the Dirac delta were observed. The first homework was announced. It is due next Wednesday.

Idea: How about a couple of you take this table of CTFT and make a new one in terms of f?

Relevant Rhea pages created by students last fall:

Do you see any mistake in these pages? Do you have questions? Feel free to write directly on these pages, expand them, or write new pages.

Previous: Lecture 1; Next: Lecture 3

Back to 2010 Fall ECE 438 Boutin

Lecture 3

Lecture 3 Blog, ECE438 Fall 2010, Prof. Boutin

Friday August 27, 2010 (Week 1) - See Course Outline.

In the third lecture, we obtained the CT Fourier transform of the "comb" and "rep" functions. We also defined the DT Fourier transform and computed the DTFT of a complex exponential.

Students do not seem at all happy about the switch from frequency in radians per time unit to frequency in hertz...

Previous: Lecture 2; Next: Lecture 4

Back to 2010 Fall ECE 438 Boutin

Lecture 4

Lecture 4 Blog, ECE438 Fall 2010, Prof. Boutin

Monday August 30, 2010.

In the fourth lecture, we obtained the frequencies of the notes in the middle scale of a piano. We then computed the CTFT of signal that would "sound" like a middle C and the CTFT of a signal that would "sound" like the next higher C. We also obtained the DTFT of a sampling of each of these signals (using the same sampling frequency). It was observed that, while the sampling of middle C yields a DT signal that also sounds like a middle C, the sampling of the higher C does not at all sound like a C.

Relevant links:

Seems like students have little recollection of the sampling material from ECE301. We shall fix this!

Any comments/questions? Please write them below.

Previous: Lecture 3; Next: Lecture 5

Back to 2010 Fall ECE 438 Boutin

Lecture 5

Lecture 5 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday September 1, 2010.

In the fifth lecture, we collected the first homework assignment and announced the second homework assignment. It was noted that the student's presentation of the first homework is less than desirable. As a result, it was announced that the second homework would be graded by double-blind peer review.

We finished our discussion of aliasing when sampling pure frequencies. It is highly suggested that students review the periodicity of discrete-time complex exponentials (including the concept of harmonics).

References

  • "Signals and systems", by Oppenheim, Wilsky, and Nawab, Section 1.3.3.

We defined the z-transform and highlighted its relationship with the DTFT. We also computed the z-transform of a signal for which the Fourier transform does not exist. The first student who creates a table of z-transform on Rhea with at least 15 signals will get a 0.5% bonus. (You must use the same format as the one use for this table of Laplace transforms.)

Related links:

Please feel free to correct the material on these pages, comment on them, or write new/better ones.

Any comments/questions? Please write them below.

Previous: Lecture 4; Next: Lecture 6

Back to 2010 Fall ECE 438 Boutin

Lecture 6

Lecture 6 Blog, ECE438 Fall 2010, Prof. Boutin

Friday September 3, 2010.

In Lecture #6, we talked about the ROC of the z-transform but we did not have time to cover the inverse z-transform. I just realized that Monday is off, so this means we will not have time to cover the inverse z-transform before the homework is due. Therefore, I will make a change in the second homework and make the computation of the inverse z-transforms part of homework number 3.

In case you want to get a head start, here are the notes on the inverse z-transform from Fall 2009 and here is another version. (Note that these were written by students, so I make no guarantee regarding the content..)

Previous: Lecture 5; Next: Lecture 7

Back to 2010 Fall ECE 438 Boutin

Lecture 7

Lecture 7 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday September 8, 2010.

In Lecture #7, we talked about convergence of the z-transform at infinity. We also talked about the time-shifting property of the z-transform. Finally, we gave an explicit formula for the inverse z-transform, and described a straightforward procedure for computing it using power series. If you do not feel completely comfortable with the geometric series, this is a good time to brush up on the subject.

Related Rhea pages (please feel free to comment/discuss directly on these pages):

The third homework is due next Wednesday. It basically consists in computing the inverse z-transforms of the signal you used in HW2 and in doing the peer review of HW2.

