A Brief Introduction To Romberg Integration

Rick Lyons January 16, 201911 comments

This blog briefly describes a remarkable integration algorithm, called "Romberg integration." The algorithm is used in the field of numerical analysis but it's not so well-known in the world of DSP.

To show the power of Romberg integration, and to convince you to continue reading, consider the notion of estimating the area under the continuous x(t) = sin(t) curve based on the five x(n) samples represented by the dots in Figure 1.

The results of performing a Trapezoidal Rule, a...


Use Matlab Function pwelch to Find Power Spectral Density – or Do It Yourself

Neil Robertson January 13, 20198 comments

In my last post, we saw that finding the spectrum of a signal requires several steps beyond computing the discrete Fourier transform (DFT)[1].  These include windowing the signal, taking the magnitude-squared of the DFT, and computing the vector of frequencies.  The Matlab function pwelch [2] performs all these steps, and it also has the option to use DFT averaging to compute the so-called Welch power spectral density estimate [3,4].

In this article, I’ll present some...


Microprocessor Family Tree

Rick Lyons January 10, 20195 comments

Below is a little microprocessor history. Perhaps some of the ol' timers here will recognize a few of these integrated circuits. I have a special place in my heart for the Intel 8080 chip.

Image copied, without permission, from the now defunct Creative Computing magazine, Vol. 11, No. 6, June 1985.


A Markov View of the Phase Vocoder Part 2

Christian Yost January 8, 2019
Introduction

Last post we motivated the idea of viewing the classic phase vocoder as a Markov process. This was due to the fact that the input signal’s features are unknown to the computer, and the phase advancement for the next synthesis frame is entirely dependent on the phase advancement of the current frame. We will dive a bit deeper into this idea, and flesh out some details which we left untouched last week. This includes the effect our discrete Fourier transform has on the...


A Markov View of the Phase Vocoder Part 1

Christian Yost January 8, 2019
Introduction

Hello! This is my first post on dsprelated.com. I have a blog that I run on my website, http://www.christianyostdsp.com. In order to engage with the larger DSP community, I'd like to occasionally post my more engineering heavy writing here and get your thoughts.

Today we will look at the phase vocoder from a different angle by bringing some probability into the discussion. This is the first part in a short series. Future posts will expand further upon the ideas...


Evaluate Window Functions for the Discrete Fourier Transform

Neil Robertson December 18, 2018

The Discrete Fourier Transform (DFT) operates on a finite length time sequence to compute its spectrum.  For a continuous signal like a sinewave, you need to capture a segment of the signal in order to perform the DFT.  Usually, you also need to apply a window function to the captured signal before taking the DFT [1 - 3].  There are many different window functions and each produces a different approximation of the spectrum.  In this post, we’ll present Matlab code that...


Feedback Controllers - Making Hardware with Firmware. Part 10. DSP/FPGAs Behaving Irrationally

Steve Maslen November 22, 2018

This article will look at a design approach for feedback controllers featuring  low-latency "irrational" characteristics to enable the creation of physical components such as transmission lines. Some thought will also be given as to the capabilities of the currently utilized Intel Cyclone V, the new Cyclone 10 GX and the upcoming Xilinx Versal floating-point FPGAs/ACAPs.    

Fig 1. Making a Transmission Line, with the Circuit Emulator

 

Additional...


Polar Coding Notes: A Simple Proof

Lyons Zhang November 8, 2018

For any B-DMC $W$, the channels $\{W_N^{(i)}\}$ polarize in the sense that, for any fixed $\delta \in (0, 1)$, as $N$ goes to infinity through powers of two, the fraction of indices $i \in \{1, \dots, N\}$ for which $I(W_N^{(i)}) \in (1 − \delta, 1]$ goes to $I(W)$ and the fraction for which $I(W_N^{(i)}) \in [0, \delta)$ goes to $1−I(W)^{[1]}$.

Mrs. Gerber’s Lemma

Mrs. Gerber’s Lemma provides a lower bound on the entropy of the modulo-$2$ sum of two binary random...


Polar Coding Notes: Channel Combining and Channel Splitting

Lyons Zhang October 19, 2018

Channel Combining  

Channel combining is a step that combines copies of a given B-DMC $W$ in a recursive manner to produce a vector channel $W_N : {\cal X}^N \to {\cal Y}^N$, where $N$ can be any power of two, $N=2^n, n\le0^{[1]}$.  

