Padé Delay is Okay Today

Jason Sachs March 1, 20164 comments

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 \( p=126, q=130 \) Padé approximation of a time delay:

Impressed? Maybe you should be. This...


Go Big or Go Home - Generating $500,000 for Contributors

Stephane Boucher February 18, 20168 comments
In a Nutshell
  • A new Vendors Directory has been created
  • Vendors will be invited to pay a sponsorship fee to be listed in the directory
  • 100% of the basic sponsorship fee will be distributed to the *Related Sites community through a novel reward system
  • The goal is for the directory to eventually generate - drum roll please -  $500,000 on a yearly basis for contributing members on the *Related Sites
  • Members will choose how the reward money gets distributed between...

The New Forum is LIVE!

Stephane Boucher February 18, 20161 comment

After months of hard word, I am very excited to introduce to you the new forum interface.  

Here are the key features:

1- Easily add images to a post by drag & dropping the images in the editor

2- Easily attach files to a post by drag & dropping the files in the editor

3- Add latex equations to a post and they will be rendered with Mathjax (tutorial)

4- Add a code snippet and surround the code with


Autocorrelation and the case of the missing fundamental

Allen January 21, 201610 comments

[UPDATED January 25, 2016:  One of the examples was broken, also the IPython notebook links now point to nbviewer, where you can hear the examples.]

For sounds with simple harmonic structure, the pitch we perceive is usually the fundamental frequency, even if it is not dominant.  For example, here's the spectrum of a half-second recording of a saxophone.

The first three peaks are at 464, 928, and 1392 Hz.  The pitch we perceive is the fundamental, 464 Hz, which is close to...


Generating pink noise

Allen January 20, 20161 comment

In one of his most famous columns for Scientific American, Martin Gardner wrote about pink noise and its relation to fractal music.  The article was based on a 1978 paper by Voss and Clarke, which presents, among other things, a simple algorithm for generating pink noise, also known as 1/f noise.

The fundamental idea of the algorithm is to add up several sequences of uniform random numbers that get updated at different rates. The first source gets updated at...


Ancient History

Mike January 18, 201612 comments

The other day I was downloading an IDE for a new (to me) OS.  When I went to compile some sample code, it failed.  I went onto a forum, where I was told "if you read the release notes you'd know that the peripheral libraries are in a legacy download".  Well damn!  Looking back at my previous versions I realized I must have done that and forgotten about it.  Everything changes, and keeping up with it takes time and effort.

When I first started with microprocessors we...


Dealing With Fixed Point Fractions

Mike January 5, 20163 comments

Fixed point fractional representation always gives me a headache because I screw it up the first time I try to implement an algorithm. The difference between integer operations and fractional operations is in the overflow.  If the representation fits in the fixed point result, you can not tell the difference between fixed point integer and fixed point fractions.  When integers overflow, they lose data off the most significant bits.  When fractions overflow, they lose data off...


Optimizing the Half-band Filters in Multistage Decimation and Interpolation

Rick Lyons January 4, 201615 comments

This blog discusses a not so well-known rule regarding the filtering in multistage decimation and interpolation by an integer power of two. I'm referring to sample rate change systems using half-band lowpass filters (LPFs) as shown in Figure 1. Here's the story.

Figure 1: Multistage decimation and interpolation using half-band filters.

Multistage Decimation – A Very Brief Review

Figure 2(a) depicts the process of decimation by an integer factor D. That...


The DFT Output and Its Dimensions

Leonid Ovanesyan December 29, 20155 comments

The Discrete Fourier Transform, or DFT, converts a signal from discrete time to discrete frequency. It is commonly implemented as and used as the Fast Fourier Transform (FFT). This article will attempt to clarify the format of the DFT output and how it is produced.

Living in the real world, we deal with real signals. The data we typically sample does not have an imaginary component. For example, the voltage sampled by a receiver is a real value at a particular point in time. Let’s...


Amplitude modulation and the sampling theorem

Allen December 18, 20156 comments

I am working on the 11th and probably final chapter of Think DSP, which follows material my colleague Siddhartan Govindasamy developed for a class at Olin College.  He introduces amplitude modulation as a clever way to sneak up on the Nyquist–Shannon sampling theorem.

Most of the code for the chapter is done: you can check it out in this IPython notebook.  I haven't written the text yet, but I'll outline it here, and paste in the key figures.

Convolution...