Did everybody hand in their homework 2 in the "Assignment 2" box in Prof. Mimi's dropbox? Note that this is NOT the same as Prof. Mimi's dropbox.

Previous: Lecture 6; Next: Lecture 8

Back to 2010 Fall ECE 438 Boutin

Lecture 8

Lecture 8 Blog, ECE438 Fall 2010, Prof. Boutin

Friday September 10, 2010.

In Lecture #8, I showed by example how to compute inverse z-transforms. I gave students two exercises (case b) and case c) in your notes) to try at home. Please don't forget to do them! I will answer your questions in class this coming Monday.

For those of you wishing to brush up on Fourier series, here are two collective study pages:

Previous: Lecture 7; Next: Lecture 9

Back to 2010 Fall ECE 438 Boutin

Lecture 9

Lecture 9 Blog, ECE438 Fall 2010, Prof. Boutin

Monday September 13, 2010.

In Lecture #9, we first had the visit of Prof. Jan Allebach, who told us about a former ECE438 student who now uses DSP in her work. Her company is called N-ask, and it is part of the Purdue industrial round table today and tomorrow. Here is a flyer. In case you missed the presentation, here is the video.

We discussed the relationship between the poles/zeros of the z-transform and the magnitude of the DT Fourier transform. We also began talking about sampling. It was announced that the deadline for the peer-review is now pushed back. (I will announce when later.)

Related Rhea pages:

Several students asked me after class how to obtain the ROC of a z-transform. There is a really good example on this page. Feel free to add comments/questions.

Previous: Lecture 8; Next: Lecture 10

Back to 2010 Fall ECE 438 Boutin

Lecture 10

Lecture 10 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday September 15, 2010.

In Lecture #10, we

Previous: Lecture 9; Next: Lecture 11

Back to 2010 Fall ECE 438 Boutin

Lecture 11

Lecture 11 Blog, ECE438 Fall 2010, Prof. Boutin

Friday September 17, 2010.

In Lecture #11, we talked further about the reconstruction of signals. More specifically, we compared the band-limited reconstruction obtained using Whitaker-Kotelnikov-Shannon expansion with the band-unlimited reconstruction obtained with the zero-order hold. We then begin talking about the relationship between the Fourier transform of a signal x(t) and the sampling

$ x_d[n]=x\left(nT\right). $

Note that the peer review is due next Wednesday.

Previous: Lecture 10; Next: Lecture 12

Back to 2010 Fall ECE 438 Boutin

Lecture 12

Lecture 12 Blog, ECE438 Fall 2010, Prof. Boutin

Monday September 20, 2010 (Week 5) - See Course Outline.

In Lecture #12, we obtained the relationship between the Fourier transform of a signal x(t) and the Fourier transform of its sampling y[n]=x(nT). We then talked about resampling. More specifically, we obtained the relationship between two different samplings of a signal, viewed from the frequency domain. Note that it is VERY IMPORTANT that you understand this relationship.

Don't forget to complete the peer review before Wednesday 6pm!

Previous: Lecture 11; Next: Lecture 13

Back to 2010 Fall ECE 438 Boutin

Lecture 13

Lecture 13 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday September 22, 2010.

In Lecture #13, we continued considering the sampling

$ x_1[n]=x(T_1 n) $

of a continuous-time signal x(t). We obtained and discussed the relationship between the DT Fourier transform of $ x_1[n] $ and that of a downsampling $ y[n]=x_1[Dn] $, for some integer D>1. (Yes, I know it was a lot of math, but this is good for you, trust me!) We then obtained the relationship between the DT Fourier transform of $ x_1[n] $ and that of an upsampling of x[n] by a factor D. From this relationship, we concluded that, under certain circumstances, a low-pass filter could be applied to this upsampling so to obtain the signal

$ x_2[n]=x\left( n \frac{T_1}{D} \right) $.

