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...
How precise is my measurement?
Some might argue that measurement is a blend of skepticism and faith. While time constraints might make you lean toward faith, some healthy engineering skepticism should bring you back to statistics. This article reviews some practical statistics that can help you satisfy one common question posed by skeptical engineers: “How precise is my measurement?” As we’ll see, by understanding how to answer it, you gain a degree of control over your measurement time.
An accurate, precise...Embedded World 2018 - More Videos!
After the interview videos last week, this week I am very happy to release two more videos taken at Embedded World 2018 and that I am proud of.
For both videos, I made extensive use of my two new toys, a Zhiyun Crane Gimbal and a Sony a6300 camera.
The use of a gimbal like the Zhiyun makes a big difference in terms of making the footage look much more stable and cinematographic.
As for the Sony camera, it takes fantastic slow-motion footage and...
Embedded World 2018 - The Interviews
Once again this year, I had the chance to go to Embedded World in Nuremberg Germany. And once again this year, I brought my video equipment to try and capture some of the most interesting things at the show.
Something new this year, I asked Jacob Beningo if he would partner with me in doing interviews with a few vendors. I would operate the camera while Jacob would ask the right questions to the vendors to make them talk about the key products/features that...
Linear Feedback Shift Registers for the Uninitiated, Part XIII: System Identification
Last time we looked at spread-spectrum techniques using the output bit sequence of an LFSR as a pseudorandom bit sequence (PRBS). The main benefit we explored was increasing signal-to-noise ratio (SNR) relative to other disturbance signals in a communication system.
This time we’re going to use a PRBS from LFSR output to do something completely different: system identification. We’ll show two different methods of active system identification, one using sine waves and the other...
Circuit Board Standoffs
If you are unable to find a circuit board mount in the size you need, there is an alternative. You could make them from tubing, like steel brake line, with a bolt in the middle. You could use plastic tubing with a bolt.Using a solid rod is also an option.
If you opt to use some type of rod, there are some things to keep in mind. Drill rod is very tough, but could be hard to thread smaller bolts. Mild steel rod isn’t quite as tough, but it easier to thread. ...
Is it a Bug or an Error?
Probably you’ve heard the story of how Adm. Grace Hopper attached a moth that was dislodged from a relay in the Harvard Mark II mainframe to an engineering notebook and labeled it the “First actual case of bug being found.”
Designers of electronics, including Thomas Edison, had been using the term bug for decades. But it was mostly after this amusing 1947 event hat the use of words like “bugs” and “debugging” took off in the emerging software realm.
So why is it that if a...
A Wish for Things That Work
As the end of the year approaches, I become introspective. This year I am frustrated by bad user interfaces in software.
Actually, every year, throughout the year, I am frustrated by bad user interfaces in software. And yet here it is, the end of 2017, and things aren’t getting much better! Argh!
I wrote about this sort of thing a bit back in 2011 (“Complexity in Consumer Electronics Considered Harmful”) but I think it’s time to revisit the topic. So I’m...
An overview of Linux Boot Process for Embedded Systems
This Text provides an insight in to the Embedded Linux Boot Process. Reader should have a basic Knowledge of Boot Process in general and should be familiar with Embedded Linux Boot Process.
.................PART-A................(1) Software components Involved in Embedded Linux Boot Process (a) Bootloader (b) kernel Image (c) root file system - either an initrd image or a NFS location(2) Steps during Booting process of a conventional...Examining The Stack For Fun And Profit
Well, maybe not so much for profit, but certainly for fun. This is a wandering journey of exploration and discovery, learning a variety of interesting and useful things.
One of the concerns with an embedded system is how much memory it needs, known as the memory footprint. This consists of the persistent storage needed for the program (i.e. the flash memory or filesystem space that stores the executable image), and the volatile storage needed to hold the data while executing over long...
Announcing the 2021 Embedded Online Conference!
Once again this year, Jacob Beningo and I are putting together the Embedded Online Conference. Last year's edition was a very rewarding experience, with over 6,000 registrants, fantastic & insightful talks, and lots of positive feedback. For this year's edition, we are delighted to announce that none other than Jack Ganssle will be giving a Keynote presentation about the 50th anniversary of the Microprocessor.
The 2021 Embedded Online Conference will...
Back from Embedded World 2019 - Funny Stories and Live-Streaming Woes
When the idea of live-streaming parts of Embedded World came to me, I got so excited that I knew I had to make it happen. I perceived the opportunity as a win-win-win-win.
- win #1 - Engineers who could not make it to Embedded World would be able to sample the huge event,
- win #2 - The organisation behind EW would benefit from the extra exposure
- win #3 - Lecturers and vendors who would be live-streamed would reach a (much) larger audience
- win #4 - I would get...
