Thank you cleared my some of the misconceptions like I am confused why besides arrow number like 1 or 2 or 3 written instead of infinite. Thank you I relate this with force multiplied by time Ft = change in momentum = mass.chage in velocity = mass.acceleration.
@@iain_explains Yes I agree Force = Mass.Acceleration Force = Mass.( change in Velocity / change in Time) Force . change in Time = Mass.( change in Velocity) Force.delta time = Mass.delta velocity . Impuluse = Net times the length of time over which that force is applied. and also change in momentum. Example 4 Newton force applied for (1/4) second. 4N.1/4s = 1 N.s Delta newton force or very very tinny newton force applied for (1/Delta time or very very tinny time) Delta newton force.(1/Delta time)=1 N.s=impulse ------------------------------------------------------------ 2.(1 N.s)=2.Impulse. 3.(1 N.s)=3.Impulse. 4.(1 N.s)=4.Impulse. 7.(1 N.s)=7.Impulse. 0.5.(1 N.s)=0.5.Impulse. 0.8.(1 N.s)=0.8.Impulse. 1.54.(1 N.s)=1.54.Impulse. 2.66.(1 N.s)=2.66.Impulse. Thank you, Once again thank you for your valuable time and your valuable information for replying to my comment it helpful me to look throughly. Thank you.
Are there any useful properties of distributions in signal processing or communications beyond what we're exposed to in a signals and systems course? Or to state this in another way, do signal processing or communications engineers benefit from studying the theory of distributions (I'm a circuit engineer, so I really don't know. But I do like maths so finding out that there is an entire field on this fascinated me)?
I'm not sure what you mean by "the theory of distributions" sorry. Perhaps you mean the distribution functions of random variables? In which case, yes, there are a great many applications of that theory. It relates to anything that we model as being "random". These videos give more details: "What is a Random Variable?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-MM6QM3y8pvI.html and "What is a Probability Density Function (pdf)?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-jUFbY5u-DMs.html and "What is a Cumulative Distribution Function (CDF) of a Random Variable?" ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-WZffV55o9T8.html
Without getting much into my 20 years old notebooks I would say that the amplitude in the frequency domain cannot stay 1.. it should go to zero when delta goes to infinity...
Your memory is pretty good, but if you do go back and check your 20-year-old notebooks, you'll see that the DC (zero frequency) amplitude goes to zero (in the frequency domain) as the width of the Rect function goes to zero (in the time domain), _for a constant height Rect function_ . But the Rect function I'm talking about goes to an infinite height (1/Delta), so this cancels out the "DC-shrinking" factor (Delta).
Paul Dirac introduced the delta function in 1927. We didn't have computers and digital processing until after Alan Turing and Claud Shannon in the 1930's and 1940's.
Hi Iain, couldn't find the summary of this one in the website as well. I hope you don't mind me pointing these out. Since I am going through this videos, I thought it might help you to just point it out.
Thanks Bob, I'm in the process of adding the missing Summary Sheets, but this one is already there. Just to clarify, are you saying you couldn't find the listing for it? (www.iaincollings.com/signals-and-systems#h.mti8x6b4saki under the Basic Concepts heading), or that the link didn't work for the download? (drive.google.com/file/d/1TdSySWlFgfI549rJorhrx_rFSu4h37A4/view )
Hi , thank you for explaining impulse function. I had questions at comments of your one particular video, about discrete time impulse function and CT to DT conversion. Nowadays I am asking this question to different platforms, so let me repeat it :) I don't understand how we transform continuous time impulse to the discrete-time, as its amplitude is 1. How this process works ? How discrete time dirac delta is 1 ? The actual mathematical operation of the "converter" is not clear. What I mean is , what is the operator that converts : ""impulse(t) >> to impulse[n] with amplitude of 1"" or ""x(t) . p(t) impulse train >> to x[n] as a sequence"" x(t) . p(t) could be represented as = summation the series of x(nT) . impulse ( t - nT ) But this is still not equal to a sequence of x[n] , because it contains scaled impulses with amplitude of infinity, right?
There is no "operator" that converts between the two. One is a continuous-time function, and the other is a discrete-time function. They exist on a totally different class of basis functions. As you point out, the CT delta function has infinite height, and so does not actually exist in the real world. The DT delta function also does not exist in the real world, but for a different reason: it is an infinitely long vector with only one non-zero component - but we can't have an infinitely long vector in the real world. In practice, we have finite length signals/vectors with finite amplitudes/values. Both the CT and DT delta functions are mathematical models that help us to understand the real world, and they can be related to each other conceptually, but they are on different classes of basis functions.
@@iain_explains What " different class of basis function" means? If there is not a converting process or a converter operator, what sampling is for? What sampling and discretization actually means? Continuous time functions are somehow converted into discrete time functions, but how it's identified? I mean, why the DT impulse is 1, how we determined this? I know I am asking a lot, but I need answers to understand the concept. A few videos could be helpful. Thank you for your answers.
A "discrete time signal" is not really a "signal" in the real world. It is just a sequence of numbers (stored on a computer or other digital storage and processing device). "Discrete time" does not exist in the real world. The real world is "continuous" (unless you're looking at the quantum physics level). And likewise, "continuous time" does not exist in a computer, which is driven by a digital clock waveform with a non-zero period.
@@iain_explains I already understand the difference of DT and CT signals. My question is , how x(t) is transformed to x[n] mathematically ? And why the amplitude of DT impulse is 1, while CT impulse has amplitude of infinity ? I know dirac(t) is a kind of distribution function, and we can simply represent it like a rectangular function. But I dont understand the DT impulse. I read a sentence like this : "Mathematically , sampling of a signal x(t), is equivalent to its multiplication with a delta impulse train." It seems contradictive to me, because dirac(t) has infinite amplitude, with scalable area. Impulse train : p(t) = summation (k= -inf to +inf ) dirac( t - kTs ) Sampler : x(t) . p(t) = summation (k= -inf to +inf ) x(kTs) . dirac( t - kTs ) = impulses at times kTs , with area x(kTs) The amplitudes are still infinity, so how x[n] is obtained by this multiplication ? Thank you for your help. To underline it, a bunch of new videos can be helpful.