Side notes:

Previous: Lecture 12; Next: Lecture 14

Back to 2010 Fall ECE 438 Boutin

Lecture 14

Lecture 14 Blog, ECE438 Fall 2010, Prof. Boutin

Friday September 25, 2010.

In Lecture #14, we defined and motivated the Discrete_Fourier_Transform (DFT).

Relevant Link:

Previous: Lecture 13; Next: Lecture 15

Back to 2010 Fall ECE 438 Boutin

Lecture 15

Lecture 15 Blog, ECE438 Fall 2010, Prof. Boutin

Monday September 28, 2010.

In Lecture #15, we recalled that, before computing the "DFT of discrete-time signal"(*see note below), one first needs to truncate the signal. Subsequently, one needs to repeat the resulting finite duration signal in order to create a periodic DT signal. The DFT of that periodic signal then corresponds to a sampling of the DTFT of the truncated signal.

We discussed the artifacts created by signal truncation (leakage) and the problems created by sampling the DTFT (the "picket fence effect"). To illustrate the leakage effect, we looked at the Fourier transform of a window function.


  • Note: Technically, the DFT is only defined for periodic signals.

Previous: Lecture 14; Next: Lecture 16

Back to 2010 Fall ECE 438 Boutin

Lecture 16

Lecture 16 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday September 30, 2010.

In Lecture #16, we obtained a "practical" formula for reconstructing the DTFT of a finite duration signal from the DFT of its periodic repetition. The formula was observed to hold whenever the periodic repetition has a period that is at least as long as the signal duration. We finished the lecture by introducing a matrix equation to represent the transformation from a finite duration signal to the DFT.

We also emphasized the need to be able to compute Fourier series, as computing DFTs is essentially the same as computing Fourier series coefficients.

Relevant Links:

Previous: Lecture 15; Next: Lecture 17

Back to 2010 Fall ECE 438 Boutin

Lecture 17

Lecture 17 Blog, ECE438 Fall 2010, Prof. Boutin

Friday October 1, 2010.

Actually, there was no "Lecture 17" per say, as class time was used for giving the first mid-term exam.

Previous: Lecture 16; Next: Lecture 18

Back to 2010 Fall ECE 438 Boutin

Lecture 18

Lecture 18 Blog, ECE438 Fall 2010, Prof. Boutin

Monday October 4, 2010 (Week 7) - See Course Outline.

Recovering from the first midterm exam, we attacked the Fast Fourier Transform (FFT). More specifically, we illustrated how "decimating by a factor two" yield a significant decrease in the number of "complex operations" (CO) involved in the computation of a DFT.

Previous: Lecture 17; Next: Lecture 19

Back to 2010 Fall ECE 438 Boutin

Lecture 19

Lecture 19 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday October 6, 2010.

We continued our discussion of the FFT by presenting the "Radix-two" algorithm for computing the DFT of a discrete-time signal with finite duration $ 2^M $. (Although technically, the DFT is used to transform periodic signals only, so to be correct, one should write "the DFT of the periodic repetition with period N of a signal with finite duration N"). If you found my diagrams hard to read on the board, I highly recommend reading Prof. Pollak's notes on the FFT.

We finished the lecture by beginning to discuss DT systems (definition and basic properties). Our emphasis this semester will be on "filtering".

Previous: Lecture 18; Next: Lecture 20

Back to 2010 Fall ECE 438 Boutin

Lecture 20

Lecture 20 Blog, ECE438 Fall 2010, Prof. Boutin

Friday October 8, 2010.

Having defined DT systems in the previous lecture and described some basic system properties, we focused our discussion in this lecture on Linear-Time-Invariant (LTI) DT systems. We listed some important properties of such systems, which led us to the concepts of "Frequency Response" and "Transfer function" of a system. We then defined a simple filter with low-pass characteristics (Filter A) and another filer with band-pass characteristics (Filter B). The behavior of these two filters will be further studied when we return from Fall Break. Enjoy your time off!


