Intuitive Guide to Fourier Analysis and Spectral Estimation book

The Intuitive Guide to Fourier Analysis and Spectral Estimation
with Matlab
For science and engineering students and practicing engineers
Hardcover, 320 pages, printed in color, available now.
Book is in second printing now. If you have the first printing and
want to exchange it for the new one, please email me.

Errata Sheet – Please post errors/comments  here. Thank you.

Matlab code is below.

28 comments on “Intuitive Guide to Fourier Analysis and Spectral Estimation book
  1. Charan L. says:

    Post comments, questions here. Thank you and please post a review of my book on Amazon (only if you like it!)

    • Mykola says:

      Hey Charan! I have read the first 6 chapters of the book and I really enjoyed it. I like the way the material is presented to the reader (along with the examples) and the overall structure of the book. Specifically, I am reading the 2nd edition of Kindle version available on Amazon. I think I might have encountered typos in couple of places and come up with some points which might be improved in the next edition of the book.

      Please find the comments below.

      // Typos
      On page 73, in the code snippet for “xd”, the symbol “}” is probably unnecesary.
      The equations 3.8 and 3.9 do not seem be consistent. You have already divided the argument to tri function by the period T, division by T is not needed in 3.8.
      On page 79, in the code snippet for a sinc function “habs = abs(h1)”, there is no variable “h1” defined. It should be probably “h”.
      In equation 3.34, the power multiplier “k” for the first exponential is not needed.
      In the comment to figure 3.19 explanation for cases (a) and (b) are misplaced.
      On page 98, to describe equation 3.38 you refer to equation 2.25. It should be 2.24.
      Figure 3.23 is missing some samples for case (a) – 8 samples instead of 10.
      In example 3.10 on page 103, where you compute Ck, sigma symbol is missing in the formulas.
      In example 3.11 on page 104, where you compute C1, C2, C3, the formulas are missing 1/4 multiplier and the sum should loop over “n” instead of “k”.
      In equation 4.22 (2nd row), “j” has already been moved out of the sin expression. “j” squared is not needed inside the sin expression.
      In example 4.5, the power “-1” is missing to indicate that it is inverse transform for x(t) expression.
      Before the equation 4.32, you provide a formula to calculte X(w) for the Gaussian. Can you move 1/2 multipler out of the integral? It seems to come from the final integration result.
      In example 4.8, where you replace X(w) with 1, should you change integral bounds from -W to W as well?
      In equation 4.34, argument to sinc function should not be divided by PI.
      On page 137, the formula for x(t) and the computations based on x(t) are missing “k” in the power of the complex exponential. It is correctly used in equation 4.35.
      After equation 5.6, you write “Here we show a easy”. Should be probably “an easy”.
      In example 5.2, bottom of the page, “imaginary” part should have “+” before the second sin parameter.
      In example 5.4, you refer to figure 5.7 (at the top of page 158). Should be figure 5.11.
      Equation 6.3 is missing minus sign in the power of the complex exponential.
      In a comment to figure 6.5, it is said “DTFT is shown as a dashed line for reference”. The DTFT is shown as a solid blue line.
      In example 6.2, X[1] should be 2 – j + 3 + 4j = 5 + 3j. In example 6.3, X[1] should be 5 + 3j, and X[3] should be 5 – 3j with the reverse step updated respectively.
      On page 182, where you define the twiddle factor, a minus sign in the complex exponential is missing for the equation 6.11 to be valid. Note that equation 6.15 correctly includes minus sign in the twiddle factor.
      In equation 6.14, the normalization factor probably should not be part of the formula for the inverse matrix. It is not clear what is the intention behind the symbol “*” as a power.
      In equation 6.16, the matrix element n = k = 3, should be -j.
      In example 6.4 you refer to equation 6.13. It should be 6.3.
      In example 6.4 the formula for DTF is not correctly written for -3 and 5 samples. Their exponential powers should be -j*4*PI*k/5 and -j*8*PI*k/5. The formula for computing DTFT on the next page should be updated as well.
      On page 189, for the matlab code, you might want to rename variable DFT7 to DFT5 to be consistent in naming.

      // Things that might be improved or additionally clarified
      In equation 3.2 you start using “symbol” of delta function without elaborating much on its definition/usage.

      In equation 3.4 you start using convolution symbol “*” without explaining the meaning behind it and the convolution operation.
      Might be a good idea to add “Convolution operation detour” section.

      In chapter “Reconstruction of an analog signal from discrete samples”, you say that “signals are often sampled to reduce their bandwidth”. What is bandwidth? I do not recall you mentioning signal bandwidth before in the book. As a reader who does not have much knowledge about signal processing I am feeling a bit lost by this statement. It sounds “empty” and out of context. I do see that the notion of bandwidth is introduced later in the chapter on Shannon’s Theorem.

      The definition of the rect function (equation 3.6) looks rather incomplete to me. As a reader, I would like to see the actual definition of the function instead of simply giving the idea of usage since it is used for the calculations.

      On page 120, at the bottom, you state “we are missing the same term from all coefficients, hence, the Fourier transform determines relative amplitudes”. It is not clear from the description what “the same term” is.

