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...
Voltage - A Close Look
My first boss liked to pose the following problem when interviewing a new engineer. “Imagine two boxes on a table one with a battery the other with a light. Assume there is no detectable voltage drop in the connecting leads and the leads cannot be broken. How would you determine which box has the light? Drilling a hole is not allowed.”
The answer is simple. You need a voltmeter to tell the electric field direction and a small compass to tell the magnetic field...
What is Electronics
IntroductionOne answer to the question posed by the title might be: "The understanding that allows a designer to interconnect electrical components to perform electrical tasks." These tasks can involve measurement, amplification, moving and storing digital data, dissipating energy, operating motors, etc. Circuit theory uses the sinusoidal relations between components, voltages, current and time to describe how a circuit functions. The parameters we can measure directly are...
Linear Regression with Evenly-Spaced Abscissae
What a boring title. I wish I could come up with something snazzier. One word I learned today is studentization, which is just the normalization of errors in a curve-fitting exercise by the sample standard deviation (e.g. point \( x_i \) is \( 0.3\hat{\sigma} \) from the best-fit linear curve, so \( \frac{x_i - \hat{x}_i}{\hat{\sigma}} = 0.3 \)) — Studentize me! would have been nice, but I couldn’t work it into the topic for today. Oh well.
I needed a little break from...
Linear Feedback Shift Registers for the Uninitiated, Part XIV: Gold Codes
Last time we looked at some techniques using LFSR output for system identification, making use of the peculiar autocorrelation properties of pseudorandom bit sequences (PRBS) derived from an LFSR.
This time we’re going to jump back to the field of communications, to look at an invention called Gold codes and why a single maximum-length PRBS isn’t enough to save the world using spread-spectrum technology. We have to cover two little side discussions before we can get into Gold...
Crowdfunding Articles?
Many of you have the knowledge and talent to write technical articles that would benefit the EE community. What is missing for most of you though, and very understandably so, is the time and motivation to do it.
But what if you could make some money to compensate for your time spent on writing the article(s)? Would some of you find the motivation and make the time?
I am thinking of implementing a system/mechanism that would allow the EE community to...
Simple Automated Log Processing
Text log data offers a wealth of information from an embedded system. At least during prototyping and development phases, most systems have some kind of serial log output, or use semihosting methods to log to a serial output channel in a debugger. Then you can capture the logs to a file.
The problem is that they tend to accumulate large volumes of data. Logs can be many thousands of lines long, especially when you run long duration tests. Finding information and evaluating trends in the...
Ten Little Algorithms, Part 3: Welford's Method (and Friends)
Other articles in this series:
- Part 1: Russian Peasant Multiplication
- Part 2: The Single-Pole Low-Pass Filter
- Part 4: Topological Sort
- Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
- Part 6: Green’s Theorem and Swept-Area Detection
Last time we talked about a low-pass filter, and we saw that a one-line...
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...
Important Programming Concepts (Even on Embedded Systems) Part V: State Machines
Other articles in this series:
- Part I: Idempotence
- Part II: Immutability
- Part III: Volatility
- Part IV: Singletons
- Part VI: Abstraction
Oh, hell, this article just had to be about state machines, didn’t it? State machines! Those damned little circles and arrows and q’s.
Yeah, I know you don’t like them. They bring back bad memories from University, those Mealy and Moore machines with their state transition tables, the ones you had to write up...
VHDL tutorial
When I was first introduced to "Programmable Logic" several years ago, it was an answer to many of the challenges that I was struggling with. Though the parts were primitive by today's standards (simple PALs verses FPGA), they were an extremely cost effective tool addressing the need for specialized logic blocks.
I have continued to incorporate these powerful blocks into many of my latest designs. My current favorite part line is the Xilinx CoolRunner series (XC2Cxxx). In this...
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...
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...
Free Goodies from Embedded World - Full Inventory and Upcoming Draw Live-Streaming Date
Chances are that you already know that I went to Embedded World a few weeks ago and came back with a bag full of "goodies". Initially, my vision was to do a single draw for one person to win it all, but I didn't expect to come back with so much stuff and so many development kits. Based on your feedback, it seems like you guys agree that It wouldn't make sense for one person to win everything as no-one could make good use of all the boards and there would be lots of...
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...
From bare-metal to RTOS: 5 Reasons to use an RTOS
Developers can come up with amazing and convoluted reasons to not use an RTOS. I have heard excuses ranging from they are too expensive (despite open source solutions) all the way to they aren’t efficient and use too much memory. In some circumstances some excuses are justified but there are many reasons why a developer should look to an RTOS to help with their real-time scheduling needs.
From bare-metal to RTOS Quick LinksBoot 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 - 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...
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...
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'...