Previous: Lecture 19; Next: Lecture 21

Back to 2010 Fall ECE 438 Boutin

Lecture 21

Lecture 21 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday October 13, 2010.

Coming back from the Fall break, the graded midterms were handed back and we went over the solution. The grade distribution and the gradelines are posted here.


Previous: Lecture 20; Next: Lecture 22

Back to 2010 Fall ECE 438 Boutin

Lecture 22

Lecture 22 Blog, ECE438 Fall 2010, Prof. Boutin

Friday October 15, 2010.

Hello "Makers"!

Given the disappointing results on the first midterm, I have decided to give you more opportunities to practice solving problems. So before the lecture begins, I will post the following practice question. Please feel free to write your solution/questions below the question, and I will look at it and reply this weekend. Note that the practice question is related to the next homework.

Today in class, we continued looking at a specific low-pass filter (filter A) and a specific band-pass filter (filter B). We noticed the two different ways of writing the transfer function (as a function of z, and as a function of 1/z) and noted that it is just as easy to find the poles/zeros with either representation (using a change of variable when the function is in terms of 1/z). We then began talking about systems defined by difference equations with constant coefficients. Our focus is going to be on "causal" systems, so the general form of equations we are interested in is

$ \sum_{l=1}^N a_l y[n-l]= \sum_{k=1}^M b_k x[n-k]. $

Comments:

Also, if possible I was hoping to work though some of the exam problems in a little more detail. In class, Prof. Boutin suggested that a lunch help session might be useful in answering these question and asked that we try to find a time for such a meeting. Would some time around 12:30 Monday, Wednesday, or Friday work for anyone else who is interested? -Clayton

12:30 is NanoElectronics for me. MWF. And Lab/ECE400 T/TH.
11:30 and 1:30 are suitable all days but Tuesday. ~Ajfunche
11:30-1:30 anytime between then MWF or TH before 12:30 ~Whaywood
Monday and Wednesday at 1230pm works for me, but not Friday. ~ksoong

Would Monday 12:00-1:00 suit everybody? In particular, Clayton, would this time work for you? -pm

12-1 on Monday would work for me. Thank you Professor. -Clayton

Ok, let's begin next week then. We will meet in MSEE383. (By the way I saw you in the newspaper. Nice work!) -pm

Previous: Lecture 21; Next: Lecture 23

Back to 2010 Fall ECE 438 Boutin

Lecture 23

Lecture 23 Blog, ECE438 Fall 2010, Prof. Boutin

Monday October 18, 2010.

Continuing our practice problems series, here is a simple question on computing the z-transform of a signal and a slightly more complicated question on computing the inverse z-transform.

Today in the lecture, we continued our discussion of systems defined by difference equations with constant coefficients. We reemphasized the fact that boundary conditions need to be given for the system to be uniquely determine, and pointed out that such boundary conditions can either be given by fixing the value of the output y[n] at N different points, or by fixing the value of the unit impulse response h[n] at N different points. We then observed that assuming causality of the system would also uniquely determine the system, as causal systems always have h[n]=0 for n<0. We obtained a general expression for the transfer function of a system defined by a difference equation with constant coefficients, and observed that the ROC of the transfer function must be the outside of a circle if the system is causal. Thus if one is trying to define a causal system for which the frequency response is well defined, then the poles of the transfer function should all be inside the unit circle in the complex plane.


Note: Your friend Clayton was asking in the previous lecture blog whether some of you want to meet with Prof. Mimi for lunch every week to go over problems. Don't forget to answer!

Related Rhea pages

Previous: Lecture 22; Next: Lecture 24

Back to 2010 Fall ECE 438 Boutin

Lecture 24

Lecture 24 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday October 20, 2010.

Continuing our practice problems series, here is an occasion to make sure you understand sampling from the frequency domain viewpoint.

