## Generating Partially Correlated Random Variables

IntroductionIt is often useful to be able to generate two or more signals with specific cross-correlations. Or, more generally, we would like to specify an $\left(N \times N\right)$ covariance matrix, $\mathbf{R}_{xx}$, and generate $N$ signals which will produce this covariance matrix.

There are many applications in which this technique is useful. I discovered a version of this method while analysing radar systems, but the same approach can be used in a very wide range of...

## Free Goodies from Embedded World - Full Inventory and Upcoming Draw Live-Streaming Date

March 22, 2019

Chances are that you already know that I went to Embedded World a few weeks ago and came back with a bag full of "goodies".  Initially, my vision was to do a single draw for one person to win it all, but I didn't expect to come back with so much stuff and so many development kits.   Based on your feedback, it seems like you guys agree that It wouldn't make sense for one person to win everything as no-one could make good use of all the boards and there would be lots of...

## Angle Addition Formulas from Euler's Formula

Introduction

This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT), but only indirectly. The main intent is to get someone who is uncomfortable with complex numbers a little more used to them and relate them back to already known Trigonometric relationships done in Real values. It is essentially a followup to my first blog article "The Exponential Nature of the Complex Unit Circle".

Polar Coordinates

The more common way of...

## Demonstrating the Periodic Spectrum of a Sampled Signal Using the DFT

One of the basic DSP principles states that a sampled time signal has a periodic spectrum with period equal to the sample rate.  The derivation of can be found in textbooks [1,2].  You can also demonstrate this principle numerically using the Discrete Fourier Transform (DFT).

The DFT of the sampled signal x(n) is defined as:

$$X(k)=\sum_{n=0}^{N-1}x(n)e^{-j2\pi kn/N} \qquad (1)$$

Where

X(k) = discrete frequency spectrum of time sequence x(n)

## Free Goodies from Embedded World - What to Do Next?

I told you I would go on a hunt for free stuff at Embedded World in order to build a bundle for someone to win.

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

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...

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

February 21, 2019

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

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'

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!

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...

## A Fixed-Point Introduction by Example

Introduction

The finite-word representation of fractional numbers is known as fixed-point.  Fixed-point is an interpretation of a 2's compliment number usually signed but not limited to sign representation.  It extends our finite-word length from a finite set of integers to a finite set of rational real numbers [1].  A fixed-point representation of a number consists of integer and fractional components.  The bit length is defined...

## Adventures in Signal Processing with Python

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 article — I do hope they can improve their software and reduce the price. Please note this...

## A Quadrature Signals Tutorial: Complex, But Not Complicated

Introduction Quadrature signals are based on the notion of complex numbers and perhaps no other topic causes more heartache for newcomers to DSP than these numbers and their strange terminology of j operator, complex, imaginary, real, and orthogonal. If you're a little unsure of the physical meaning of complex numbers and the j = √-1 operator, don't feel bad because you're in good company. Why even Karl Gauss, one the world's greatest mathematicians, called the j-operator the "shadow of...

## Ten Little Algorithms, Part 2: The Single-Pole Low-Pass Filter

Other articles in this series:

I’m writing this article in a room with a bunch of other people talking, and while sometimes I wish they would just SHUT UP, it would be...

## Understanding the 'Phasing Method' of Single Sideband Demodulation

There are four ways to demodulate a transmitted single sideband (SSB) signal. Those four methods are:

• synchronous detection,
• phasing method,
• Weaver method, and
• filtering method.

Here we review synchronous detection in preparation for explaining, in detail, how the phasing method works. This blog contains lots of preliminary information, so if you're already familiar with SSB signals you might want to scroll down to the 'SSB DEMODULATION BY SYNCHRONOUS DETECTION'...

## An Interesting Fourier Transform - 1/f Noise

Power law functions are common in science and engineering. A surprising property is that the Fourier transform of a power law is also a power law. But this is only the start- there are many interesting features that soon become apparent. This may even be the key to solving an 80-year mystery in physics.

It starts with the following Fourier transform:

The general form is tα ↔ ω-(α+1), where α is a constant. For example, t2 ↔...

## Handling Spectral Inversion in Baseband Processing

The problem of "spectral inversion" comes up fairly frequently in the context of signal processing for communication systems. In short, "spectral inversion" is the reversal of the orientation of the signal bandwidth with respect to the carrier frequency. Rick Lyons' article on "Spectral Flipping" at http://www.dsprelated.com/showarticle/37.php discusses methods of handling the inversion (as shown in Figure 1a and 1b) at the signal center frequency. Since most communication systems process...

## Free DSP Books on the Internet

While surfing the "net" I have occasionally encountered signal processing books whose chapters could be downloaded to my computer. I started keeping a list of those books and, over the years, that list has grown to over forty books. Perhaps the list will be of interest to you.

## Python scipy.signal IIR Filtering: An Example

May 19, 2013
Introduction

In the last posts I reviewed how to use the Python scipy.signal package to design digital infinite impulse response (IIR) filters, specifically, using the iirdesign function (IIR design I and IIR design II ).  In this post I am going to conclude the IIR filter design review with an example.

Previous posts:

## Understanding and Preventing Overflow (I Had Too Much to Add Last Night)

December 4, 2013

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 under 21024, and if you go beyond that you have problems:

for k in [10, 100, 1000, 1020, 1023, 1023.9, 1023.9999, 1024]: try: ...

## Free Goodies from Embedded World - Full Inventory and Upcoming Draw Live-Streaming Date

March 22, 2019

Chances are that you already know that I went to Embedded World a few weeks ago and came back with a bag full of "goodies".  Initially, my vision was to do a single draw for one person to win it all, but I didn't expect to come back with so much stuff and so many development kits.   Based on your feedback, it seems like you guys agree that It wouldn't make sense for one person to win everything as no-one could make good use of all the boards and there would be lots of...

## Free Goodies from Embedded World - What to Do Next?

I told you I would go on a hunt for free stuff at Embedded World in order to build a bundle for someone to win.

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

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...

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

February 21, 2019

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

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...

## Live Streaming from Embedded World!

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...

February 5, 2019

## Sensors Expo - Trip Report & My Best Video Yet!

This was my first time at Sensors Expo and my second time in Silicon Valley and I must say I had a great time.

Before I share with you what I find to be, by far, my best 'highlights' video yet for a conference/trade show, let me try to entertain you with a few anecdotes from this trip.  If you are not interested by my stories or maybe don't have the extra minutes needed to read them, please feel free to skip to the end of this blog post to watch the...

## Who else is going to Sensors Expo in San Jose? Looking for roommate(s)!

This will be my first time attending this show and I must say that I am excited. I am bringing with me my cameras and other video equipment with the intention to capture as much footage as possible and produce a (hopefully) fun to watch 'highlights' video. I will also try to film as many demos as possible and share them with you.

I enjoy going to shows like this one as it gives me the opportunity to get out of my home-office (from where I manage and run the *Related sites) and actually...

## Crowdfunding Articles?

Many of you have the knowledge and talent to write technical articles that would benefit the EE community.  What is missing for most of you though, and very understandably so, is the time and motivation to do it.

But what if you could make some money to compensate for your time spent on writing the article(s)?  Would some of you find the motivation and make the time?

I am thinking of implementing a system/mechanism that would allow the EE community to...