Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

[SOLVED] Major Understanding Issue in Discrete-Time Signals

Status
Not open for further replies.

dzafar

Member level 4
Joined
Jan 17, 2017
Messages
76
Helped
1
Reputation
2
Reaction score
1
Trophy points
8
Activity points
690
Hello there,

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

Untitled.png

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

Untitled.png

Also, please answer the questions in the image below

Untitled.png

Thanks :)
 
Last edited:

nomigoraya

Full Member level 5
Joined
Jul 31, 2007
Messages
285
Helped
45
Reputation
90
Reaction score
44
Trophy points
1,308
Location
Trieste
Activity points
3,316
A is amplitude and yeas your interpretation is correct.
 
  • Like
Reactions: dzafar

    dzafar

    Points: 2
    Helpful Answer Positive Rating

dzafar

Member level 4
Joined
Jan 17, 2017
Messages
76
Helped
1
Reputation
2
Reaction score
1
Trophy points
8
Activity points
690
Thanks nomigoraya! What about the question in the second image? Thanks
 

CataM

Advanced Member level 4
Joined
Dec 23, 2015
Messages
1,275
Helped
314
Reputation
628
Reaction score
312
Trophy points
83
Location
Madrid, Spain
Activity points
8,416
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".
 

dzafar

Member level 4
Joined
Jan 17, 2017
Messages
76
Helped
1
Reputation
2
Reaction score
1
Trophy points
8
Activity points
690
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:

CataM

Advanced Member level 4
Joined
Dec 23, 2015
Messages
1,275
Helped
314
Reputation
628
Reaction score
312
Trophy points
83
Location
Madrid, Spain
Activity points
8,416
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:
  • Like
Reactions: dzafar

    dzafar

    Points: 2
    Helpful Answer Positive Rating
Status
Not open for further replies.

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Top