About me

I am a consultant in comm systems. I worked for last 20 years at
Loral Space Systems In Palo Alto, CA, where I had a Distinguished Engineer position. I was involved in all sorts of communication system designs. My work involved simulation of signal quality through the satellite links. I used SPW by Synopsys for most of my work but also Matlab.

Before Loral, I worked at Booz, Allen Hamilton, Aerospace Corporation and Northrup, in Los Angeles. I have a MSEE from USC.

I write these tutorials for fun and for love for my field. It is forever challenging and fascinating. I am currently writing a book on link budgets and, hence have not been able to add any new tutorials.

I will be giving a talk in Ukraine on May 16th on the use of Matlab for spectral estimation.

I was born in India, came to US with my parents while young and went to school in California. I am also the author of children books, “The Reading Lesson” and “The Verbal Math Lesson“. These are wonderful books, if you have young children, please check them out.

I am married, live in Danville, CA, and have two grown children. One works at Apple Computer and the other runs a Publishing company. Over my 45 year career in engineering, I have given many talks to school and college groups on topics related to electrical engineering as well, as women in engineering. I have had a wonderful, rewarding career and if you would like me to talk about any of these topics, I am happy to do so.

If you have questions/comments on digital communications or signal processing, please post them on the relevant topic page.

Charan Langton

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LinkedIn page:

66 Comments on “About me

    • Definitely a fantastic website.One has been referring to it since 2007 .One is proud to have benefitted from your hard work Charan , knowing that you hail from India.I have purchased the Kindle edition of your Fourier Series book which is proving useful in preparation for a forthcoming interview.It is extremely well written as are your other tutorials, having a very fundamental approach enabling good understanding by the reader.Great work

  1. I greatly appreciate your efforts in putting these pages together. I have seen your previous versions and this one seems to be more refined. Facebook page has increased its utility even further. I am not directly involved in Digital comm but I do read material on the subject to keep my self updated. I also share these with my students and colleagues. Thanks one more time for efforts and time.

  2. I started my career in Digital comm and moved to Audio DSP.
    I came across the OFDM article that i took a print of some years ago and was lying in the desk. I didnt understand it then but read it again recently. It was so clearly written an simple to understand. It was an “Aha” moment and want to mention my thanks.
    Keep up the good work


    • Srikanth,

      This paper on OFDM seems to be most popular of all my articles.
      Probably because the issue of the inverse FFT is so confusing.
      Glad you liked it.

      Charan Langton

  3. Hi,

    Just wanted to let you know that I’ve found your tutorials hugely helpful. I spent a lot of time looking at different books and tutorials and yours are my favorite.

    Please write a few chapters on equalizers! I’ve now read many different tutorials/book-chapters and I never manage to keep up with the mathematical notation.



  4. Dear Charan Madam,

    I have doubt in Digital signal Processing.My question is that for determining frequency component of the samples we are using DFT which involves complex quantity.we kow that this DFT is derived from the complex fourier series of a Periodic signal by tending its time period to infinity then we discretize the fourier transform for finite length sequence.can’t we use the Fourier transform which is derived from the real Fourier series of the periodic signal by tending its time period to infinity then we make it use for finite length sequence which will have only real quantity. this is the Discrete Hartley Transform.This also has fast computation algorithm.Could you explain me abou this.


    Arunpradhap Natarajan

    • Discrete signals are different than continuous signals in that we can not determine the true frequency of the underlying signal. A discrete signal can represent a lot of different analog frequencies. Because of this the DTFT repeats and CTFT does not. We can not sample CTFT to represent the DTFT for this main reason.

      Once the signal is sampled, then you can use either DFS (discrete Fourier series) or DTFT or DFT but not CTFT.

      BTW, whenever we are talking about any kind of “fast algorithm”, we are referring to computation on a discrete series.

      Charan Langton

      • cant we derive the CTFT in terms of real quantity from real fourier series if so give me that equation


        Arunpradhap Natarajan

        • No you can not. There is no per say connection between real quantity and CTFT. One is a quality of a signal and the other a mathematical procedure on the whole signal.

          This is a very general question you are asking. It does not have a answer in a “equation”.