Today in the lecture, we continued talking about filters and filter design using the transfer function. It seems like many students find it difficult to see the point of this study. Perhaps reading Druv's summary of filtering or his page on audio filtering could help. If another student has an alternative explanation or can provide more connections to real life applications, please consider writing a Rhea page to help your colleagues!


Note: Your friend Clayton was asking in the previous lecture blog whether some of you want to meet with Prof. Mimi for lunch every week to go over problems. Don't forget to answer!


Previous: Lecture 23; Next: Lecture 25

Back to 2010 Fall ECE 438 Boutin

Lecture 25

Lecture 25 Blog, ECE438 Fall 2010, Prof. Boutin

Friday October 22, 2010.

We presented a simple method to obtain a causal FIR filter from an ideal filter using time shifting and windowing in the time domain. It is important to understand how the filter obtained in this fashion differs from the original ideal filter (in the frequency domain). Note: the picture of filter I drew should have been repeated periodically with period $ 2 \pi $. It is important to remember this for any filter in discrete-time. In the last part of the lecture, we saw how the heat equation for an infinite length rod can be used to define an LTI system (by letting the heat evolve for a fixed amount of time), and we observed that the frequency response of this system has low-pass characteristics. We then discretized this differential equation by approximating each derivative using a standard numerical scheme. This gave us a simple discrete-time LTI system defined by a constant coefficient difference equation (but not causal).

Related Rhea page previously created by students: (Feel free correct/comment, expand on them, or simply write new pages on the subject)

Previous: Lecture 24; Next: Lecture 26

Back to 2010 Fall ECE 438 Boutin

Lecture 26

Lecture 26 Blog, ECE438 Fall 2010, Prof. Boutin

Monday October 25, 2010 (Week 10) - See Course Outline.

We looked at the output of a DT system using the DFT. The main result we presented is quite simple: the DFT of the ouput is the product of the DFT of the input, and the DFT of the unit impulse response of the system:

$ Y_N[k]=X_N[k] H_N[k], \text{ for all }k\in {\mathbb Z} $

However, our discussion was complicated by the fact that, technically, the DFT is defined for periodic signals only (thus not for finite duration signals), while in application the input is typically of finite duration. We also had to worry about the fact that the input, the unit impulse response, and the output have different durations, and so we need to make sure to use the N-point DFT, where N is at least as long as x[n], h[n], and y[n].


Previous: Lecture 25; Next: Lecture 27

Back to 2010 Fall ECE 438 Boutin

Lecture 27

Lecture 27 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday October 27, 2010 (Week 10) - See Course Outline.

We finished our discussion of the "DFT view of filtering" by obtaining the relationship between the circular convolution and the usual convolution.

Additional Reference:

Next lecture, we will begin talking about speech signals!

Previous: Lecture 26; Next: Lecture 28

Back to 2010 Fall ECE 438 Boutin

Lecture 28

Lecture 28 Blog, ECE438 Fall 2010, Prof. Boutin

Friday October 29, 2010 (Week 10) - See Course Outline.

Today we talked about speech signals. After discussing some applications and challenges related to speech processing, we defined the "phoneme" as the basic unit of speech. We described the difference between "voiced" and "unvoiced" phonemes and discussed methods for determining whether a given 5-10 ms block of a sound signal corresponds to an unvoiced or voiced phoneme.

It has come to my attention that some students do not know about the course outline, which lists several references for the different topics we are covering in class, including the relevant pages in the official textbook, whenever appropriate. Some online references are also given. Please check it out!

Note: I will be holding a lunch "office hour" in MSEE383 this coming Monday 12-1pm. Bring your lunch and your questions!

Relevant Rhea pages:

Previous: Lecture 27; Next: Lecture 29

Back to 2010 Fall ECE 438 Boutin

Lecture 29

Lecture 29 Blog, ECE438 Fall 2010, Prof. Boutin

Monday November 1, 2010 (Week 11) - See Course Outline.

Today we continued talking about speech signals.


Note: I am holding a lunch office hour in MSEE383 every Monday 12-1pm. Bring your lunch and your questions!

