Implementing Simultaneous Digital Differentiation, Hilbert Transformation, and Half-Band Filtering
Recently I've been thinking about digital differentiator and Hilbert transformer implementations and I've developed a processing scheme that may be of interest to the readers here on dsprelated.com.
Multimedia Processing with FFMPEG
FFMPEG is a set of libraries and a command line tool for encoding and decoding audio and video in many different formats. It is a free software project for manipulating/processing multimedia data. Many open source media players are based on FFMPEG libraries.
Approximating the area of a chirp by fitting a polynomial
Once in a while we need to estimate the area of a dataset in which we are interested. This area could give us, for example, force (mass vs acceleration) or electric power (electric current vs charge).
Deconvolution by least squares (Using the power of linear algebra in signal processing).
When we deal with our normal discrete signal processing operations, like FIR/IIR filtering, convolution, filter design, etc. we normally think of the signals as a constant stream of numbers that we put in a sequence
Roll Your Own Differentiation Filters
Introduction
There are many times in digital signal processing that it is necessary to obtain estimates of the derivative of some signal or process from discretely sampled values. Such numerical derivatives are useful in applications such as edge detection, rate of change estimation and optimization, and can even be used as part of quick and efficient dc-blocking filters.
Suppose then, that we want to approximate the derivative of a function at a set of points $\{x_i:i=1,...,N\}$ from...
Helping New Bloggers to Break the Ice: A New Ipad Pro for the Author with the Best Article!
Breaking the ice can be tough. Over the years, many individuals have asked to be given access to the blogging interface only to never post an article.
GPS - some terminology!
Hi!
For my first post, I will share some information about GPS - Global Positioning System. I will delve one step deeper than a basic explanation of how a GPS system works and introduce some terminology.
GPS, like we all know is the system useful for identifying one's position, velocity, & time using signals from satellites (referred to as SV or space vehicle in literature). It uses the principle of trilateration (not triangulation which is misused frequently) for...
Welcoming MANY New Bloggers!
The response to the latest call for bloggers has been amazing and I am very grateful.
In this post I present to you the individuals who, so far (I am still receiving applications at an impressive rate and will update this page as more bloggers are added), have been given access to the blogging interface. I am very pleased with the positive response and I think the near future will see the publication of many great articles, given the quality of the...
Bayes meets Fourier
Joseph Fourier never met Thomas Bayes—Fourier was born in 1768, seven years after Bayes died. But recently I have been exploring connections between the Bayes filter and the Fourier transform.
By "Bayes filter", I don't mean spam filtering using a Bayesian classifier, but rather recursive Bayesian estimation, which is used in robotics and other domains to estimate the state of a system that evolves over time, for example, the position of a moving robot. My interest in...
Number Theory for Codes
Everything in the digital world is encoded. ASCII and Unicode are combinations of bits which have specific meanings to us. If we try to interpret a compiled program as Unicode, the result is a lot of garbage (and beeps!) To reduce errors in transmissions over radio links we use Error Correction Codes so that even when bits are lost we can recover the ASCII or Unicode original. To prevent anyone from understanding a transmission we can encrypt the raw data...
Helping New Bloggers to Break the Ice: A New Ipad Pro for the Author with the Best Article!
Breaking the ice can be tough. Over the years, many individuals have asked to be given access to the blogging interface only to never post an article.
Deconvolution by least squares (Using the power of linear algebra in signal processing).
When we deal with our normal discrete signal processing operations, like FIR/IIR filtering, convolution, filter design, etc. we normally think of the signals as a constant stream of numbers that we put in a sequence
Exact Near Instantaneous Frequency Formulas Best at Peaks (Part 1)
Introduction
This is an article that is a another digression from trying to give a better understanding of the Discrete Fourier Transform (DFT). Although it is not as far off as the last blog article.
A new family of formulas for calculating the frequency of a single pure tone in a short interval in the time domain is presented. They are a generalization of Equation (1) from Rick Lyons' recent blog article titled "Sinusoidal Frequency Estimation Based on Time-Domain Samples"[1]. ...
A brief look at multipath radio channels
Summary: Discussion of multipath propagation and fading in radio links
Radio channels, their effects on communications links and how to model them are a popular topic on comp.dsp. Unfortunately, for many of us there is little or no opportunity to get any "hands-on" experience with radio-related issues, because the required RF measurement equipment is not that easily available.This article gives a very simple example of a radio link that shows multipath propagation and...
Benford's law solved with DSP
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...
Sonos, Shut Up and Take My Money! - Is Spatial Audio Finally Here?
Although I generally agree that money can't buy happiness, I recently made a purchase that has brought me countless hours of pure joy. In this blog post, I want to share my excitement with the DSPRelated community, because I know there are many audio and music enthusiasts here, and also because I suspect there is a lot of DSP magic behind this product. And I would love to hear your opinions and experiences if you have also bought or tried the Sonos ERA 300 wireless speaker, or any other...