          • Dear Charan Madam,

            If I have rectangular pulse with duration 0 to T whose fourier transform is sinc function of only positive frequency or it includes negative frequency also.If it includes negative frequency what is the meaning of negative frequency in the puslse having positive duration only


            Arunpradhap Natarajan

          • Dear Madam,

            if we can’t derive the fourier tranform from real fourier series then how the Discrete Hartley Transform exists

            thanks with regards

            Arunpradhap Natarajan

  5. Dear Madam,
    In Hilbert Transform -90 dgree phase shift is produced if we the signal frequency is f>0

    and produces +90 degree phase shift for the signal if the signal frequency is f<0.If I have a bandwidth

    of frequencies 0 Hz to B Hz how could the Hilbert transform will produce the +90 degree phase shift since

    I don't have negative frequency

    Arunpradhap Natarajan

  6. Dear Charan Madam,

    If I have rectangular pulse with duration 0 to T whose fourier transform is sinc function of only positive frequency or it includes negative frequency also.If it includes negative frequency what is the meaning of negative frequency in the puslse having positive duration only


    Arunpradhap Natarajan

  7. Hi Charan,

    Just a quick email to say thanks for your great website. We’re a maritime VSAt operator (incidentally using various SSL-built satellites..) and your tutorials have been very useful for a number of our guys.

    Many thanks again and keep up the good work!

    Kind regards,

    Bertrand Hartman
    OmniAccess S.L.

  8. Hello Charan,

    I love this website. I just finished my MSEE project, and your tutorials on MIMO and OFDM were both extremely helpful in learning these topics (especially since my program isn’t up to date and doesn’t quite cover these topics).

    Just a note: On tutorial 10 (TWTAs), the right side of some figures and equations seem to “end early.”

    Thanks for your using your free time to teach the next and existing generations of comm engineers πŸ™‚

  9. Thank you so much for the effort you have put in to make these topics so approachable. Your section on modulation (All About Modulation Part 1) is the most understandable description of the topic I have found. I wonder if you would be open to adding a short section showing the spectrum of, for example, QPSK modulation, being the convolution of the baseband and carrier signals. I would be happy to help if you find your time too committed at this time. And if you want to leave well enough alone, it is still a great explanation of the topic!

  10. I am currently doing my Master’s in telecommunication, and while I am hardly a DSP guy, OFDM is clearly important in everything. I have really enjoyed your simple (and example-supported) explanation, and wanted to thank you for all your effort. The tutorial definitely goes in my “background folder” if ever need to refresh my memory!

    Best Regards

  11. Hi Charan,

    This website is awesome. You write the tutorial in such style that a beginner like me can understand the concept. You did a great job. I really want to say thank you for what you are doing.

    I am also looking for LDPC Code tutorial. But unfortunately I did not find it in here. Could you please write a tutorial about LDPC Coding and Decoding? I really like your explanation style. I hope you grant my request.

    Thank you again.

    Best Regard,

  12. It’s been 20 years since I needed to delve deeply into these concepts. I’ve been building lasers, imagers, and other photonic devices until recently and was struggling to come back up to speed. Your website and very lucid explanations have helped considerably. I’m so glad I stumbled into it. Thanks for your efforts to educate us all.

  13. Hello Charan,

    I have referred your tutorial on MAP turbo decoding algorithm, it guides the engineers who implements the algorithm and have not found anywhere such a clear explanation.it is great work. Request you to update the tutorial on Max-log-Map turbo decoding algorithm also, since it is difficult to represent the data in fixed point for MAP decoding algorithm.

    Best Regards

    • Thanks Ramamurthy.

      I remember, it was a tough one to do.
      I had someone point some errors but have not had time to update.
      Thank you for you comment.

  14. Hello,

    This May, the Institution of Engineering and Technology will release a publication that I feel will be of interest to you entitled Digital Communications: Principles and Systems.

    Digital Communications: Principles and Systems provides a thorough grounding in digital communications using an innovative engineering-first approach to build a nonmathematical overview covering building blocks, signal processing tasks, general features and design considerations. Topics covered include transmission channels, source coding, digital baseband transmission, digital modulation, noise impact in digital transmission, error control coding, advanced signal enhancement techniques for wireless channels and digital transmission link analysis and design.

    The reader is given an insight into the engineering concept and the underlying physical considerations, a clear appreciation of the parameters involved, and an understanding of the interplay of these parameters. The book includes several unpublished original derivations, new insights and alternative approaches that make the understanding of key topics and their application much easier.