How to Build a Fixed-Point PI Controller That Just Works: Part II
In Part I we talked about some of the issues around discrete-time proportional-integral (PI) controllers:
- various forms and whether to use the canonical form for z-transforms (don't do it!)
- order of operation in the integral term: whether to scale and then integrate (my recommendation), or integrate and then scale.
- saturation and anti-windup
In this part we'll talk about the issues surrounding fixed-point implementations of PI controllers. First let's recap the conceptual structure...
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.
Lost Secrets of the H-Bridge, Part IV: DC Link Decoupling and Why Electrolytic Capacitors Are Not Enough
Those of you who read my earlier articles about H-bridges, and followed them closely, have noticed there's some unfinished business. Well, here it is. Just so you know, I've been nervous about writing the fourth (and hopefully final) part of this series for a while. Fourth installments after a hiatus can bring bad vibes. I mean, look what it did to George Lucas: now we have Star Wars Episode I: The Phantom Menace and
PID Without a PhD
I both consult and teach in the area of digital control. Through both of these efforts, I have found that while there certainly are control problems that require all the expertise I can bring to bear, there are a great number of control problems that can be solved with the most basic knowledge of simple controllers, without resort to any formal control theory at all.
This article will tell you how to implement a simple controller in software and how to tune it without getting into heavy...
Advice For High School Students
ContentsMSP430 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...
Arduino robotics #4 - HC-SR04 ultrasonic sensor
Arduino Robotics
Arduino 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.Introduction to Microcontrollers - 7-segment displays & Multiplexing
Doing the 7 Segment Shuffle
The 7 segment display is ubiquitous in the modern world. Just about every digital clock, calculator and movie bomb has one. The treadmills at my gym have 6 or 7, each one displaying 3 or 4 digits. What makes the 7-seg interesting is that it presents an opportunity to make a trade off between GPIO (output pins) for time. Every 7-seg display requires 8 outputs (the 7 segments and usually either a decimal point or a...
Delayed printf for real-time logging
You often debug by adding a few printfs and looking at the logs. In some real-time/low-level contexts though, you don't have time for text formatting.
You don't want prints to affect timing too much, because then timing-related bugs you're chasing might disappear. And you certainly don't want the system to stop functioning altogether because prints cause it to miss real-time deadlines.
A common alternative to prints is more "raw" logging - an event buffer, where event is a union keeping...
Important Programming Concepts (Even on Embedded Systems) Part IV: Singletons
Other articles in this series:
- Part I: Idempotence
- Part II: Immutability
- Part III: Volatility
- Part V: State Machines
- Part VI: Abstraction
Today’s topic is the singleton. This article is unique (pun intended) in that unlike the others in this series, I tried to figure out a word to use that would be a positive concept to encourage, as an alternative to singletons, but
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...
Android for Embedded Devices - 5 Reasons why Android is used in Embedded Devices
The embedded purists are going to hate me for this. How can you even think of using Android on an embedded system ? It’s after all a mobile phone operating system/software.
Sigh !! Yes I did not like Android to begin with, as well - for use on an Embedded System. But sometimes I think the market and needs decide what has to be used and what should not be. This is one such thing. Over the past few years, I have learned to love Android as an embedded operating system....
Introduction to Microcontrollers - Button Matrix & Auto Repeating
Too Many Buttons, Not Enough InputsAssigning 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...
The habitat of hardware bugs
The Moscow apartment which little me called home was also home to many other creatures, from smallish cockroaches to biggish rats. But of course we rarely met them face to face. Evolution has weeded out those animals imprudent enough to crash your dinner. However, when we moved a cupboard one time, we had the pleasure to meet a few hundreds of fabulously evolved cockroaches.
In this sense, logical bugs aren't different from actual insects. You won't find...
Two Capacitors Are Better Than One
I was looking for a good reference for some ADC-driving circuits, and ran across this diagram in Walt Jung’s Op-Amp Applications Handbook:
And I smiled to myself, because I immediately remembered a circuit I hadn’t used for years. Years! But it’s something you should file away in your bag of tricks.
Take a look at the RC-RC circuit formed by R1, R2, C1, and C2. It’s basically a stacked RC low-pass filter. The question is, why are there two capacitors?
I...
Round Round Get Around: Why Fixed-Point Right-Shifts Are Just Fine
Today’s topic is rounding in embedded systems, or more specifically, why you don’t need to worry about it in many cases.
One of the issues faced in computer arithmetic is that exact arithmetic requires an ever-increasing bit length to avoid overflow. Adding or subtracting two 16-bit integers produces a 17-bit result; multiplying two 16-bit integers produces a 32-bit result. In fixed-point arithmetic we typically multiply and shift right; for example, if we wanted to multiply some...