Relevant Rhea pages:

Previous: Lecture 28; Next: Lecture 30

Back to 2010 Fall ECE 438 Boutin

Lecture 30

Lecture 30 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday November 3, 2010 (Week 11) - See Course Outline.

We began with a couple of exercises to understand the different ways of constructing periodic signals we have seen. We then continued modeling the vocal tract as a sequence of tubes and analyzing this model. We observed that the relationship between the airflow at each end of a cylindrical tube is just a time delay (positive for the air flowing right, and negative for the air flowing left). We wrote this relationship in matrix form. Next lecture, we will describe what happens when the air flows from one cylinder to the next.

Hw9 is now posted. It is due next week. I hope you will have fun analyzing the speech signal of Neil Armstrong as he stepped foot on the moon.

Note: There was a very interesting question on the disccusion page of HW8, which made me realize that I forgot to say the following in class: "Although the FFT makes the computation of a DFT faster on a computer, it does not make it faster for the DFT that we ask you to compute by hand. The idea is that, for N large, the number of operations needed to compute an FFT is much lower than that for computing a DFT using the formula. However, when we ask you to compute a DFT by hand, N is typically very small, so using the FFT usually only makes things more complicated."

Previous: Lecture 29; Next: Lecture 31

Back to 2010 Fall ECE 438 Boutin

Lecture 31

Lecture 31 Blog, ECE438 Fall 2010, Prof. Boutin

Friday November 5, 2010 (Week 11) - See Course Outline.

Today, we continued modeling the vocal track as a sequence of tubes. We obtained the relationship between the airflows before and after the junction of two tubes. Combining this with our previous knowledge of the relationship between the airflows at the beginning and end of a single tubes, we obtained a matrix equation relating the airflows at the end of the glottis and at the exit of the mouth. I then attempted to write this expression explicitly for a sequence of 3 tubes. I now realize that the expression is too long for nothing. Next time, I will write the explicit expression for a sequence of two tubes.

Previous: Lecture 30; Next: Lecture 32

Back to 2010 Fall ECE 438 Boutin

Lecture 32

Lecture 32 Blog, ECE438 Fall 2010, Prof. Boutin

Monday November 8, 2010 (Week 12) - See Course Outline.

We began the lecture by obtaining an approximation of the transfer function of the vocal tract system using a simple model consisting of tubes of equal length connected to a tube of zero diameter. We observed that the transfer function of such a system is an all pole filter cascaded with a time delay. The poles of this filter determine the location of the local maxima of the voiced phonemes we pronounced; these local maxima are called "formants" and play an important role in the recognition of speech.

Related Rhea Pages:

Previous: Lecture 31; Next: Lecture 33

Back to 2010 Fall ECE 438 Boutin

Lecture 33

Lecture 33 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday November 10, 2010 (Week 12) - See Course Outline.

We began the lecture by discussing how to use formants to recognize voiced phonemes. More specifically, we discussed how phoneme samples (i.e. recordings of different people saying the phoneme in different situations) can be used to define regions in space (for example, a 2D plane) corresponding to different phonemes. It was noted that this is an example of the use of a standard technique from Decision Theory. If you are interested in learning more about Decision theory, you should consider participating in this coming Decision Theory maymester or taking my Decision Theory graduate course.

Many questions were raised regarding the changes induced in the formant frequencies by changes in pitch (e.g., men versus women voices). I would like to encourage each of you to try to experiment with actual voice samples to see what happens. Students sharing their results on Rhea will receive bonus points.

The second part of the lecture was spent talking about the short-time Fourier transform and sound spectograms. The issue of window function length and shapes were discussed, and the uncertainty principle of spectograms was stated.


Previous: Lecture 32; Next: Lecture 34

Back to 2010 Fall ECE 438 Boutin

Lecture 34

Lecture 34 Blog, ECE438 Fall 2010, Prof. Boutin

Friday November 12, 2010 (Week 12) - See Course Outline.

