The Eternal Thing

Shifting, reversal and scaling are the common operations we perform on an analog (or) digital signal. In this post, we will see how can we visualize shifted version of a time-reversed signal. To put it simply, here is what we are gonna do: Given a signal x(t) , how to plot x(-t+1) Note: If you are already good at this, maybe this post is not for you. You can safely stop reading now. But if you still want to proceed, you are always welcome!! Before discussing how to plot our signal, let's have a small talk about - Time Shifting: For a given x(t) , we can say that x(t+1) is a time-shifted signal. In general, we talk about the shifting of the waveform relative to the time axis, and we use the terms "left shift" and "right shift" to denote two types of movements possible for the waveform. However, we have to note that the terms indicate only half the story. There is an underlying assumption for these to work, which is the dir...

  The divisibility rule of 3 is simple: For a given number, add the individual digits. If the sum is divisible by 3, then the overall number is divisible by 3. Otherwise, it's not. But why the sum of the digits? How can we prove that this is robust for any given number? If you wanna think it out yourself, take a pause. Otherwise, just continue reading below... The Proof: Consider a generalized decimal number, with the total number of digits as n+1, and the coefficients being a 0 , a 1 , a 2 , and so on up to a n . So, our number can be expressed as: a 0 10 0 + a 1 10 1 + a 2 10 2 + ... + a n 10 n . Now, the powers of 10 can be written in terms of 9s, right? 10 1 = 10 = 9 + 1 10 2 = 100 = 99 + 1 10 3 = 1000 = 999 + 1 and similarly, 10 n = 100..0 = 99..9 + 1. Then, our number becomes: a 0 + a 1 (9 + 1) + a 2 (99 + 1) + .... + a n (99..9 + 1) = [a 0 + a 1 + a 2 + ... + a n ] + [9*a...

 There will be some movies, which we will never forget with time. We keep on remembering some of our favourite scenes. We try to rewatch them. When we rewatch it, we understand some hidden elements, which further makes us love the movie more..! So, this post is dedicated to sharing some thoughts on the Malayalam movie - "Koode". (You didn't know about the movie? No problem, please click on the image and enjoy the movie on Hotstar, for free..!!) **Spoiler Alert** There will be a discussion of the story plot, so proceed with caution...! **Back to content** Josh never cries till the end of the movie: We can never miss a person if we are never close to a person. Even though Josh loves his sister, he never has very great memories with her. He never talked to her, they never even fought.  Only when he actually 'misses' her near the end, does his heart gets shattered. 'Cha' - it's the word Jenny says when Josh leaves for Dubai: Jenny says at a later point tha...

     They were the B. Tech days, and we were taught about Verilog and VHDL programming languages. Obviously, learning the syntax was never enough. We need to use it - have to write programs.      As it is a hardware language, we need to develop the codes for electronic blocks. Starting with trivial ones like AND gates, and OR gates and going up to priority encoder, kind of blocks.     However, we are taught that that was not enough. We need to code another part, which is called "testbench."  We were given a few examples of the test benches for some blocks. Honestly, the testbench part looked almost the same for all the designs. We simply concluded that the test bench was easier to code than the design part.     Cut to the training period in the initial days of the core company. The good news is that the hardware languages we were taught and that the companies use are almost similar, even though that is not enough. After the basic tr...

Hi, How are you doing? I think you remember a scene in the Saaho movie, where the hero jumps off the mountain cliff along with a parachute bag. Of course, if the hero jumps along with the bag, there is no problem and no need for this post. But, the bag goes down before our hero, and still, he outruns the bag and catches it before reaching the ground! Before we dive in, here is the scene for your reference. (You can safely skip if you already watched/remembered it) But how is it even possible to catch the bag theoretically?  What do we think when we see an object falling? The object gets accelerated because of the gravitational force. So the velocity increases as it goes down and finally hits the ground. As per that logic, the bag and hero fall one after the other, so the former should hit the ground first and then the hero. Right? Not exactly, though. It turns out that we are missing a concept called Terminal Velocity from our analysis! What is a terminal velocity? When a body fal...

In science, whenever we observe a novel event, we start sharpening our brains to decode it. We make a couple more observations related to that event, and try to get a reason for it. It was also the same with the previous generation of scientists. They observed various new phenomena and they gathered as much information as possible to get the accurate reason behind them. But there was a problem with the human mind. In the past days, when there was limited information at hand and more time was required for getting new information, scientists had to make the best possible theories (i.e., explanations) with whatever data was available. It was like a competition, where the scientist with the best theory would win. This "winner" scientist, should be able to explain the data from future experiments with the theory. Consider that, a new experiment happened later, but the results were not explained by the theory of our scientist, then the theory was to be changed, and again the compet...

  We know 1 + 1 + 1 + 1 + ..... reaches infinity.  So, in a similar way, 0.9 + 0.9 + 0.9 + 0.9 + ...... reaches infinity. What about 1/2 + 1/3 + 1/4 + 1/5 + ....?  Do you believe it reaches infinity?  If yes, you can ignore the rest of the post. If you want to try it yourself, you can close this page. But if you do not believe it reaches infinity, you are not alone!  Warning:  This post is about proving the sum as simply as possible. Please don't expect more ;) How do we want to prove it? By comparison. Say we have the value A, with us. Suppose we get another value B, with two conditions:- A > B. B reaches infinity. So, we can conclude A reaches infinity!! Job done. Splitting of our sum for comparing:- Take the first terms of our sum -  1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10. Yeah, stop at 1/10. Now, how many terms it has?  9. Now take another sum. 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 + 1/10 (yeah, 9 times). You c...