Implementing Simultaneous Digital Differentiation, Hilbert Transformation, and Half-Band Filtering
Recently I've been thinking about digital differentiator and Hilbert transformer implementations and I've developed a processing scheme that may be of interest to the readers here on dsprelated.com.
Exponential Smoothing with a Wrinkle
IntroductionThis is an article to hopefully give a better understanding to the Discrete Fourier Transform (DFT) by providing a set of preprocessing filters to improve the resolution of the DFT. Because of the exponential nature of sinusoidal functions, they have special mathematical properties when exponential smoothing is applied to them. These properties are derived and explained in this blog article.
Basic Exponential Smoothing
Exponential smoothing is also known as...
Design Square-Root Nyquist Filters
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].
BackgroundSingle-carrier modulation, such as QAM, uses filters to limit the bandwidth of the signal. Figure 1 shows a simplified QAM system block...
Above-Average Smoothing of Impulsive Noise
In this blog I show a neat noise reduction scheme that has the high-frequency noise reduction behavior of a traditional moving average process but with much better impulsive-noise suppression.
In practice we may be required to make precise measurements in the presence of highly-impulsive noise. Without some sort of analog signal conditioning, or digital signal processing, it can be difficult to obtain stable and repeatable, measurements. This impulsive-noise smoothing trick,...
Reducing IIR Filter Computational Workload
This blog describes a straightforward method to significantly reduce the number of necessary multiplies per input sample of traditional IIR lowpass and highpass digital filters.
Reducing IIR Filter Computations Using Dual-Path Allpass Filters
We can improve the computational speed of a lowpass or highpass IIR filter by converting that filter into a dual-path filter consisting of allpass filters as shown in Figure 1.
...Third-Order Distortion of a Digitally-Modulated Signal
Analog designers are always harping about amplifier third-order distortion. Why? In this article, we’ll look at why third-order distortion is important, and simulate a QAM signal with third-order distortion.
In the following analysis, we assume that signal phase at the amplifier output is not a function of amplitude. With this assumption, the output y of a non-ideal amplifier can be written as a power series of the input signal x:
$$y=...
Collaborative Writing Experiment: Your Favorite DSP Websites
You are invited to contribute to the content of this blog post through the magic of Google Docs' real time collaboration feature.
I discovered this tool several months ago when I was looking for a way to coordinate our annual family halloween party (potluck) and avoid the very unpleasant situation of ending up with too much chips and not enough chocolate (first world problem!). It was amusing to keep an eye on the "food you will bring" document we had created for this and watch...
Learn to Use the Discrete Fourier Transform
Discrete-time sequences arise in many ways: a sequence could be a signal captured by an analog-to-digital converter; a series of measurements; a signal generated by a digital modulator; or simply the coefficients of a digital filter. We may wish to know the frequency spectrum of any of these sequences. The most-used tool to accomplish this is the Discrete Fourier Transform (DFT), which computes the discrete frequency spectrum of a discrete-time sequence. The DFT is easily calculated using software, but applying it successfully can be challenging. This article provides Matlab examples of some techniques you can use to obtain useful DFT’s.
Project introduction: Digital Filter Blocks in MyHDL and their integration in pyFDA
Hi everyone! After a lot of hesitation and several failed attempts, I have finally entered the world of blogging. A little about myself : My name is Sriyash Caculo and I’m a third year undergrad student at BITS Pilani K.K. Birla Goa Campus pursuing a major in Electronics and Instrumentation engineering. Being an electronics engineer, I developed an interest in Digital Signal Processing and its implementation on hardware.
This blog-post is the first of many to come for the...
A Remarkable Bit of DFT Trivia
I recently noticed a rather peculiar example of discrete Fourier transform (DFT) trivia; an unexpected coincidence regarding the scalloping loss of the DFT. Here's the story.
DFT SCALLOPING LOSS As you know, if we perform an N-point DFT on N real-valued time-domain samples of a discrete sine wave, whose frequency is an integer multiple of fs/N (fs is the sample rate in Hz), the peak magnitude of the sine wave's positive-frequency spectral component will be
where A is the peak amplitude...
Bank-switched Farrow resampler
Bank-switched Farrow resampler SummaryA modification of the Farrow structure with reduced computational complexity.Compared to a conventional design, the impulse response is broken into a higher number of segments. Interpolation accuracy is achieved with a lower polynomial order, requiring fewer multiplications per output sample at the expense of a higher overall number of coefficients.
Example codeThis code snippet provides a Matlab / Octave implementation.And
Multilayer Perceptrons and Event Classification with data from CODEC using Scilab and Weka
For my first blog, I thought I would introduce the reader to Scilab [1] and Weka [2]. In order to illustrate how they work, I will put together a script in Scilab that will sample using the microphone and CODEC on your PC and save the waveform as a CSV file.
Deconvolution by least squares (Using the power of linear algebra in signal processing).
When we deal with our normal discrete signal processing operations, like FIR/IIR filtering, convolution, filter design, etc. we normally think of the signals as a constant stream of numbers that we put in a sequence