We began the lecture by discussing the students solution of the homework assignment, in which they were supposed to determine whether Neil Armstrong said "for man" or "for a man" when he stepped foot on the moon. Some people tried the upsampling+filtering approach in order to increase the resolution of the signal. Unfortunately, no one reported being able to hear the "a" sound with that approach. The second approach that was discussed was the formant comparison approach. The main difficulty with that approach is to determine the formants of the appropriate "a" sound to compare with. Some students used formant tables from the literature, some students tried to obtained the formants directly from words, in some cases directly from the speech sound of Neil Armstrong. The third approach that was discussed is to compare the "for man" part of the sound with the "for mankind" part of the sound, the idea being that if the signal between "for" and "man" in "for man" does not contain an "a", then it should be very similar (from the frequency domain point of view) to the signal between "for" and "man-" in "for mankind". Although the person who used that approach was not able to conclude definitively, I find this a very clever and original approach.

I am hoping several students will share their report on Rhea!

We continued with a discussion of wide-band and narrow-band spectrograms, looking at two illustrations from this document by Mike Brookes (the "my" sound, and the arpegio). Notice the constant formant frequencies in the wideband spectrum! We finished the lecture by giving a filtering view of the short-time Fourier transform, the proof of which will be given in the next lecture.


Previous: Lecture 33; Next: Lecture 35

Back to 2010 Fall ECE 438 Boutin

Lecture 35

Lecture 35 Blog, ECE438 Fall 2010, Prof. Boutin

Monday November 15, 2010 (Week 13) - See Course Outline.

We began the lecture with a proof of the linear filtering view of the STFT. Then we obtained a formula to reconstruct a signal from its STFT. This concluded the material on speech processing. We then began talking about image processing. Since images are signals depending on two (space) variables, we defined the 2D Fourier transform, which is also called the "continuous-space Fourier transform".

Previous: Lecture 34; Next: Lecture 36

Back to 2010 Fall ECE 438 Boutin

Lecture 36

Lecture 36 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday November 17, 2010 (Week 13) - See Course Outline.

We covered the inverse continuous-space Fourier transform (CSFT) and some basic properties of the CSFT. The emphasis was put on understanding how to extent these to the 2D versions of the other Fourier transforms we say (e.g., DTFT and DFT). We also defined some basic 2D signals.

Related Rhea pages:


Previous: Lecture 35; Next: Lecture 37

Back to 2010 Fall ECE 438 Boutin

Lecture 37

Lecture 37 Blog, ECE438 Fall 2010, Prof. Boutin

Friday November 19, 2010 (Week 13) - See Course Outline.

Today, we discussed the particularities of the CSFT of separable signals. We then listed some important CSFT pairs. We ended our discussion of the CSFT by giving the formulas for the CSFT in polar coordinates and discussed two properties (rotation and circular symmetry) that that can easily be derived from this other way of expressing the CSFT. We finished the class with a short introduction to image processing using an LTI system.


Related Rhea pages:

Previous: Lecture 36; Next: Lecture 38

Back to 2010 Fall ECE 438 Boutin

Lecture 38

Lecture 38 Blog, ECE438 Fall 2010, Prof. Boutin

Monday November 22, 2010 (Week 14) - See Course Outline.

Today, we showed how to process an discrete-space image by convolution with a function h[n,m]. We also looked at this processing from the frequency domain perspective. We looked an an example in detail (the low-pass filter illlustrated on top of this page).

Related Rhea Page:


Previous: Lecture 37; Next: Lecture 39

Back to 2010 Fall ECE 438 Boutin

Lecture 39

Lecture 39 Blog, ECE438 Fall 2010, Prof. Boutin

Monday November 29, 2010 (Week 15) - See Course Outline.

Today, we went over the solution of some old midterms, in preparation for the second midterm this coming Friday. We spent a lot of time on the representation of the vocal tract as a sequence of tubes and the corresponding transfer function.

