DSPRelated.com

Add a Power Marker to a Power Spectral Density (PSD) Plot

Neil Robertson February 7, 2021

Perhaps we should call most Power Spectral Density (PSD) calculations relative PSD, because usually we don’t have to worry about absolute power levels.  However, for cases (e.g., measurements or simulations) where we are concerned with absolute power, it would be nice to be able to display it on a PSD plot.  Unfortunately, you can’t read the power directly from the plot.  For example, the plotted spectral peak of a narrowband signal, such as a sinewave, is lower than the...


A Simpler Goertzel Algorithm

Rick Lyons February 4, 2021

In this blog I propose a Goertzel algorithm that is simpler than the version of the Goertzel algorithm that is traditionally presented DSP textbooks. Below I very briefly describe the DSP textbook version of the Goertzel algorithm followed by a description of my proposed simpler algorithm.

The Traditional DSP Textbook Goertzel Algorithm

The so-called Goertzel algorithm is used to efficiently compute a single mth-bin sample of an N-point discrete Fourier transform (DFT) [1-4]. The...


60-Hz Noise and Baseline Drift Reduction in ECG Signal Processing

Rick Lyons January 23, 20216 comments

Electrocardiogram (ECG) signals are obtained by monitoring the electrical activity of the human heart for medical diagnostic purposes [1]. This blog describes a very efficient digital filter used to reduce both 60 Hz AC power line noise and unwanted signal baseline drift that often contaminate ECG signals.

PDF_HERE

We'll first describe the ECG noise reduction filter and then examine the filter's performance in a real-world ECG signal filtering example.Proposed ECG Noise Reduction Digital...


Find Aliased ADC or DAC Harmonics (with animation)

Neil Robertson January 11, 20212 comments

When a sinewave is applied to a data converter (ADC or DAC), device nonlinearities produce harmonics.  If a harmonic frequency is greater than the Nyquist frequency, the harmonic appears as an alias.  In this case, it is not at once obvious if a given spur is a harmonic, and if so, its order.  In this article, we’ll present Matlab code to simulate the data converter nonlinearities and find the harmonic alias frequencies.  Note that Analog Devices has an online tool for...


Adaptive Beamforming is like Squeezing a Water Balloon

Christopher Hogstrom January 9, 20214 comments

Adaptive beamforming was first developed in the 1960s for radar and sonar applications. The main idea is that signals can be captured using multiple sensors and the sensor outputs can be combined to enhance the signals propagating from specific directions and attenuate (null out) signals from other directions. It has grown immensely in recent years as processors have become faster and cheaper. Today, adaptive beamforming applications include smart speakers (like the Amazon Echo),...


Compute Images/Aliases of CIC Interpolators/Decimators

Neil Robertson November 1, 20202 comments

Cascade-Integrator-Comb (CIC) filters are efficient fixed-point interpolators or decimators.  For these filters, all coefficients are equal to 1, and there are no multipliers.  They are typically used when a large change in sample rate is needed.  This article provides two very simple Matlab functions that can be used to compute the spectral images of CIC interpolators and the aliases of CIC decimators.

1.  CIC Interpolators

Figure 1 shows three interpolate-by-M...


Exploring Human Hearing Range

Stephen Morris October 31, 20204 comments
Human Hearing Range

In this post, I'll look at an interesting aspect of Audacity – using it to explore the threshold of human hearing. In my book Digital Signal Processing: A Gentle Introduction with Audio Examples, I go into this topic and I include a side note on the amazing hearing range of our canine companions.

Creating a Test Audio File

Audacity allows for the generation of a variety of test signals. If you click the Generate->Tone menu, it looks something like...


The DSP Online Conference - Right Around the Corner!

Stephane Boucher September 20, 2020

It is Sunday night as I write this blog post with a few days to go before the virtual doors of the very first DSP Online Conference open..

It all started with a post in the DSPRelated forum about three months ago.  We had just had a blast running the 2020 Embedded Online Conference and we thought it could be fun to organize a smaller event dedicated to the DSP community.  So my goal with the post in the forum was to see if...


The Zeroing Sine Family of Window Functions

Cedron Dawg August 16, 20202 comments
Introduction

This is an article to hopefully give a better understanding of the Discrete Fourier Transform (DFT) by introducing a class of well behaved window functions that the author believes to be previously unrecognized. The definition and some characteristics are displayed. The heavy math will come in later articles. This is an introduction to the family, and a very special member of it.

This is one of my longer articles. The bulk of the material is in the front half. The...


Design Square-Root Nyquist Filters

Neil Robertson July 13, 2020

In his book on multirate signal processing, harris presents a nifty technique for designing square-root Nyquist FIR filters with good stopband attenuation [1].  In this post, I describe the method and provide a Matlab function for designing the filters.  You can find a Matlab function by harris for designing the filters at [2].

Background

Single-carrier modulation, such as QAM, uses filters to limit the bandwidth of the signal.  Figure 1 shows a simplified QAM system block...


Optimizing the Half-band Filters in Multistage Decimation and Interpolation

Rick Lyons January 4, 201616 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...


Evaluate Window Functions for the Discrete Fourier Transform

Neil Robertson December 18, 20184 comments

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...


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

Stephane Boucher March 22, 20191 comment

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...


A Differentiator With a Difference

Rick Lyons November 3, 200712 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...


The Power Spectrum

Neil Robertson October 8, 2016

Often, when calculating the spectrum of a sampled signal, we are interested in relative powers, and we don’t care about the absolute accuracy of the y axis.  However, when the sampled signal represents an analog signal, we sometimes need an accurate picture of the analog signal’s power in the frequency domain.  This post shows how to calculate an accurate power spectrum.

Parseval’s theorem [1,2] is a property of the Discrete Fourier Transform (DFT) that...


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...


The Most Interesting FIR Filter Equation in the World: Why FIR Filters Can Be Linear Phase

Rick Lyons August 18, 201517 comments

This blog discusses a little-known filter characteristic that enables real- and complex-coefficient tapped-delay line FIR filters to exhibit linear phase behavior. That is, this blog answers the question:

What is the constraint on real- and complex-valued FIR filters that guarantee linear phase behavior in the frequency domain?

I'll declare two things to convince you to continue reading.

Declaration# 1: "That the coefficients must be symmetrical" is not a correct


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...


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...


Free Goodies from Embedded World - What to Do Next?

Stephane Boucher March 6, 20193 comments

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.


New Papers / Theses Section

Stephane Boucher March 21, 20081 comment

The new 'Papers & Theses' section is now online: http://www.dsprelated.com/documents.phpThe idea is to list and organize in one place as many DSP related dissertations (PhD & Masters) and papers/articles as possible.If you are the author of a thesis or paper and would like to have it listed on DSPRelated.com, please follow these steps:- Make sure that you are allowed to share the document online (copyright).- If you don't already have one, make a 'pdf' copy of your document. ...


New Blog Section!

Stephane Boucher September 19, 20072 comments

By now, chances are you have noticed the new blogs section (you are actually in it right now!).

Following an email I sent to the members of the site, a few weeks ago, asking for dsp engineers willing to blog here, I received around 50 propositions. I have selected an initial set of 10 bloggers (that I will soon introduce into a seperate post) and I am currently in the process of creating their accounts. Markus and Parth have already...


New Discussion Group: DSP & FPGA

Stephane Boucher September 11, 20078 comments

I have just created a new discussion group for engineers implementing DSP functions on FPGAs. The creation of this group has been on my todo list for a long time. If you want to join the group, send a blank email to: fpgadsp-subscribe@yahoogroups.com

As usual, it should take a few weeks before there are enough members for interesting discussions to get started.