Signed serial-/parallel multiplication

Markus Nentwig February 16, 2014

Keywords: Binary signed multiplication implementation, RTL, Verilog, algorithm

Summary
  • A detailed discussion of bit-level trickstery in signed-signed multiplication
  • Algorithm based on Wikipedia example
  • Includes a Verilog implementation with parametrized bit width
Signed serial-/parallel multiplication

A straightforward method to multiply two binary numbers is to repeatedly shift the first argument a, and add to a register if the corresponding bit in the other argument b is set. The...


DSP Related Math: Nice Animated GIFs

Stephane Boucher April 24, 20143 comments

I was browsing the ECE subreddit lately and found that some of the most popular posts over the last few months have been animated GIFs helping understand some mathematical concepts.  I thought there would be some value in aggregating the DSP related gifs on one page.  

The relationship between sin, cos, and right triangles: Constructing a square wave with infinite series (see this...

Optimizing the Half-band Filters in Multistage Decimation and Interpolation

Rick Lyons January 4, 201615 comments

This blog discusses a not so well-known rule regarding the filtering in multistage decimation and interpolation by an integer power of two. I'm referring to sample rate change systems using half-band lowpass filters (LPFs) as shown in Figure 1. Here's the story.

Figure 1: Multistage decimation and interpolation using half-band filters.

Multistage Decimation – A Very Brief Review

Figure 2(a) depicts the process of decimation by an integer factor D. That...


Spline interpolation

Markus Nentwig May 11, 20142 comments

A cookbook recipe for segmented y=f(x) 3rd-order polynomial interpolation based on arbitrary input data. Includes Octave/Matlab design script and Verilog implementation example. Keywords: Spline, interpolation, function modeling, fixed point approximation, data fitting, Matlab, RTL, Verilog

Introduction

Splines describe a smooth function with a small number of parameters. They are well-known for example from vector drawing programs, or to define a "natural" movement path through given...


A poor man's Simulink

Markus Nentwig January 24, 20153 comments

Glue between Octave and NGSPICE for discrete- and continuous time cosimulation (download) Keywords: Octave, SPICE, Simulink

Introduction

Many DSP problems have close ties with the analog world. For example, a switched-mode audio power amplifier uses a digital control loop to open and close power transistors driving an analog filter. There are commercial tools for digital-analog cosimulation: Simulink comes to mind, and mainstream EDA vendors support VHDL-AMS or Verilog-A in their...


Sinusoidal Frequency Estimation Based on Time-Domain Samples

Rick Lyons April 20, 201715 comments

The topic of estimating a noise-free real or complex sinusoid's frequency, based on fast Fourier transform (FFT) samples, has been presented in recent blogs here on dsprelated.com. For completeness, it's worth knowing that simple frequency estimation algorithms exist that do not require FFTs to be performed . Below I present three frequency estimation algorithms that use time-domain samples, and illustrate a very important principle regarding so called "exact"...


Two jobs

Stephane Boucher December 5, 201223 comments

For those of you following closely embeddedrelated and the other related sites, you might have noticed that I have been less active for the last couple of months, and I will use this blog post to explain why. The main reason is that I got myself involved into a project that ended up using a better part of my cpu than I originally thought it would.

I currently have two jobs: one as an electrical/dsp engineer recycled as a web publisher and the other as a parent of three kids. My job...


The Exponential Nature of the Complex Unit Circle

Cedron Dawg March 10, 20152 comments
Introduction

This is an article to hopefully give an understanding to Euler's magnificent equation:

$$ e^{i\theta} = cos( \theta ) + i \cdot sin( \theta ) $$

This equation is usually proved using the Taylor series expansion for the given functions, but this approach fails to give an understanding to the equation and the ramification for the behavior of complex numbers. Instead an intuitive approach is taken that culminates in a graphical understanding of the equation.

Complex...

Setting the 3-dB Cutoff Frequency of an Exponential Averager

Rick Lyons October 22, 20126 comments

This blog discusses two ways to determine an exponential averager's weighting factor so that the averager has a given 3-dB cutoff frequency. Here we assume the reader is familiar with exponential averaging lowpass filters, also called a "leaky integrators", to reduce noise fluctuations that contaminate constant-amplitude signal measurements. Exponential averagers are useful because they allow us to implement lowpass filtering at a low computational workload per output sample.

Figure 1 shows...


Benford's law solved with DSP

Steve Smith February 23, 20087 comments

I have a longtime interest in the mystery of 1/f noise. A few years ago I came across Benford’s law, another puzzle that seemed to have many of the same characteristics.

Suppose you collect a large group of seemingly random numbers, such as might appear in a newspaper or financial report. Benford’s law relates to the leading digit of each number, such as "4" in 4.268, "3" in 0.0312, and "9" in -932.34. Since there are nine possible leading digits...