Hello Mariusz Do you have suggestions for reference materials such as books, online, etc? Thank you, John

HI, Looking forward to this study group, but i will not be in every session Live! Impossible. I do all my important thing early in the morning which conflict with the time in some day. For me, it will be a great Review, in addition to learn Matematica since what i have used in the past is MATLAB.

References: There are too many books in Signal and System and many of them using Matlab. So Ignore Matlab and learn to transfer to Mathematica. The study group has already has all the book prepare. Thank you!!!!!!!!!! This is great.

BOOK: 1. Check Proakis,
2. Another is M.J Robert "Signal and System" but ignore MATLAB and learn Mathematica (what I will be doing, personally). 3. SCHAUMS's series has a great paperback "Signal and systems" . I always buy a paperback low cost for every course i have taken in my life, from electronics, physic, chemistry, control etc.

Below several links of webpages dedicated to signals and systems http://www.dspguide.com/pdfbook.htm (DSP GUIDE --goes thru Signal and systems) https://www.thefouriertransform.com https://lpsa.swarthmore.edu (La Place) https://fourierandwavelets.org/ https://ocw.mit.edu/search/?q=signal+and+systems (MIT free recorded courses)

Will there be exercises available to download? Thank you, John

Hi John, That is correct. For each lesson (except for L01) you will have a set of exercises, shared after the session is completed.

Thank you, Leila Enjoyed your class today. I am new this topic and new to Mathematica. This class will be helpful for both.

Hello:

I am traveling and only have the cloud available to me for Mathematica. Furthermore, I do not have the availability, with my subscription to the cloud, to upload notebooks into my cloud account. Consequently, I will not be able to reviewing the exercises and their solutions in "notebook" format and that is why I asked if the exercises and their solutions could be made available in possibly PDF format.

Thanks,

Mitch Sandlin

TO EVERYONE (STUDENTS) Above I place some links. I do recommend checking the MIT free Course on Signal and system Why? it aligns with this study group in the Topics, you can download each Chapter and Video and the professor is Professor Oppenheim. I am sure you can find the entire Book not chapter by Chapter.

To download faster use "Chrome" or IE 11 (not Microsoft edge) so that you use "right click and save the MP4 videos". Any Other course free in the MIT you can download videos and resources. They have over 600 courses free (good for refresh material if you have attended any engineering school).

If you use Microsoft edge, you will not see the download link and will default to ply the Video. Also check this link https://fourierandwavelets.org/ and download the free two Books and the Matematica books with the PDF. They will complement the learning on this study group. The Workbook ZIP/TAR provide is just the syntax under Mathematica along with the exercise. I will attend the Fridays class and sporadic during he week.

https://ocw.mit.edu/courses/res-6-007-signals-and-systems-spring-2011/pages/introduction/ Instructor: Prof. Alan V. Oppenheim
Course Number: RES.6-007 Departments: Supplemental Resources
As Taught In: Spring 2011

Hi Jacek, An email was just sent out with a link to download the exercises. Please check again.

OK, thank you. Now I can see the exercise folder populated. It was empty earlier today. But the exercises start with lesson 2. today's is missing

Jacek, That's correct. There are no exercises for Lesson 1 (Introduction). For today's session, you have L02 exercises.We covered L01 and L02 today.

Hi Wilfredo, I will ask our team to include Poll questions if possible. As for the cell brackets, in the notebook, if you evaluate the following, it will hide the cell brackets for all your notebooks: SetOptions[$FrontEnd, ShowCellBracket -> False]

Hi Wilfredo, thanks for the additional links and great suggestions for additional course materials. As I posted earlier, Oppenheim's version is my preferred Signals and Systems reference. There are of course other notable authors in this area - Lathi in particular. Oppenheim's recordings are great but be forewarned, their length, each a typical class session, requires a level of commitment that many nowadays find challenging. However, if you are up to it, absolutely, dive in and learn from one of the premier educators in this area of electrical engineering. I am also a great fan of your other suggestion - the Foundations of Signal Processing by Vetterli and Kovacevic. As the title suggests, it truly is an introduction to the mathematical foundations of signal processing and the most recent attempt to redefine how this topic is taught.

I tend to use Matlab in conjunction with Mathematica. Is it worth getting the Signal Processing Toolbox.

I find it useful that you can run python, Julia and Octave scripts in a Mathematica notebook.

Hi, do we need to turn in the "exercises" notebooks or is it only for our own practicing and learning?

Arturo, They are for just for practice, nothing to turn in. Later in the course, they will post quizzes to be completed online and these will count towards the certificate of course completion. Steve

Hi;

What was the answer to Poll #1 of Lesson 6. As an aside, it would be helpful if the speaker in speaking, would slow down a little and place a little more emphasis on articulation.

