Linear Feedback Shift Registers for the Uninitiated, Part XVIII: Primitive Polynomial Generation
Last time we figured out how to reverse-engineer parameters of an unknown CRC computation by providing sample inputs and analyzing the corresponding outputs. One of the things we discovered was that the polynomial \( x^{16} + x^{12} + x^5 + 1 \) used in the 16-bit X.25 CRC is not primitive — which just means that all the nonzero elements in the corresponding quotient ring can’t be generated by powers of \( x \), and therefore the corresponding 16-bit LFSR with taps in bits 0, 5,...
Sensors Expo - Trip Report & My Best Video Yet!
This was my first time at Sensors Expo and my second time in Silicon Valley and I must say I had a great time.
Before I share with you what I find to be, by far, my best 'highlights' video yet for a conference/trade show, let me try to entertain you with a few anecdotes from this trip. If you are not interested by my stories or maybe don't have the extra minutes needed to read them, please feel free to skip to the end of this blog post to watch the...
R1C1R2C2: The Two-Pole Passive RC Filter
I keep running into this circuit every year or two, and need to do the same old calculations, which are kind of tiring. So I figured I’d just write up an article and then I can look it up the next time.
This is a two-pole passive RC filter. Doesn’t work as well as an LC filter or an active filter, but it is cheap. We’re going to find out a couple of things about its transfer function.
First let’s find out the transfer function of this circuit:
Not very...
Linear Feedback Shift Registers for the Uninitiated, Part XVII: Reverse-Engineering the CRC
Last time, we continued a discussion about error detection and correction by covering Reed-Solomon encoding. I was going to move on to another topic, but then there was this post on Reddit asking how to determine unknown CRC parameters:
I am seeking to reverse engineer an 8-bit CRC. I don’t know the generator code that’s used, but can lay my hands on any number of output sequences given an input sequence.
This is something I call the “unknown oracle”...
Making a connection 1
In order for your system to control devices, you must be able to connect it to those devices.
Besides different sizes based on wire size, there are a few different styles of connectors that can be used. There are also weather-resistant terminals that can be used if needed.
Ring
(Parks, 16)
- used for circuits that you don’t want to become easily disconnected
- ground wire attached to a stud
Push-On
- can be used on relay terminals
(Parks, 18)
- could be...
Linear Feedback Shift Registers for the Uninitiated, Part XVI: Reed-Solomon Error Correction
Last time, we talked about error correction and detection, covering some basics like Hamming distance, CRCs, and Hamming codes. If you are new to this topic, I would strongly suggest going back to read that article before this one.
This time we are going to cover Reed-Solomon codes. (I had meant to cover this topic in Part XV, but the article was getting to be too long, so I’ve split it roughly in half.) These are one of the workhorses of error-correction, and they are used in...
Troubleshooting notes from days past, TTL, Linear
General Troubleshooting
- Follow safety precautions.
- Always think “what if”.
- Analytical procedures
- Precautions when probing equipment
- Insulate all but last 1/8” of probe tip
- Learn from mistakes
- Don’t start with electronic test equipment, start with analytical thinking.
- If you get stuck, sleep on it.
- Many problems have simple solutions.
- Whenever possible, try to substitute a working unit.
- Don’t blindly trust test instruments.
- Coincidences do happen, but are relatively...
Linear Feedback Shift Registers for the Uninitiated, Part XV: Error Detection and Correction
Last time, we talked about Gold codes, a specially-constructed set of pseudorandom bit sequences (PRBS) with low mutual cross-correlation, which are used in many spread-spectrum communications systems, including the Global Positioning System.
This time we are wading into the field of error detection and correction, in particular CRCs and Hamming codes.
Ernie, You Have a Banana in Your EarI have had a really really tough time writing this article. I like the...
Tenderfoot: How to Write a Great Bug Report
I am an odd sort of person. Why? Because I love a well written and descriptive bug report. I love a case that includes clear and easy to follow reproduction steps. I love a written bug report that includes all the necessary information on versions, configurations, connections and other system details. Why? Because I believe in efficiency. I believe that as an engineer I have a duty to generate value to my employer or customer. Great bug reports are one part of our collective never-ending...
Who else is going to Sensors Expo in San Jose? Looking for roommate(s)!
This will be my first time attending this show and I must say that I am excited. I am bringing with me my cameras and other video equipment with the intention to capture as much footage as possible and produce a (hopefully) fun to watch 'highlights' video. I will also try to film as many demos as possible and share them with you.
I enjoy going to shows like this one as it gives me the opportunity to get out of my home-office (from where I manage and run the *Related sites) and actually...