The notation $u_1^N$ as shorthand for denoting a row vector $(u_1, \dots , u_N)$.  

The vector channel $W_N$ is the virtual channel between the input sequence $u_1^N$ to a linear encoder and the output sequence $y^N_1$ of $N$...


Project Report : Digital Filter Blocks in MyHDL and their integration in pyFDA

Sriyash Caculo August 13, 20181 comment

The Google Summer of Code 2018 is now in its final stages, and I’d like to take a moment to look back at what goals were accomplished, what remains to be completed and what I have learnt.

The project overview was discussed in the previous blog posts. However this post serves as a guide to anyone who wishes to learn about the project or carry it forward. Hence I will go over the project details again.

Project overview

The project “Digital Filter Blocks in MyHDL and PyFDA integration" aims...


Linear-phase DC Removal Filter

Rick Lyons March 30, 200823 comments

This blog describes several DC removal networks that might be of interest to the dsprelated.com readers.

Back in August 2007 there was a thread on the comp.dsp newsgroup concerning the process of removing the DC (zero Hz) component from a time-domain sequence [1]. Discussed in that thread was the notion of removing a signal's DC bias by subtracting the signal's moving average from that signal, as shown in Figure 1(a).

Figure 1.

At first I thought...


Time Machine, Anyone?

Andor Bariska March 7, 20086 comments

Abstract: Dispersive linear systems with negative group delay have caused much confusion in the past. Some claim that they violate causality, others that they are the cause of superluminal tunneling. Can we really receive messages before they are sent? This article aims at pouring oil in the fire and causing yet more confusion :-).

PDF version of this article.

Introduction 

In this article we reproduce the results of a physical experiment...


Frequency-Domain Periodicity and the Discrete Fourier Transform

Eric Jacobsen August 6, 2012

Introduction

Some of the better understood aspects of time-sampled systems are the limitations and requirements imposed by the Nyquist sampling theorem [1]. Somewhat less understood is the periodic nature of the spectra of sampled signals. This article provides some insights into sampling that not only explain the periodic nature of the sampled spectrum, but aliasing, bandlimited sampling, and the so-called "super-Nyquist" or IF sampling. The approaches taken here include both mathematical...


A Differentiator With a Difference

Rick Lyons November 3, 20078 comments

Some time ago I was studying various digital differentiating networks, i.e., networks that approximate the process of taking the derivative of a discrete time-domain sequence. By "studying" I mean that I was experimenting with various differentiating filter coefficients, and I discovered a computationally-efficient digital differentiator. A differentiator that, for low fequency signals, has the power of George Foreman's right hand! Before I describe this differentiator, let's review a few...


A Beginner's Guide to OFDM

Qasim Chaudhari May 1, 20176 comments

In the recent past, high data rate wireless communications is often considered synonymous to an Orthogonal Frequency Division Multiplexing (OFDM) system. OFDM is a special case of multi-carrier communication as opposed to a conventional single-carrier system. 

The concepts on which OFDM is based are so simple that almost everyone in the wireless community is a technical expert in this subject. However, I have always felt an absence of a really simple guide on how OFDM works which can...


Accurate Measurement of a Sinusoid's Peak Amplitude Based on FFT Data

Rick Lyons December 14, 201110 comments

There are two code snippets associated with this blog post:

Flat-Top Windowing Function for the Accurate Measurement of a Sinusoid's Peak Amplitude Based on FFT Data

and

Testing the Flat-Top Windowing Function

This blog discusses an accurate method of estimating time-domain sinewave peak amplitudes based on fast Fourier transform (FFT) data. Such an operation sounds simple, but the scalloping loss characteristic of FFTs complicates the process. We eliminate that complication by...


Computing the Group Delay of a Filter

Rick Lyons November 19, 200817 comments

I just learned a new method (new to me at least) for computing the group delay of digital filters. In the event this process turns out to be interesting to my readers, this blog describes the method. Let's start with a bit of algebra so that you'll know I'm not making all of this up.

Assume we have the N-sample h(n) impulse response of a digital filter, with n being our time-domain index, and that we represent the filter's discrete-time Fourier transform (DTFT), H(ω), in polar form...