      Many thanks!

  2. Ramakrishna says:

    maam, how can i get this book?
    Is there any online seller who sell these books?
    Explanation is very good maaam, thank you for helping

  3. Ramakrishna says:

    very good explanation maam!

  4. Muhammad says:

    Respected author

    You have done an excellent job by providing a masterpiece of work in the form of Intuitive Guide to Fourier Analysis and Spectral Estimation book. It is really an excellent text on the claimed topic.

    Wonderful explanation with beautiful figures. Simply beautiful. Waiting for more such useful text in future. Keep it up.

    • Charan L. says:

      So very touching of you to say that. I am humbled by it! Thank you.
      I hope you purchased the book on Amazon. In Kindle it is quite inexpensive.
      Thank you very much again for your kind words – Charan

  5. David Morley says:

    I have read enough of your tutorials to know that your book will be excellent but you need to add a link to places that sell it. 🙂
    Thank you for providing Matlab to go with it. For anyone who doesn’t have or can’t afford Matlab, Scilab is an open source alternative that can run all Matlab code. This is a link to it
    Freemat is another Malab clone but I don’t know as much about it (

  6. John says:

    Any chance of getting the answers to the book questions?

    Also, will there be an update to the ebook if you’ve already purchased?

    Great book so far…love it.

    • Charan L. says:

      Since the book is being used as a text book, I am asked not to provide the answers on the open forum. The questions are actually designed to be pretty simple. Perhaps, I will create a page, where students can post their answers.

      Thanks a bunch for letting me know, you liked the book. I have looked into how to provide update to the Kindle eBook but really can not figure out a way to do that. Amazon does not offer updates of Kindle eBooks. I wish they would let you download the latest version.

      Thanks again,

      • Sven E Widmalm says:

        Excellent book! However, as having to learn on my own, I find it frustrating that all those question pages are left without answers. If a teacher is using it as a textbook it would be a wonderful help for his/her students to prepare for exams IF answers were given. You may think they are simple. Everything is simple for those who already know the topic. All the questions may or may not be simple for all readers. Anyway, the learning curve would be less steep for most readers if answers were provided, and any professional teacher should be able to write variations of the questions instead of just copying your Question-pages. I am unfortunately in the group who needs to know if my answers are correct. The teachers should not need your help. Many students do.

        • Charan L. says:

          Hello Sven,
          I understand your concern. However, because the book is used in some universities (MIT for example), the publisher ask us not to provide the answers. However, most of these questions are really very simple. Most I think can answered without doing any calculations. If you have a problem with a particular question, please ask here. I will try to answer it.
          Glad you like the book and are getting something out it. – Charan

  7. John says:

    Thanks for the response.

    I didn’t know the book was going to be a “text” book as it didn’t seem to be styled like one so I thought I’d ask about the answer sheet. Sometimes it’s frustrating trying to do a problem and not knowing whether you got it correct…hence the inquiry.

    BTW, it’s refreshing to read about the Fourier transforms the way you’ve presented it. Many books don’t even mention the DTFT or if they do they don’t distinguish it from the others in a clear manner. Hence, many texts end up just making it more confusing than it needs to be. You’ve done a terrific job clearing most of that up.


  8. Mike says:

    Hi Dr Langton
    Would you be able to advise me when your book will be available in hard copy.

    I’ve read some introductory chapters and I must say, the book is very well written. Keen to have a copy.

    • Charan L. says:

      The book will be available end of this month. Look on Amazon around June 10th.
      I am glad you like it. Appreciate your saying so.
      Thank, Charan

  9. Mike C says:

    I just bought this book in hardcover–I like the color graphs. They make the waveforms easier to see and understand. I have two questions: 1) Why no index? As a reference book, it really needs one. 2) When will you publish the MatLab code?

    • Charan L. says:

      Hello Mike,
      The code is here on the website, perhaps a bit hard to find. Here is the link.

      The index will be added back in the next printing. We were initially going to do the book only in Kindle, which has searching capabilities and hence index is superfluous. So I guess in the next version, we will put the index back. I might add it on online here first. I will let you know when I do that. Thanks for your comments. Hope the book is useful to you.

  10. Noel Zacheria says:

    Hi Dr. Langton,

    I like the material on this site and I would like to buy the FFT book but I don’t see the 2nd edition. Is it available on kindle or print?. If I were to buy the kindle version can I update to the 2nd version when available?. What about the book on Link Budgets.


  11. Adam says:

    Love your book, very good introduction to the subject.
    I wonder where could I get the matlab or python code for the examples in the book?

    Best Adam

  12. Shahzad Aslam-Mir says:

    Hi Id like to buy the second printing of your Fourier book. I cant see how I specify that on Amazon – can get it from your direct ?

  13. james says:

    Hi Dr. Langton,

    love this book so far.Question is second printing means second edition? i bought kindle format on amazon, will be updates?


    • Charan L. says:

      Hi James,
      I try to keep the book updated on Kindle. There is no second edition, just second printing that fixed some of the errors, but not all.
      Its tough to catch them all.

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