Any update on getting the exercises in a PDF format?

Thanks,

Mitch Sandlin

To what extent the course's focus is going to continue on electrical circuits (this is seemingly such an old content XIX/XX c. :-) ) ? Such focus seems unnecessary (and it may be create a barrier for some people) in order to get at signal types/characteristics and signal processing. Though I am an electrical engineer by original training, my current interest in signal processing is more general. My specific interest is from the perspective of analyzing human neuro-physiological signals and the systems I study are human-machine systems. Hence my domain agnostic interest in signal processing.

Also: Are we going to get to multiresolution wavelet analysis?

Thanks - Jacek

I'm a little confused about the solution to Exercise 6 (the last) in L07CTSolutionMethods.

Find the solution of the following nonhomogeneous differential equation with given initial conditions:

y''(t)+Sqrt[2]y'(t)+y(t)=sin(t), 	y'(0)=0, y(0)=0

The forcing function is sin(t) but in the solution the DSolveValue has the equation with "Sin[t] * UnitStep[t]" (i.e. UnitStep[t] is added):

DSolveValue[{y''[t] + Sqrt[2] y'[t] + y[t] == Sin[t] UnitStep[t], 
   y'[0] == 0, y[0] == 0}, y[t], t] // Simplify

Why is the UnitStep function added to the equation here? Are there some underlying assumptions about this question that I've missed?

Dear Zbigniew, one of the two reasons for the solution method I suggested for finding the impulse response is actually exemplified by your calculations. I did not want to explain the presence of the unevaluated Heaviside[0]. Also, most undergrad engineering students enter a course like this with some basic introduction to differential equations which usually does not include a discussion of singularity functions.

I do want the notebooks to address the needs of students with and without familiarity with Mathematica. The step-by-step evaluations are for the latter.

BTW, I get the following results:

In[2]:= Integrate[Sin[x] DiracDelta[x - 2], {x, -\[Infinity] , \[Infinity]}]

Out[2]= Sin[2]

and

In[3]:= Integrate[Sin[x] DiracDelta[x - 2], {x, 0 , 5}]

Out[3]= Sin[2]

[WSG22] Daily Study Group: Signals, Systems and Signal Processing

If of any help, I checked for eventually different output emerging from different input and, as it is seen below, we get the same result:

Thanks @Mariusz Jankowski Thanks for explaining. The current study group content is very much what I was learning in mid-1980s in Poland (Politechnika Lódzka) when I studied electrical engineering and control systems, just without Mathematica :-) . A nice refresher! (I moved later to human factors engineering and psychology).

Do you know of any study group which would focus on multiresolution analysis using wavelets (discrete)?

Sometimes there seems to be little correlation between the video and the lesson notebooks eg Convolution.

Is there a notebook of the video lecture that corresponds to L09CTConvolution.nb ?

Dear Mariusz, Thanks for this careful explanation. I understand completely why the method that Leila and you recommend works. What I don't understand, however, is this:

• Why HeavisideTheta[0] does not reduce to zero? Why is it left UNDEFINED? And
• Why HeavisideTheta[t] does not reduce to one for t > 0?

In other words, why Mathematica fails? The two solutions I presented earlier and you just repeated have to be equivalent, as they are the solutions of the SAME problem. Both should result in Exp[ -t ].

Hi Doug, the convolution video is actually an outlier in terms of how much it differs from the lesson notebook. Most videos will stay much closer to the text in the notebooks.

The reason for the difference you observed is the nice explanation of convolution as a superposition of responses to scaled and shifted pulses that was added to the video but is missing in the notebook.

So, here is a notebook that re-creates that part of the video.

Hi Zbigniew, sorry, I am not able to answer that question, but will forward it to the Calculus and Algebra Team at Wolfram for comments.

Thanks Mariusz The video on convolution piqued my interest regarding Convolutional neural networks.

Can we classify neural networks under this current mathematical scheme? Neural networks are time invariant but nonlinear , so a form of nonlinear time invariant systems .

Is there a correlation between the mathematical convolution integral and the mathematical bases for convolutional neural network or is this just a "classification " error and unrelated?

Thanks! how do I download it to a local .nb file? When I click on download and select "Continue with FIle Download" it downloads something, but it is not an .nb file - for me it looks like ".com.google.Chrome.tU6ZVD"

You are replying on a totally different topic. I am talking about a link to a "Embedded Notebook" from a reply in this forum. Download does not work for me.

Click on "Make your own copy" to open a copy of the notebook in Cloud. Then File> Download. You could also click on a cell bracket here in the notebook, copy the cell and paste it into your own notebook.

I copied the following as input text. Without attaching the notebook, how do I copy and post WL input like this to our community group so it is more readable and also easy for readers to copy and execute in a notebook?