    Digital communications: Principles and Systems is an ideal textbook for those who wish to:
    β€’ gain a thorough understanding of the core principles;
    β€’ undertake digital communication systems analysis;
    β€’ design and computer simulations;
    β€’ deal with specialized applications;
    β€’ keep up to date with advances in the technology.
    Topics covered include:
    β€’ overview of digital communication
    β€’ linear channels and systems
    β€’ nonlinear systems
    β€’ sampling of baseband and band-pass signals
    β€’ quantization and PCM
    β€’ source coding and lossless data compression
    β€’ line codes
    β€’ transmission through band-limited AWGN channels
    β€’ transmitted digital signals
    β€’ noise impact in digital transmission
    β€’ error control coding
    β€’ digital transmission link analysis and design
    About the Author:
    Ifiok Otung is a Chartered Engineer with broad and international experience of research and teaching at various universities in Europe and Africa. He has previously worked as a consultant for the UK Electrical and Electronic Engineering Assessment Network and the Engineering Subject Centre of the UK Higher Education Academy. He has authored over 110 publications, and is a regular reviewer of technical articles and textbooks for some of the world’s leading academic publishers. Ifiok Otung is currently Professor of Satellite Communications at the University of Glamorgan, where he teaches MSc courses in Satellite, Mobile and Digital Communications.

  15. Dear Mrs Langton,

    This is a spontaneous email after one of the can’t remember how many times I have visited your website. The material you provide has helped me incredibly. The way you present all these complex topics is compact and clear at the same time. You are a great teacher and I hope you keep providing us with your wonderful tutorials.

    Best Regards,
    Panos Papaioannou

  16. Dear madam,
    Its great and best website and was very helpful in communication field. I always look for this website frequently.
    I am doing a project on ‘MIMO-OFDM with Beamforming’.
    The aim of project is : to write a code in matlab and calculate BER rate accordingly and also calculate inter user interference(IUI) if more than 2 users are transmitting at the same time to a base station.

    I am very confused on how to implement OFDM with beamfoming technique.
    It will be a great help and very pleased if i get any related codes/concepts which make me understand and get going.

    Your’s Faithfully,
    IIT Madras

  17. Great website! Loved the explanations, your notes, wonderful resource for teaching. (I have been invited as a guest lecturer at COEP, your notes are helping me a lot! πŸ™‚ )

  18. Thank you so much for the great website and your effort. After so many searches in the internet finally found the website with amazing understandable tutorials.

  19. Hi, glad i found this website.

    just reading how dft is borned from womb of fourier series…

    but still confusing and many questions are arised fOr me while reading,


    I WILL NOT ASK YOU UNTILL I GET DEFEAT WITH THESE CONCEPTS( means iput my 100% first and then i will ask you admin)

    (from: india)

  20. Hi. I was going through the first part of modulation tutorial. The Offset QPSK section has an inaccuracy in the I and Q channel diagrams. The Q channel is supposed to be offset by half a symbol time i.e. one bit time. But the figure shows the offset of half a bit time. Please correct me if I am wrong else correct the figure πŸ™‚

    Thanks and regards

  21. Mam,
    I really loved the contents on provided by you. I am planning to design a communication payload system for c-band for which i did the eirp calculation considering the ber of 10^-5 and noise temperature to be only 293k. Mam how should I proceed to get the specification of various components

  22. Hello Charan,

    First of all thank you for your efforts in building up such a good platform for people who are interested in DSP and other related fields to communicate and study. I just started touching DSP for like 3 months and I take a look at one of your tutorials that is called ‘Fourier Transform of continuous and discrete signals’, and it really does help. It clarifies lots of conceptional questions that confused me for quite a long time, and even my prof cannot clearly answer some of those. I haven’t finish reading that tutorial, and so far I have a question regarding the FT of the Periodic signal. As you mentioned in that tutorial, even though historically initially we use FT for aperiodic signals, but it is also applicable for periodic signals, and the result will be the discrete replicas of the FT of the original time domain function. I also heard about the Poisson Summation, and in fact they look quite similar, so I am wondering if there is any potential relationship in between?

    Another example is when you take the FT of an sin function, which means you are taking the FT of a periodic function, but we usually will do the truncation and will only take the FT within one period, which will yields two impulses at two side of the frequency domain. And if I choose to consider the whole frequency domain instead of within one period, then the finally frequency spectrum will be the replicas of the impulse, is that a right inference? Is that the reason why we usually choose to do FT of periodic signals within one period? Thank you.



    • The CTFT and the DTFT of a sine wave is just two impulses at the frequency of the signal. When you do the DFT, if the length of the DFT is not equal to the integer multiple of the period length (in samples) then, you will see other components. I am not sure about your Poisson comment. I will have to look into that.

