Monty Hall at his show Let's Make a Deal

The Reason Why the Monty Hall Problem Continues to Perplex Everyone

The Monty Hall problem is an interesting puzzle loosely based on an American TV game show Let’s Make a Deal hosted by Monty Hall. While the puzzle looked simple, it perplexed some of the brightest mathematical minds in the United States, including the great Paul Erdös who was one of the most prolific mathematicians of the 20th century. This continues to be the case today. I looked upon a number of references to find the source of confusion in the Monty Hall problem but failed. All I found was different solutions. Therefore, I built one myself with the usual from

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Spectrum of the cascade of CIC filters with a wideband compensation filter for rate change factor 10, unit differential delay and 4 stages

Cascaded Integrator Comb (CIC) Filters – A Staircase of DSP

In olden days, people used to have lots of kids. A famous Urdu satirist once wrote: "It has been observed that the last kid is usually the most mischievous of them all. Therefore, there should be no last kid in a family!" I remembered this line today because I have observed that starting a write-up is the most difficult task of them all. Therefore, there is no introductory paragraph in this article. Suffice it to say that this is the only topic I have found that takes you from a very small first step (just two additions) to really advanced

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A line plot in 3D

An Intuitive Guide to Linear Regression

We have described before how supervised learning can help us predict a continuous-valued output or organize the input into discrete categories, commonly known as regression and classification problems, respectively. In this article, we describe linear regression and leave the classification algorithms for a future post. What is Linear Regression? Suppose that you are a young investor living in a region with cold climate. One day an idea flashes in your mind that perhaps the shares in the regional stock market climb linearly with the temperature: the better the weather, the higher the prices. You already know what the temperature is

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Converging towards angle 30

Coordinate Rotation Digital Computer (CoRDiC)

Digitial Signal Processing (DSP) plays a crucial role in algorithm implmentation for building digital and wireless communication systems. A common theme in all those algorithms is that they can be implemented with the following simple operations: addition multiplication shift In fact, these are the basic principles on which a digital signal processor is constructed. However, when it comes to implementation of real-time systems in hardware such as FPGAs, we find ways to reduce the complexity even further. Which operation (out of the above three) do you think is the most demanding in computations? It is the multiplications. Therefore, it is

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(Top) An 8-PSK waveform. (Bottom) Two constellation diagrams: one at the Tx shown by thick red lines and the other at the Rx for a phase offset of 17 degrees shown by dotted purple lines

I/Q Signals 101: Neither Complex Nor Complicated

There was a recent discussion on GNU Radio mailing list in regards to the simplest possible intuition behind I/Q signals. Why is I/Q sampling required? Question: The original question from Kristoff went like this: “… when you mention `GNU Radio complex numbers’, you also have to mention I/Q signals, which is a topic that is very difficult to explain in 10 seconds to an audience who has never seen anything about I/Q sampling before.” Comment: According to Jeff Long: “This is a great thing to try to figure out. If we can come up with an answer that gives someone

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