Introduction to Microcontrollers - Button Matrix & Auto Repeating
Too Many Buttons, Not Enough Inputs
Assigning one GPIO input to each button can use up a lot of GPIO pins. Numeric input requires at least 10 buttons, plus however many additional control or function buttons. This can quickly get expensive, GPIO pin-wise, and also connector-wise if the keypad is off the uC PCB as it often would be. A very common response to this expense is to wire buttons (keys, etc) in a matrix. By connecting our buttons in an...
Adventures in Signal Processing with Python
Author’s note: This article was originally called Adventures in Signal Processing with Python (MATLAB? We don’t need no stinkin' MATLAB!) — the allusion to The Treasure of the Sierra Madre has been removed, in deference to being a good neighbor to The MathWorks. While I don’t make it a secret of my dislike of many aspects of MATLAB — which I mention later in this article — I do hope they can improve their software and reduce the price. Please note this...
Linear Feedback Shift Registers for the Uninitiated, Part I: Ex-Pralite Monks and Finite Fields
Later there will be, I hope, some people who will find it to their advantage to decipher all this mess.
— Évariste Galois, May 29, 1832
I was going to call this short series of articles “LFSRs for Dummies”, but thought better of it. What is a linear feedback shift register? If you want the short answer, the Wikipedia article is a decent introduction. But these articles are aimed at those of you who want a little bit deeper mathematical understanding,...
Lazy Properties in Python Using Descriptors
This is a bit of a side tangent from my normal at-least-vaguely-embedded-related articles, but I wanted to share a moment of enlightenment I had recently about descriptors in Python. The easiest way to explain a descriptor is a way to outsource attribute lookup and modification.
Python has a bunch of “magic” methods that are hooks into various object-oriented mechanisms that let you do all sorts of ridiculously clever things. Whether or not they’re a good idea is another...
Digital PLL's -- Part 1
1. Introduction
Figure 1.1 is a block diagram of a digital PLL (DPLL). The purpose of the DPLL is to lock the phase of a numerically controlled oscillator (NCO) to a reference signal. The loop includes a phase detector to compute phase error and a loop filter to set loop dynamic performance. The output of the loop filter controls the frequency and phase of the NCO, driving the phase error to zero.
One application of the DPLL is to recover the timing in a digital...
Boot sequence for an ARM based embedded system -2
In the last post, we discussed about the startup execution sequence on an ARM based embedded system in broader terms. In this post, we are going to cover the details of a startup code.These details are also available through various ARM resources , however for the sake of completion of our discussion , here is - the flow the startup code for an ARM based embedded system.
Step 1: The reset
On startup, the processor will jump to fixed location ,(most ARM cores support two vector...
Cortex-M Exception Handling (Part 1)
This article describes how Cortex-M processors handle interrupts and, more generally, exceptions, a concept that plays a central role in the design and implementation of most embedded systems. The main reason of discussing this topic in detail is that, in the past few years, the degree of sophistication (and complexity) of microcontrollers in handling interrupts steadily increased, bringing them on a par with general-purpose processors.
Using the Beaglebone PRU to achieve realtime at low cost
Introduction
I work as an engineer in a synchrotron facility. A few weeks ago, I helped the people in charge of the power supply developments to integrate a realtime control algorithm on a prototype platform: a BeagleBone Black (BBB) running Linux. I had already worked with this board in the past, and I found it very interesting given its excellent resources versus price ratio (around 40 euros). This time, I was impressed by its realtime capabilities. I thought it would be a good idea to...
Introduction to Microcontrollers - Buttons and Bouncing
What Is A Button?To your hardware, that is. As discussed in Introduction to Microcontrollers - More On GPIO, a button (or key, or switch, or any form of mechanical contact) is generally hooked up to a microcontroller so as to generate a certain logic level when pushed or closed or "active," and the opposite logic level when unpushed or open or "inactive." The active logic level can be either '0' or '1', but for reasons both historical and electrical, an...
MSP430 LaunchPad Tutorial - Part 3 - ADC
In this new episode of our journey into MSP430 I will explain the basics of Analog to Digital Conversion on the MSP430G2231.We will write a program that will read an ADC channel and will toggle some leds based on the result of the conversion.
We start as usual with the inclusion of the header file for the MSP430G2231, the leds stuff and with the definition of a variable that will store the result of the conversion. We also declare a function that will initialize the ADC...