Oscilloscope Dreams

Jason Sachs January 14, 20125 comments

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 are basically just fancy expensive boxes for graphing voltage vs. time. They span a wide range of features and prices:...


Digital PLL's -- Part 1

Neil Robertson June 7, 201618 comments
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...


Generating pink noise

Allen Downey 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...


DSPRelated Finally on Twitter!

Stephane Boucher February 20, 20132 comments

Hello!

It's been a while since you've heard from me - and there are many reasons why:

1 - I've made a clown of myself (video here)

2 - I've been working on unifying the user management system.  You can now participate to the three related sites (DSPRelated, FPGARelated and EmbeddedRelated) with only one account (same login info). 

3- I've been working on getting up to speed with social networks and especially Twitter.   I have resisted the idea for a while - at 40...


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.

edit - video of the event:

I currently have two jobs: one as an electrical/dsp engineer recycled as a web publisher and the other...


Do you like the new Comments System?

Stephane Boucher September 19, 20124 comments

I have just finished implementing a new comments system for the blogs.  Do you like it?

Please share your thoughts with me by adding a comment.

I'll wait a few days and make sure it works properly and then I'll port it to the code snippets and papers section.

Thanks!


DSP Papers, Articles, Theses, etc

Stephane Boucher March 17, 20111 comment

As you may already know, there is a 'Papers and Theses' section on DSPRelated:http://www.dsprelated.com/documents.phpThere are hundreds of DSP Related documents (articles, papers, theses, dissertations, etc) scattered all around the web, and the goal with this section is to find and list as many of those documents as possible in one place. There are, at the moment, a little over 100 documents listed, which I believe is only a small subset of what is available out there, and I need your help...


Code Snippets Suggestions

Stephane Boucher January 19, 20115 comments

Despite being only a couple of months old, the Code Snippet section ( DSPRelated.com/code.php ) already contains tens of snippets, thanks to the contributors who have taken the time to share their code. 

But let's not stop here - there is room for several hundreds more snippets before the database can be said to cover a decent portion of the DSP field.  

To keep the momentum going, I will do two things:  

First, I am modifying the rewards program.  Instead of...


Latest DSP Books

Stephane Boucher December 1, 2010

As you may already know, Rick Lyons has just published a new edition of his highly acclaimed book: "Understanding Digital Signal Processing".   This book has been getting very high ratings and positive reviews from the DSP community since the publication of the first edition.  The 3rd edition seems to contain more than enough new material to justify replacing your old copy.

Also of possible interest to you, a new DSP book by C. Britton Rorabaugh titled "


Code Snippets Section Now LIVE

Stephane Boucher November 2, 20101 comment

The new code sharing section is now live and can be accessed HERE.  

Please take a few minutes to rate and/or comment the snippets that you have the expertise to judge.

If you think of some code snippets that you would like to share with the DSP community, please apply to become a contributor HERE.

If you are not aware of the reward program for contributors, your can learn about it HERE.

As always, your comments and suggestions are...


New Code Sharing Section & Reward Program for Contributors!

Stephane Boucher October 15, 201012 comments

UPDATE (11/02/2010): The code section is now live.

UPDATE 2 (01/31/2011): The reward program has changed.  A flat fee of $20 per code snippet submitted will now be paid.  

_______________

I am very happy to finally announce the imminent launch of the new code sharing section.  My vision for this new section is a rich library of high quality code snippets for the DSP community, from processor specific functions to Matlab or Scilab routines, from the simplest filter...


50,000th Member Announced!

Stephane Boucher January 11, 2010

In my last post, I wrote that DSPRelated.com was about to reach the 50,000 members mark.  Well, I am very happy to announce that it happened during the holidays, and the lucky person is Charlie Tsai from Taiwan.  Charlie is an assistant professor in the Department of Electrical Engineering at the National Central University in Taiwan where he teaches the "Biomedical Signal Processing" class.  He is also the advisor of the


Almost 50,000 Members!

Stephane Boucher November 26, 20091 comment

I am very happy to announce that DSPRelated.com will reach the 50,000 registered members mark before the end of 2009. To celebrate this milestone, I will buy a BMW 5 to the 50,000th person to register (please make sure to confirm you email address to activate your registration).  Please read the fine prints after the picture.

I am just having fun here and it's not even April's fool day.  The 50,000th member won't get a BMW (I wish I could offer it!),...