GraphicsGrid[Table[
  DiscretePlot[((2/3)^(n/2) Subscript[\[ConstantC], 1] + (-1)^
       n (2/3)^(n/2) Subscript[\[ConstantC], 2]) UnitStep[n], {n, -5, 
    20}, PlotRange -> {-2, 2}, PlotStyle -> PointSize[0.02`], 
   AxesLabel -> {n, y}, ImageSize -> {400, 400}, 
   PlotLabel -> ("\!\(\*SubscriptBox[\(\[ConstantC]\), \(1\)]\) = " <>
       ToString[N[Subscript[\[ConstantC], 1], 2]] <> 
      ", \!\(\*SubscriptBox[\(\[ConstantC]\), \(2\)]\) = " <> 
      ToString[
       N[Subscript[\[ConstantC], 2], 2]])], {Subscript[\[ConstantC], 
   1], {-1, 1/2, 3/2}}, {Subscript[\[ConstantC], 
   2], {-1, 1/3, -3/2}}]]

Same here.

Hello all, I thought some of you may be interested in seeing the details of the convolution example shown in a recent lesson video. Here is a copy with some small edits.

Regretfully I need to unsubscribe from the Signal Processing study group. I thought I would have time to participate, but my current schedule will not allow.

Hello Rui and welcome! If you have signed up for the study group you will receive emails with the updated material. If you have registered and have not received the material, please send an email to our Wolfram U team at wolfram-u@wolfram.com.

Can we get Fridays recording please (Week 2 Review and Fourier Series)

In case you missed today's online session, we've released six of the eight course quizzes, for the material covered during the first three weeks of this Study Group. Successful completion of all eight quizzes is required to earn a certificate. Check your recording notification email today for links to the quizzes.

Looking forward to any discussion, but please send any technical questions about the auto-graded quizzes by email to wolfram-u@wolfram.com, so we can address those directly. Also, we ask that everyone refrain from discussing specific quiz questions on this Community forum. Thanks!

Could you please release the Vid for June 1st, as it is still not available.

While traveling, I am relying solely on the Wolfram Cloud to perform all required calculations associated with the Signals Daily Study Group.

However, when copying Problem 1 in Lesson 11 (see attached) to the cloud and then trying to execute the solution to the problem using RSolveValue[], I receive an error message which does not allow me to duplicate the calculations that you performed in the lesson notebook (see attached). I am going to need to use the cloud in answering the Quiz problems associated with the Study Group.

If the cloud is incapable of performing the calculations, I may need to wait until returning home in mid July to complete the Quizzes.

Thanks,

Mitch Sandlin

Attachments:

Screen Shot 2022...png

Screen Shot 2022...png

Thanks, Restarting the session did the job.

Mitch Sandlin

Gerald, did you find a solution to your problem?

FindMaximum seems to work:

FindMaximum[g[t], {t, 2.0}]

{0.503408, {t -> 2.25}}

Note that it give a warning about tolerance.

Hello Hakan, please take a look at the attached notebook and let me know if you have more questions.

The links of all recordings of the study sessions can be found on this page.

The link you're looking for can be found here.

I have two questions:

(1) In the interface for this community share, next to the "Add Notebook" icon is an icon to add a code sample. When I place my cursor over it, it states "Code Sample < pre> < code> Ctrl+K". Please explain exactly how to use this to enter a readable code sample. When I try it, I get the same thing as when I just copy and paste. (I am using the Google Chrome browser.) For example, I get the following:

Subscript[X, \[Delta]](j \[Omega])=1/(2 \[Pi]) \[ScriptCapitalF]{x(t)}*\[ScriptCapitalF]{Subscript[x, \[Delta]](t)}

(2) In file L30_Sampling.nb, I have two questions about the derivation following the cell that states "The Fourier transform of the signal Subscriptx, [Delta] may now be obtained by making use of the Fourier transform time-multiplication theorem (symbol * denotes convolution):" In the first line of the derivation should the argument of the rightmost Fourier transform be Subscript[Delta], T rather than Subscriptx, [Delta] ? Second, please show the detailed steps used to derive the Fourier transform of Subscript[Delta], T as shown in the second line of the derivation. (I assume linearity is used so that the derivation involves transforming the individual terms in the definition of Subscript[Delta], T.)

Quiz 8 has been released as part of the course framework made available to our Study Group participants. Please check your recording notification email sent today and upcoming reminder emails for your link to the pre-released course framework.

Hello, to the staff, could you please double check the "correct" answers for Quiz 6. Thanks.

Hi, I see there's no video for L31, but the certification requires the watching...

@Arturo Pazmino, we have double checked Quiz 6, and the correct answers all check out OK.

If you are experiencing something in the course that doesn't look right, please report it to us at wolfram-u@wolfram.com. Thank you!