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    Major Understanding Issue in Discrete-Time Signals

    Hello there,

    I am reading this book "Discrete-Time Signal Processing" by Alan V. Oppenheim and Ronald W. Schafer. Here it says,

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    Below is my understanding. Can someone please explain, where I am going wrong?

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    Also, please answer the questions in the image below

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    Thanks :)
    Last edited by dzafar; 19th May 2017 at 05:55.

    •   Alt19th May 2017, 05:36

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    Re: Major Understanding Issue in Discrete-Time Signals

    A is amplitude and yeas your interpretation is correct.


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    •   Alt19th May 2017, 11:47

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    Re: Major Understanding Issue in Discrete-Time Signals

    Thanks nomigoraya! What about the question in the second image? Thanks



    •   Alt19th May 2017, 13:03

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    Re: Major Understanding Issue in Discrete-Time Signals

    You have already answered that simple question.
    u[5]= 0+0+0+0.....+1+0+0+0+0+0 = 1 Where is the problem ?

    u[12454352]=0+0+0+0+0+....1+0+0+0+0+0+0.... = 1

    u[1324583425893245738984237441394]=0+0+0+0+0+....1+0+0+0+0+0+0.... = 1

    Do you see it now ?

    What you have written in the question is wrong because it is a sum of values i.e. it is 0+0+0+.....+1+0+0+0.... that "1" at delta[0]=1 makes the sum to be "1".



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    Re: Major Understanding Issue in Discrete-Time Signals

    Umm.. okay! The problem that I am having is that at n = 5, u[5] = 1 whereas, impulse[5] = 0!
    So for n = 5, they are not equal!
    I understand that impulse function is with a summation. But that just means it's 1 at n = 0.

    Q1: So does it not matter what the impulse is at n = 5?!

    Q2: If so, we can then just remove the summation and say:
    u[n] = impulse[0] for any index n?!

    Also, if they just mean the maginitude of u[n] equals the magnitude of the summation of impulses,

    Q3: Why don't they use the magnitude symbol:
    |u[n]| = |summation of impulses|?

    Q4: Also, why does the summation stop at n?! We can easily have it upto positive infinity (as the magnitude will still be 1)?!

    Thanks! I hope someone can answer my doubts in the same order (of questions asked) so that I have a better understanding.

    Thanks :)
    Last edited by dzafar; 19th May 2017 at 17:41. Reason: Extra detail



    •   Alt19th May 2017, 17:28

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    Re: Major Understanding Issue in Discrete-Time Signals

    Quote Originally Posted by dzafar View Post
    Q1: So does it not matter what the impulse is at n = 5?!
    No, it does not.

    Q2: If so, we can then just remove the summation and say:
    u[n] = impulse[0] for any index n?!
    Only for "n" higher or equal to 0, otherwise u[n]=0.

    Also, if they just mean the maginitude of u[n] equals the magnitude of the summation of impulses,

    Q3: Why don't they use the magnitude symbol:
    |u[n]| = |summation of impulses|?
    In the book is written the same, u[n]=summation of impulses, isn't it ? I see no reason for the magnitude symbol here... magnitude symbol makes sense in complex numbers... but I do not see any complex number here. The module symbol on the other hand (i.e. |-3|=3) does not make sense either because there are no negative values in this case.
    The author simply gave good mathematical definition. You can remember it however you want e.g. as I have answered to Q2 but it would be useless when applying demonstrations of formulas or transforms because correct mathematical definitions can be used to prove other stuff.

    Q4: Also, why does the summation stop at n?! We can easily have it upto positive infinity (as the magnitude will still be 1)?!
    To be a finite sum and hence more easily apply transforms and convolution and etc..
    Last edited by CataM; 19th May 2017 at 18:49.


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