Spread the Word and Run a Chance to Win a Bundle of Goodies from Embedded World

Stephane Boucher February 21, 2019

Do you have a Twitter and/or Linkedin account?

If you do, please consider paying close attention for the next few days to the EmbeddedRelated Twitter account and to my personal Linkedin account (feel free to connect).  This is where I will be posting lots of updates about how the EmbeddedRelated.tv live streaming experience is going at Embedded World.

The most successful this live broadcasting experience will be, the better the chances that I will be able to do it...

Launch of EmbeddedRelated.tv

Stephane Boucher February 21, 2019

With the upcoming Embedded Word just around the corner, I am very excited to launch the EmbeddedRelated.tv platform.  

This is where you will find the schedule for all the live broadcasts that I will be doing from Embedded World next week.  Please note that the schedule will be evolving constantly, even during the show, so I suggest your refresh the page often.  For instance, I am still unsure if I will be able to do the 'opening of the doors' broadcast as...

Stereophonic Amplitude-Panning: A Derivation of the 'Tangent Law'

Rick Lyons February 20, 20199 comments

In a recent Forum post here on dsprelated.com the audio signal processing subject of stereophonic amplitude-panning was discussed. And in that Forum thread the so-called "Tangent Law", the fundamental principle of stereophonic amplitude-panning, was discussed. However, none of the Forum thread participants had ever seen a derivation of the Tangent Law. This blog presents such a derivation and if this topic interests you, then please read on.

The notion of stereophonic amplitude-panning is...

Live Streaming from Embedded World!

Stephane Boucher February 12, 2019

For those of you who won't be attending Embedded World this year, I will try to be your eyes and ears by video streaming live from the show floor.   

I am not talking improvised streaming from a phone, but real, high quality HD streaming with a high-end camera and a device that will bond three internet connections (one wifi and two cellular) to ensure a steady, and hopefully reliable, stream. All this to hopefully give those of you who cannot be there in person a virtual...

The Phase Vocoder Transform

Christian Yost February 12, 2019
1 Introduction

I would like to look at the phase vocoder in a fairly ``abstract'' way today. The purpose of this is to discuss a method for measuring the quality of various phase vocoder algorithms, and building off a proposed measure used in [2]. There will be a bit of time spent in the domain of continuous mathematics, thus defining a phase vocoder function or map rather than an algorithm. We will be using geometric visualizations when possible while pointing out certain group theory...

Compute the Frequency Response of a Multistage Decimator

Neil Robertson February 10, 20192 comments

Figure 1a shows the block diagram of a decimation-by-8 filter, consisting of a low-pass finite impulse response (FIR) filter followed by downsampling by 8 [1].  A more efficient version is shown in Figure 1b, which uses three cascaded decimate-by-two filters.  This implementation has the advantages that only FIR 1 is sampled at the highest sample rate, and the total number of filter taps is lower.

The frequency response of the single-stage decimator before downsampling is just...

Smaller DFTs from bigger DFTs

Aditya Dua January 22, 20198 comments

Let's consider the following hypothetical situation: You have a sequence $x$ with $N/2$ points and a black box which can compute the DFT (Discrete Fourier Transform) of an $N$ point sequence. How will you use the black box to compute the $N/2$ point DFT of $x$? While the problem may appear to be a bit contrived, the answer(s) shed light on some basic yet insightful and useful properties of the DFT.

On a related note, the reverse problem of computing an $N$...

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, 201933 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...

Noise shaping

Markus Nentwig December 9, 20123 comments

eywords: Quantization noise; noise shaping

A brief introduction to noise shaping, with firm resolve not to miss the forest for the trees. We may still stumble over some assorted roots. Matlab example code is included.


Fig. 1 shows a digital signal that is reduced to a lower bit width, for example a 16 bit signal being sent to a 12 bit digital-to-analog converter. Rounding to the nearest output value is obviously the best that can be done to minimize the error of each...

Computing Large DFTs Using Small FFTs

Rick Lyons June 23, 200821 comments

It is possible to compute N-point discrete Fourier transforms (DFTs) using radix-2 fast Fourier transforms (FFTs) whose sizes are less than N. For example, let's say the largest size FFT software routine you have available is a 1024-point FFT. With the following trick you can combine the results of multiple 1024-point FFTs to compute DFTs whose sizes are greater than 1024.

The simplest form of this idea is computing an N-point DFT using two N/2-point FFT operations. Here's how the trick...

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:...

How Discrete Signal Interpolation Improves D/A Conversion

Rick Lyons May 28, 20121 comment
This blog post is also available in pdf format. Download here.

Earlier this year, for the Linear Audio magazine, published in the Netherlands whose subscribers are technically-skilled hi-fi audio enthusiasts, I wrote an article on the fundamentals of interpolation as it's used to improve the performance of analog-to-digital conversion. Perhaps that article will be of some value to the subscribers of dsprelated.com. Here's what I wrote:

We encounter the process of digital-to-analog...

TCP/IP interface (Matlab/Octave)

Markus Nentwig June 17, 201210 comments

Communicate with measurement instruments via Ethernet (no-toolbox-Matlab or Octave)


Measurement automation is digital signal processing in a wider sense: Getting a digital signal from an analog world usually involves some measurement instruments, for example a spectrum analyzer. Modern instruments, and also many off-the-shelf prototyping boards such as FPGA cards [1] or microcontrollers [2] are able to communicate via Ethernet. Here, I provide some basic mex-functions (compiled C...

Plotting Discrete-Time Signals

Neil Robertson September 15, 20195 comments

A discrete-time sinusoid can have frequency up to just shy of half the sample frequency.  But if you try to plot the sinusoid, the result is not always recognizable.  For example, if you plot a 9 Hz sinusoid sampled at 100 Hz, you get the result shown in the top of Figure 1, which looks like a sine.  But if you plot a 35 Hz sinusoid sampled at 100 Hz, you get the bottom graph, which does not look like a sine when you connect the dots.  We typically want the plot of a...

Back from Embedded World 2019 - Funny Stories and Live-Streaming Woes

Stephane Boucher March 1, 20191 comment

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...

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


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, 201719 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"...

Spectral Flipping Around Signal Center Frequency

Rick Lyons November 7, 20074 comments

Most of us are familiar with the process of flipping the spectrum (spectral inversion) of a real signal by multiplying that signal's time samples by (-1)n. In that process the center of spectral rotation is fs/4, where fs is the signal's sample rate in Hz. In this blog we discuss a different kind of spectral flipping process.

Consider the situation where we need to flip the X(f) spectrum in Figure 1(a) to obtain the desired Y(f) spectrum shown in Figure 1(b). Notice that the center of...