Boot sequence for an ARM based embedded system -2
In the last post, we discussed about the startup execution sequence on an ARM based embedded system in broader terms. In this post, we are going to cover the details of a startup code.These details are also available through various ARM resources , however for the sake of completion of our discussion , here is - the flow the startup code for an ARM based embedded system.
Step 1: The reset
On startup, the processor will jump to fixed location ,(most ARM cores support two vector...
Arduino robotics #1 - motor control
Arduino Robotics
Beginner robotics is a series of article chronicling my first autonomous robot build, Clusterbot. This build is meant to be affordable, relatively easy and instructive. The total cost of the build is around $50.
1. Arduino robotics - motor control2. Arduino robotics - chassis, locomotion and power3. Arduino robotics - wiring, coding and a test run4.Data Hiding in C
Strictly speaking, C is not an object-oriented language. Although it provides some features that fit into the object-oriented paradigm it has never had the full object-oriented focus that its successor C++ offers. C++ introduced some very useful concepts and abilities that I miss when I’m developing in ANSI C. One such concept is protected member variables and functions.
When you declare a class in C++ you can also declare member variables and functions as part of that class. Often, these...
How to Build a Fixed-Point PI Controller That Just Works: Part I
This two-part article explains five tips to make a fixed-point PI controller work well. I am not going to talk about loop tuning -- there are hundreds of articles and books about that; any control-systems course will go over loop tuning enough to help you understand the fundamentals. There will always be some differences for each system you have to control, but the goals are the same: drive the average error to zero, keep the system stable, and maximize performance (keep overshoot and delay...
Ten Little Algorithms, Part 1: Russian Peasant Multiplication
This blog needs some short posts to balance out the long ones, so I thought I’d cover some of the algorithms I’ve used over the years. Like the Euclidean algorithm and Extended Euclidean algorithm and Newton’s method — except those you should know already, and if not, you should be locked in a room until you do. Someday one of them may save your life. Well, you never know.
Other articles in this series:
- Part 1:
Endianness and Serial Communication
Endianness is a consideration that is easily overlooked in the design of embedded systems. I myself am amply guilty of this oversight. It’s something you don’t ever have to worry about if you’re only working with a single processor or two processors that have the same endianness. You can even avoid it if you have two processors that have different endianness but never transmit data between themselves that consists of more than one byte. It’s easy to lull...
Introduction to Microcontrollers - Buttons and Bouncing
What Is A Button?To your hardware, that is. As discussed in Introduction to Microcontrollers - More On GPIO, a button (or key, or switch, or any form of mechanical contact) is generally hooked up to a microcontroller so as to generate a certain logic level when pushed or closed or "active," and the opposite logic level when unpushed or open or "inactive." The active logic level can be either '0' or '1', but for reasons both historical and electrical, an...
Introduction to Microcontrollers - More On GPIO
Now that we have our LED Blinky program nailed down, it's time to look more closely at outputs, add button/switch inputs, and work with reading inputs and driving outputs based on those inputs.
It's ON - No, It's OFF - No, It's ON...I have to confess, I cheated. Well, let's say I glossed over something very important. In our LED Blinky program, we never cared about whether an output '1' or an output '0' turned on the LED. Since we were just...
Unit Tests for Embedded Code
I originate from an electrical engineering background and my first industry experience was in a large, staid defense contractor. Both of these experiences contributed to a significant lack of knowledge with regards to software development best practices. Electrical engineers often have a backwards view of software in general; large defense contractors have similar views of software and couple it with a general disdain for any sort of automation or ‘immature’ practices. While there...
Embedded Toolbox: Programmer's Calculator
Like any craftsman, I have accumulated quite a few tools during my embedded software development career. Some of them proved to me more useful than others. And these generally useful tools ended up in my Embedded Toolbox. In this blog, I'd like to share some of my tools with you. Today, I'd like to start with my cross-platform Programmer's Calculator called QCalc.
I'm sure that you already have your favorite calculator online or on your smartphone. But can your calculator accept...
New TI MCU Resource Center
I am happy to announce the publication of the new "TI MCU Resource Center" on EmbeddedRelated.com, where TI will regularly add videos and articles to keep you informed on their latest and greatest MCU related products.
To access the new section, you'll find a link in the main menu of the site at the top of the page.
Blogs Section Now Online!
I am happy to announce that the blog section is now online.
Last week, I sent an email to all the members of EmbeddedRelated.com to ask for embedded systems experts who would be interested in blogging on the site. The response was very positive and I have selected 10 highly qualified individuals who will soon be writing here about all sorts of embedded systems related subjects. I am currently in the process of receiving their info (bio, photo, username, etc) and creating their bloggers'...
