Convolution notes

What is the convolution of an antipodal (that is alternating 1 and 0) pulse train with rectangular pulse of duration T in the time domain?

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What is the convolution of an antipodal (that is alternating 1 and -1) pulse train with a rectangular pulse of duration T in the time domain? I am having trouble picturing this.convolutionShareEditFollowFlagedited 6 hours agoasked 6 hours agouser443410977 bronze badges

  • 1Look up “square wave” and you’ll find images to help you picture it. I’m going to go look up what convolution means other than the standard definition, but this looks like a homework question, which means there is a minimum standard of effort. Show your attempt at a solution. How would you solve a convolution problem for a DC voltage or for a sine wave or triangle wave? – K H 6 hours ago
  • 1Ok I had to look that up. If you check out the wikipedia article on convolution, they’ve provided visual examples. The convolution appears to be a formula for the overlapping area as you move one pulse shape past the other. – K H 5 hours ago
  • 1Not a homework problem, I am in industry, I literally have no idea. – user4434 5 hours ago
  • @K H, mathematically, it is a function processing another function. I vaguely remember that I need to first understand the idea of convolution before DFT/FFT. – tlfong01 5 hours ago   
  • 1@user4434 How will knowing the convolution help you if you don’t know what it means? Did the Wikipedia article help you? – K H 5 hours ago
  • @K H, the Wiki is hard to understand, unless you spend some hours in the function stuff. But the animation in the visual explanation does help a little bit, 🙂 upload.wikimedia.org/wikipedia/commons/6/6a/…. You need to appreciate how the big square pulse guy “moves over” another big square pulse guy produces a new, smaller triangular guy. – tlfong01 5 hours ago    
  • Let me try my broken English to explain (Note 1) . (1) Let us first refresh our middle school Algebra and Trigonometry. to explain what is a function. (a) Let us say y = (2 * x). In functional denotation (Note 2) y = f(x), or if you like, y = double(x), where “double” is the name of the function f in our case. – tlfong01 5 hours ago   
  • (2) Now let us move on to a trigonometry function, y = sine(x). Now y is a (real) number, denoting a “ratio” of two side of a triangle, and x is also a real number, denoting the “angle”, or “radian”, if you like. You might to read Wiki to refresh you memory: en.wikipedia.org/wiki/Sine – tlfong01 5 hours ago   
  • (3) The animation form Wiki Sine helps: upload.wikimedia.org/wikipedia/commons/thumb/3/3b/…. Here is x axis is the angle or radian, y axis is the sine value. So we still have the general form y = f(x). 🙂 – tlfong01 5 hours ago    
  • (4) Now we will be using AC sinusoidal current wave forms to explain the convolution stuff. Those readers already forgotten what is AC wave form might like to read the following to refreshing memory: Sinusoidal AC Waveforms – Electronics Tutorials electronics-tutorials.ws/accircuits/sinusoidal-waveform.html – tlfong01 3 hours ago    
  • (5) I will be using the definitions and terms in the following picture i.imgur.com/iW0RG0X.jpeg to explain the convolution of functions in the time domain. The OP or other visitors might like to comment (eg. ‘too abstract”, “so far so good”), or make suggestions (eg. speed up, or slow down), before I move on. Cheers. – tlfong01 2 hours ago   
  • 1Do you understand the process of correlation? – Chu 1 hour ago
  • 1Is the system continuous-time or discrete-time system? Please provide a clear, well drawn picture of both the signals. Pleas add all the things you have already tried out to find tbe answer. – AJN 1 hour ago 
  • 1The answer strongly depends on the time gap between impulses and time duration of the rectangular pulse. If the impulses are spaced far apart in time/samples, the result is just a pulse train with same spacing. If not, the result is probably a mixture of staircases. – AJN 1 hour ago
  • For calculus scary guys. here is calculus free quiz for them to check if they really understand the idea of convolution. The test procedure: (1) Skim the Wikipedia on convolution, never mind the scary calculus, focus at Visualization Section, and try to understand how the convolution result say, the triangle can be arrived by consider different point in time, and use arithmetic, ie, multiplication of two points at the same time point to get the result product point (yes, discrete convolution). (2) Then get familiar with the following pic: i.imgur.com/PCcRu1a.jpg. / to cont, . – tlfong01 8 mins ago    
  • Ah, locking down supper time. Before I go, let me give everybody a trick question: (1) Now what if a small triangle guy tries to convolute a big triangle guy. what will be the result, a circle? PS, Talk is cheap, draw me a picture. Cheers. – tlfong01 3 mins ago    Edit   

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