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...
Linear Feedback Shift Registers for the Uninitiated, Part XII: Spread-Spectrum Fundamentals
Last time we looked at the use of LFSRs for pseudorandom number generation, or PRNG, and saw two things:
- the use of LFSR state for PRNG has undesirable serial correlation and frequency-domain properties
- the use of single bits of LFSR output has good frequency-domain properties, and its autocorrelation values are so close to zero that they are actually better than a statistically random bit stream
The unusually-good correlation properties...
Linear Feedback Shift Registers for the Uninitiated, Part XI: Pseudorandom Number Generation
Last time we looked at the use of LFSRs in counters and position encoders.
This time we’re going to look at pseudorandom number generation, and why you may — or may not — want to use LFSRs for this purpose.
But first — an aside:
Science Fair 1983When I was in fourth grade, my father bought a Timex/Sinclair 1000. This was one of several personal computers introduced in 1982, along with the Commodore 64. The...
Linear Feedback Shift Registers for the Uninitiated, Part X: Counters and Encoders
Last time we looked at LFSR output decimation and the computation of trace parity.
Today we are starting to look in detail at some applications of LFSRs, namely counters and encoders.
CountersI mentioned counters briefly in the article on easy discrete logarithms. The idea here is that the propagation delay in an LFSR is smaller than in a counter, since the logic to compute the next LFSR state is simpler than in an ordinary counter. All you need to construct an LFSR is
Linear Feedback Shift Registers for the Uninitiated, Part IX: Decimation, Trace Parity, and Cyclotomic Cosets
Last time we looked at matrix methods and how they can be used to analyze two important aspects of LFSRs:
- time shifts
- state recovery from LFSR output
In both cases we were able to use a finite field or bitwise approach to arrive at the same result as a matrix-based approach. The matrix approach is more expensive in terms of execution time and memory storage, but in some cases is conceptually simpler.
This article will be covering some concepts that are useful for studying the...
Linear Feedback Shift Registers for the Uninitiated, Part VIII: Matrix Methods and State Recovery
Last time we looked at a dsPIC implementation of LFSR updates. Now we’re going to go back to basics and look at some matrix methods, which is the third approach to represent LFSRs that I mentioned in Part I. And we’re going to explore the problem of converting from LFSR output to LFSR state.
Matrices: Beloved Historical DregsElwyn Berlekamp’s 1966 paper Non-Binary BCH Encoding covers some work on
Obsolete? Yes. Still in use? Yes. How do you use it? Ummm...
In today's world of constantly changing technology, quick parts availability, and seemingly endless options, some things can't change. It isn't a big deal to wait a day or less for a computer upgrade to arrive. It seems program size increases proportionally to hard drive size. The old is discarded and replaced with the new. Hard drives can hold terrabytes and even SD cards can hold gigabytes of information.
Now, suppose a system can't be changed. It is still...
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:
Introduction to Microcontrollers - Further Beginnings
Embedded Programming Basics
This tutorial entry will discuss some further embedded programming basics that you will need to understand before proceeding on to the LED blinky and other example programs. We will do this by looking at the general organization and types of instructions found in most microcontrollers, and how that organization and those instructions are reflected (or, in some cases, ignored) by the C programming language.
Basic CPU...Ten Little Algorithms, Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
Other articles in this series:
- Part 1: Russian Peasant Multiplication
- Part 2: The Single-Pole Low-Pass Filter
- Part 3: Welford's Method (And Friends)
- Part 4: Topological Sort
- Part 6: Green’s Theorem and Swept-Area Detection
Today we will be drifting back into the topic of numerical methods, and look at an algorithm that takes in a series of discretely-sampled data points, and estimates the maximum value of...
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...
Best Firmware Architecture Attributes
Architecture of a firmware (FW) in a way defines the life-cycle of your product. Often companies start with a simple-version of a product as a response to the time-to-market caveat of the business, make some cash out of the product with a simple feature set. It takes only less than 2-3 years to reach a point where the company needs to develop multiple products derived from the same code base and multiple teams need to develop...
From Baremetal to RTOS: A review of scheduling techniques
Transitioning from bare-metal embedded software development to a real-time operating system (RTOS) can be a difficult endeavor. Many developers struggle with the question of whether they should use an RTOS or simply use a bare-metal scheduler. One of the goals of this series is to walk developers through the transition and decision making process of abandoning bare-metal thinking and getting up to speed quickly with RTOSes. Before diving into the details of RTOSes, the appropriate first step...
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...
Introduction to Microcontrollers - More On Interrupts
A Little More Detail About The Interrupt MechanismIt's time to look a little closer at what happens in an interrupt request and response. Again this is in general terms, and different microcontroller designs may do things somewhat differently, but the basics remain the same. Most but not all interrupt requests are latched, which means the interrupt event sets a flag that stays set even if the interrupt event then goes away. It is this latched flag...
Use DPLL to Lock Digital Oscillator to 1PPS Signal
Introduction
There are occasions where it is desirable to lock a digital oscillator to an external time reference such as the 1PPS (One Pulse Per Second) signal output from a GPS receiver. One approach would be to synchronize a fixed frequency oscillator on the leading edge of the 1PPS signal. In many cases, this will result in adequate performance. However, in situations where simple synchronization does not provide adequate performance, digital phase-lock techniques can be applied to a...
Second-Order Systems, Part I: Boing!!
I’ve already written about the unexciting (but useful) 1st-order system, and about slew-rate limiting. So now it’s time to cover second-order systems.
The most common second-order systems are RLC circuits and spring-mass-damper systems.
Spring-mass-damper systems are fairly common; you’ve seen these before, whether you realize it or not. One household example of these is the spring doorstop (BOING!!):
(For what it’s worth: the spring...
Introduction to Microcontrollers - More On Interrupts
A Little More Detail About The Interrupt MechanismIt's time to look a little closer at what happens in an interrupt request and response. Again this is in general terms, and different microcontroller designs may do things somewhat differently, but the basics remain the same. Most but not all interrupt requests are latched, which means the interrupt event sets a flag that stays set even if the interrupt event then goes away. It is this latched flag...
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...
VHDL tutorial - A practical example - part 1 - Hardware
In previous posts I described some simple VHDL examples. This time let's try something a little more complex. This is part one of a multiple part article. This is intended to be a detailed description of one of several initial designs that I developed for a client. This design never made it into a product, but a similar design was used and is currently being produced. As a considerable amount of work was put into this effort, I decided to share this design...
Byte and Switch (Part 2)
In part 1 we talked about the use of a MOSFET for a power switch. Here's a different circuit that also uses a MOSFET, this time as a switch for signals:
We have a thermistor Rth that is located somewhere in an assembly, that connects to a circuit board. This acts as a variable resistor that changes with temperature. If we use it in a voltage divider, the midpoint of the voltage divider has a voltage that depends on temperature. Resistors R3 and R4 form our reference resistance; when...
Ten Little Algorithms, Part 4: Topological Sort
Other articles in this series:
- Part 1: Russian Peasant Multiplication
- Part 2: The Single-Pole Low-Pass Filter
- Part 3: Welford's Method (And Friends)
- Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
- Part 6: Green’s Theorem and Swept-Area Detection
Today we’re going to take a break from my usual focus on signal processing or numerical algorithms, and focus on...
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...
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 LinksImportant Programming Concepts (Even on Embedded Systems) Part II: Immutability
Other articles in this series:
- Part I: Idempotence
- Part III: Volatility
- Part IV: Singletons
- Part V: State Machines
- Part VI: Abstraction
This article will discuss immutability, and some of its variations in the topic of functional programming.
There are a whole series of benefits to using program variables that… well, that aren’t actually variable, but instead are immutable. The impact of...
Coding Step 1 - Hello World and Makefiles
Articles in this series:
- Coding Step 0 - Development Environments
- Coding Step 1 - Hello World and Makefiles
- Coding Step 2 - Source Control
- Coding Step 3 - High-Level Requirements
- Coding Step 4 - Design
Step 0 discussed how to install GCC and the make utility with the expectation of writing and compiling your first C program. In this article, I discuss how to use those tools we installed last time. Specifically, how to use GCC to compile a C program and...
Lost Secrets of the H-Bridge, Part I: Ripple Current in Inductive Loads
So you think you know about H-bridges? They're something I mentioned in my last post about signal processing with Python.
Here we have a typical H-bridge with an inductive load. (Mmmmm ahhh! It's good to draw by hand every once in a while!) There are four power switches: QAH and QAL connecting node A to the DC link, and QBH and QBL connecting node B to the DC link. The load is connected between nodes A and B, and here is represented by an inductive load in series with something else. We...