      There is no repeating of the impulses for the sine for periodic or a single basic case. I may not have explained this well in the tutorial. I will be posting a new one.


      • Really appreciate for your replay and I am looking forward to your further tutorials. If you have some ideas regarding the Poisson Summation, please leave me comments. Thank you.


  23. Dear Sir/Madam,

    i referred your material tited “Linear Time invarienr (LTI) systems and Matched filter” which is available at http://www.complextoreal.com. It is very useful for my lecture and building some applications related to the radar signal processing. Thanks for it.
    I would like to have some materials related to “Ambiguity Diagram” where i required clear description like the above mentioned topic.

    Please sir….

  24. Hi Charan,

    Your tutorials are beautifully written. I wanted to thank you for your very well written material. I would appreciate if you specifically introduce me with a well written book in digital communications. I have Digital Communications written by Proakis but unfortunately it is not rigorous enough. It has a lot of content but most of them without any proof.

    I am looking for a book that is very well teaches the concept intuitively, proves mathematically in a well understandable manner or it gives enough information that I can research the rigorous proofs myself.

    I am an engineer with almost 20 years of experience in the field of DSP so I am not completely unfamiliar with the subject.

    Thanks for your recommendation


  25. Hello Mam,

    Ihaverety started following your tutorials, you seem to have a great in depth knowledge subject specially in regard to practical aspects of it.
    I have benn reading many on same however there approach is very therotical.
    Iam obliged to be taught by the the masters in the field.
    looking forward for your book soon and specially for Indians.
    Thanks Once again.

  26. Thanks a lot, i want to know on synchronization in communication (concept,basics and foundamentals) and i would appreciate if you help me.

    • It keeps getting delayed as we find more and little errors in it. having an eBook has helped us to clean it up. But I think, now it is planned to start printing in Mid March and should be available by end of April on Amazon.
      Thanks for sending me that error. Will look at it and fix it. Thanks again! – Charan

      BTW- What did you think of the other chapters?

  27. Hello Charan,

    This is Seth the physics student from UCLA. I enjoyed our discussion on the flight from Oakland, and thank you for your insight on weighing career options.

    The work I mentioned related to solitons is referenced on our research webpage: http://acoustics-research.physics.ucla.edu/solitary-waves/

    On that page there is a video of the effect along with a few pictures and citations.

    Best Wishes!

    • Hello Seth,
      Please send me your address. I promised to send you the copy of the book which I will do.
      Hope your new school year is going well. – Charan

  28. Hello Charan,

    My students and I have greatly enjoyed your tutorials over the years. Would you possibly be available for a brief Skype conversation with my senior digital communications class, to talk about what a career in communications looks like, and to share any career advice you might have for them?

    Sincerely, Tim

  29. Dear Madam,

    I do a lot of bird song recording and song analysis in India, and In the pursuit of getting deeper understanding of song signals and fourier transform I got and read a few chapters of your book-the intuitive guide to fourier transform—– available on the net. I am very impressed by the clarity and style of presentation of the subject. I am also highly impressed by the other related material on your website which I am slowly reading. I wonder whether you can send me pdfs of last three chapters of your book, so that I could complete the reading.

    Best regards

    Pratap Singh

  30. Dear Charan Langton

    Thank you for your “all about modulation-Part I” about pi/4 QPSK and pi/4 DQPSK explain.I am an electronic engineer of china, I want to consult you about how to demodulate pi/4 QPSK and 16QAM,GSMK by I Q phase angle. Do you have any relevant tutorials?


  31. I am grateful for your wonderful tutorials. I want to express my gratitude and hope you realize how much of a difference this material is making on my life.

  32. Charan hi,
    I would like to get the second printing of your Fourier Analysis book – can you tell me how I can do that – Amazon does not say which one one gets if one selects the books/kindle version shown ?

  33. Hi Charan- I was trying to reach you via a FB message but in case good see this first could you please e-mail me? I had written up feedback for you on your nice filter write-up that I thought you would be interested in seeing. It is too long to post here and includes graphics.

  34. Very nice work here. Also, very pleasant to see that you got MSEE from USC. I guess we may have had similar time frame at USC. I had MSEE from USC too, it was about the middle of 80’s. I got also PHD from USC in 91. I love all of your tutorials. Post of your new book announcement here when it is ready. I have seen Chapter 2 of your book and it looks fascinating!

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