Chapter 1 – Trigonometric Representation of Periodic Signals

Continuous time trigonometric representation of of CT periodic signals – Chapter 1

Description: Intuitive Guide to Fourier Analysis – Chapter 1

Its not exactly the same thing as the book since it is a draft and may have typos etc.

Here is the link to the video lecture on Youtube.

28 comments on “Chapter 1 – Trigonometric Representation of Periodic Signals
  1. aman sikri says:

    i have gone through these notes. I think this is a fantastic work by you. I just want few notes on wireless basics communication. Can u add this topic also.?

    • admin says:

      HI Aman,

      Not clear what you are asking? What kind of wireless notes do you need?

      Charan Langton

      • Vishwas S Patel says:

        It will be more helpful, if you can post about the wireless communication from 1G to 4G..
        Different types of modulations used in different generations.
        Like OFDMA basic concepts for WiMAX, LTE and WIFI.. Why OFDMA was started?
        CDMA basic concepts .. why it was used earlier?
        It will be a lot more helpful…

        • Charan L. says:

          Sorry, I just saw this.

          Well it looks like a good idea for a separate tutorial. Time is usually short and my list is always too long, so it may happen.
          Thank you.


  2. sungkyu says:

    I want to say thank you for your this effort.

    I think you missed the Figure 17 on 9 page.

  3. aashika says:

    the notes given are superb and very helpful to get an idea about the concept .Thank u

  4. hunter says:

    please elaborate how have you come up with mathematical expressions of summation with 1/2pi.i really can’t understand

  5. Daniel Patiño says:

    I want to say: thank you, your work is extraordinary.

    Best regards.

  6. srikanth says:

    Unable to download or open few pdf’s (fft transforms). Please help

  7. Mete says:


    At page 10, unlike in sines case, the sum of cosines (1/k)*cos(k*2*pi*f*t) for k = 1, 3, 5 ect. does not make a square wave when I plot in MATLAB. It is kind of counter intuitive but you can try and see:

    t = 0:01;1;
    plot(t, (1/1)*sin(1*2*pi*f*t) + (1/3)*sin(3*2*pi*f*t) + (1/5)*sin(5*2*pi*f*t) + (1/7)*sin(7*2*pi*f*t));
    hold on;
    plot(t, (1/1)*cos(1*2*pi*f*t) + (1/3)*cos(3*2*pi*f*t) + (1/5)*cos(5*2*pi*f*t) + (1/7)*cos(7*2*pi*f*t),’-r’);

    • Charan L. says:

      plot(t, (1/1)*cos(1*2*pi*f*t) + (1/3)*cos(3*2*pi*f*t) – (1/5)*cos(5*2*pi*f*t) + (1/7)*cos(7*2*pi*f*t),’-r’);

      Try this one.

  8. Mete says:

    I think in cosine case there will be 1, -1/3, 1/5, -1/7:

    t = 0:0.01:1;
    plot(t, (1/1)*sin(1*2*pi*f*t) + (1/3)*sin(3*2*pi*f*t) + (1/5)*sin(5*2*pi*f*t) + (1/7)*sin(7*2*pi*f*t));
    hold on;
    plot(t, (1/1)*cos(1*2*pi*f*t) + (-1/3)*cos(3*2*pi*f*t) + (1/5)*cos(5*2*pi*f*t) + (-1/7)*cos(7*2*pi*f*t),’-r’);

  9. Abinash Kumar says:

    Thanks a lot.Could you please share some of the your strategy to simplify the difficult and confusing concept like Fourier transform.It would be really helpful for us.

  10. Stephen says:


    I would just like to point out a typo on page 5 towards the end of the page.

    In LaTeX you used \textbf{} but forgot the {}.

    Thanks for the awesome notes. Im really enjoying them!

    Will let you know if there are any more ‘issues’ 🙂


    • Stephen says:

      There is another typo on page 7 just below the equations where you mention that c(t) has an amplitude of A. It should be c(t) has an amplitude of B if we go by the equations. 🙂


    • Stephen says:

      Another one on page 9 where you say that w=2*pi*k*f but you have already included k in the equation so it would imply it becomes k^2.

    • Stephen says:

      Page 11 reads:
      “With only three terms in the addition result in a pretty decent looking square wave.”

      I think it should read:
      “With only three terms in, the addition result is a pretty decent looking square wave.”

      I know I am being petty but I am really grateful for the work done and want to improve it if I can.

      All the best,

      • Charan L. says:

        Stephen, I accept all your comments gratefully. They are really good! – Thanks Charan
        Keep reading.

    • Stephen says:

      There are a few more errors that I have found that I would like to send through to you for correcting. Would it be possible if I can do that in another way rather than through comments?


  11. Sumit says:

    Hi, awesome note. Thanks a lot. Can you help us further with the answers to your questions at the end. Thanks 🙂

    • Charan L. says:

      Not sure what you are asking, Sumit. What questions? I do not see any.
      Charan langton

      • Sumit says:

        I meant to ask the Questions at the end of chapters . For e.g. in Chapter 1 “Trigonometric Representation of Continuous-time Periodic Signals”, Question 8 states : What is the maximum amplitude of N harmonic cosine waves added together. What is it for sine waves ? These are very nice questions and the answers will further help in understanding the subject.

  12. guoqiang says:

    What if There is a term like aksin(wt+a) in a signal. Intergate aksin(wt+a)*sin(wt) could be zero. How to get the coefficient of this term.

  13. guoqiang says:

    Hi thank for your selfless help , I want to know where can I get the answer of the questions

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