Previous: Lecture 38; Next: Lecture 40

Back to 2010 Fall ECE 438 Boutin

Lecture 40

Lecture 40 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday December 1, 2010 (Week 15) - See Course Outline.

Today, we discussed the solution of some problems for previous final exams, in preparation for the second midterm this coming Friday as well as for the final exam. Note that the final exam is comprehensive and traditional style (not multiple choice).

Previous: Lecture 39; Next: Lecture 41

Back to 2010 Fall ECE 438 Boutin

Lecture 41

Lecture 41 Blog, ECE438 Fall 2010, Prof. Boutin

Friday December 3, 2010 (Week 15) - See Course Outline.

There was no lecture today per se, as we had the second midterm exam (in class).

Previous: Lecture 40; Next: Lecture 42

Back to 2010 Fall ECE 438 Boutin

Lecture 42

Lecture 42 Blog, ECE438 Fall 2010, Prof. Boutin

Monday December 6, 2010 (Week 16;dead week) - See Course Outline.

Today we had a special guest, Mark Shaw, who talked about color imaging. Mr. Shaw is an expert (Senior) Color Imaging R&D Engineer at Hewlett-Packard. You can find a copy of his slides here (pdf format).

Among other things, Mr. Shaw taught us that color perception is an "integration process" which varies depending on the person (esp. color blind individuals) and the conditions of the environment. He illustrated how our perception of color varies depending on the surroundings colors in an image, and how our perception of color varies depending on the conditions of the surrounding environment. He also pointed out that our visual system adapts to its surrounding, and that this adaptation influences our perception of color over time. Towards the end of the lecture, we saw a mathematical way to describe the perceived color in terms of the conditions of the environment.

Discussion

Any comments? Did you enjoy the talk?

  • I really enjoyed it. I'm not really into this side of DSP applications but I've heard some of the terminology before. I guess I never really realized just how much goes into deciding what a color is - especially when Mark explained about how, in the old days, they had to literally get 30 people to decide on one approximation of one color. That's ridiculous!! I'm thinking about the amount of manpower and time that goes into that sort of thing and in today's world, time is money and companies don't have that kind of time! ~ksoong
  • Post comment below.

Previous: Lecture 41; Next: Lecture 43

Back to 2010 Fall ECE 438 Boutin

Lecture 43

Lecture 43 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday December 8, 2010 (Week 16;dead week) - See Course Outline.

Today our special guest, Mark Shaw, presented the second and last part of his talk on color imaging. his talk on color imaging. Among other things, we learned about different ways to write color coordinates (e.g., in spectrogram terms versus in perception terms) and different ways to quantify color similarity. We also learned about the pipeline to map the colors of one device onto that of another device.

Discussion

Any comments? Did you enjoy the talk?

  • I really enjoyed it. I'm not really into this side of DSP applications but I've heard some of the terminology before. I guess I never really realized just how much goes into deciding what a color is - especially when Mark explained about how, in the old days, they had to literally get 30 people to decide on one approximation of one color. That's ridiculous!! I'm thinking about the amount of manpower and time that goes into that sort of thing and in today's world, time is money and companies don't have that kind of time! ~ksoong

Previous: Lecture 42; Next: Lecture 44

Back to 2010 Fall ECE 438 Boutin

Lecture 44

Lecture 44 Blog, ECE438 Fall 2010, Prof. Boutin

Friday December 10, 2010 (Week 16;dead week) - See Course Outline.

Today was the last class of the semester. I distributed the final exams and we went over the solution.

Previous: Lecture 43

Back to 2010 Fall ECE 438 Boutin

Please do not edit this page. If you want to add/remove something, just copy the code on a new page and edit only that new page. -pm

Retrieved from "https://www.projectrhea.org/rhea/index.php?title=Lecture_Blog_ECE438_F10&oldid=43690"
Shortcuts
Help Main Wiki Page Random Page Special Pages Log in
Search

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett