• Modulation Alternatives for the Software Engineer (November 2011)
• Isolated Sigma-Delta Modulators, Rah Rah Rah! (April 2013)

Each of these are about delta-sigma modulation, but they’re short and sweet, and not very in-depth. And the 2013 article was really more about analog-to-digital converters. So we’re going to revisit the...]]> Sun, 28 May 2023 16:04:50 +0000 Jason Sachs https://www.dsprelated.com/showarticle/1182/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...]]> Tue, 19 Jun 2018 15:06:45 +0000 Jason Sachs https://www.dsprelated.com/showarticle/1180/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...]]> Tue, 12 Jun 2018 04:06:17 +0000 Jason Sachs https://www.dsprelated.com/showarticle/1158/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...]]> Wed, 18 Apr 2018 05:22:04 +0000 Jason Sachs https://www.dsprelated.com/showarticle/1142/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....]]> Mon, 12 Mar 2018 05:24:20 +0000 Jason Sachs https://www.dsprelated.com/showarticle/1124/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 Fri, 29 Dec 2017 20:38:40 +0000 Jason Sachs https://www.dsprelated.com/showarticle/1058/ten-little-algorithms-part-6-green-s-theorem-and-swept-area-detection 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 5: Quadratic Extremum Interpolation and Chandrupatla's...]]> Sun, 18 Jun 2017 20:32:01 +0000 Jason Sachs https://www.dsprelated.com/showarticle/1015/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...]]> Tue, 22 Nov 2016 14:26:03 +0000 Jason Sachs https://www.dsprelated.com/showarticle/927/pad-delay-is-okay-today This article is going to be somewhat different in that I’m not really writing it for the typical embedded systems engineer. Rather it’s kind of a specialized topic, so don’t be surprised if you get bored and move on to something else. That’s fine by me.

    Anyway, let’s just jump ahead to the punchline. Here’s a numerical simulation of a step response to a \(...]]> Tue, 01 Mar 2016 14:52:08 +0000 Jason Sachs https://www.dsprelated.com/showarticle/779/ten-little-algorithms-part-2-the-single-pole-low-pass-filter Other articles in this series:

    • Part 1: Russian Peasant Multiplication
    • Part 3: Welford's Method (And Friends)
    • Part 4: Topological Sort
    • Part 5: Quadratic Extremum Interpolation and Chandrupatla's Method
    • Part 6: Green’s Theorem and Swept-Area...]]> Mon, 27 Apr 2015 15:46:56 +0000 Jason Sachs https://www.dsprelated.com/showarticle/532/overflow-i-had-too-much-to-add-last-night Happy Thanksgiving! Maybe the memory of eating too much turkey is fresh in your mind. If so, this would be a good time to talk about overflow.

      In the world of floating-point arithmetic, overflow is possible but not particularly common. You can get it when numbers become too large; IEEE double-precision floating-point numbers support a range of just...]]> Wed, 04 Dec 2013 15:21:26 +0000 Jason Sachs https://www.dsprelated.com/showarticle/444/signal-processing-contest-in-python-dealing-with-the-worst-encoder-in-the-world When I posted an article on estimating velocity from a position encoder, I got a number of responses. A few of them were of the form "Well, it's an interesting article, but at slow speeds why can't you just take the time between the encoder edges, and then...." My point was that there are lots of people out there which take this approach, and don't take into account that the time between...]]> Sat, 07 Sep 2013 21:59:03 +0000 Jason Sachs https://www.dsprelated.com/showarticle/359/adventures-in-signal-processing-with-python-matlab-we-don-t-need-no-stinkin-matlab 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...]]> Sun, 23 Jun 2013 17:56:52 +0000 Jason Sachs https://www.dsprelated.com/showarticle/268/oscilloscope-dreams My coworkers and I recently needed a new oscilloscope. I thought I would share some of the features I look for when purchasing one.

      When I was in college in the early 1990's, our oscilloscopes looked like this:

      Now the cathode ray tubes have almost all been replaced by digital storage scopes with color LCD screens, and they look like these:

      Oscilloscopes...]]> Sun, 15 Jan 2012 03:14:49 +0000 Jason Sachs