Maximum Likelihood Estimation
Any observation has some degree of noise content that makes our observations uncertain. When we try to make conclusions based on noisy observations, we have to separate the dynamics of a signal from noise.
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
Practical guide to constructing differentiation filters from sampled signals using interpolation rather than messy Taylor expansions. It shows how Lagrange polynomials produce forward, backward and central derivative formulas, and how the pseudospectral differentiation matrix D = X'X^{-1} maps sample vectors to derivative estimates. Includes a compact MATLAB snippet and a discussion of node-choice tradeoffs and ill-conditioning for large N.
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!
A big influx of new voices just joined DSPRelated, and Stephane Boucher introduces the growing roster of contributors and their backgrounds. The post lists dozens of newly approved bloggers, highlights the range of DSP and embedded expertise they bring, and asks readers to leave constructive feedback on posts. It also explains why some applicants may not have been accepted yet and how to apply properly.
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...
Compute Images/Aliases of CIC Interpolators/Decimators
CIC filters provide multiplier-free interpolation and decimation for large sample-rate changes, but their images and aliases can trip up designs. This post supplies two concise Matlab functions and hands-on examples to compute interpolator images and decimator aliases, showing spectra and freqz plots. Readers will learn how interpolation ratio and number of stages alter passband, stopband, and aliasing behavior.
Finding the Best Optimum
Optimization is seductive but often misleading, especially when mathematical models don't match messy reality. Tim Wescott shares stories from circuits and communications to show how chasing the theoretical global optimum can waste time and money. He recommends framing 'best' in practical terms, validating models, and optimizing for cost and impact so products ship on time and actually work in the real world.
Overview of my Articles
Cedron presents a guided tour of his DSPRelated articles that teach the discrete Fourier transform through derivations, numerical examples, and sample code. The collection centers on novel "bin value" formulas and exact frequency estimators for complex and real tones, with methods for phase and amplitude recovery and iterative multitone resolution. The overview also points to a zeroing-sine window family and an integer pseudo-differentiator for efficient peak and zero-crossing detection.
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.
ESC Boston's Videos are Now Up
In my last blog, I told you about my experience at ESC Boston and the few videos that I was planning to produce and publish. Here they are, please have a look and any feedback (positive or negative) is appreciated.
Short HighlightThis is a very short (one minute) montage of some of the footage that I shot at the show & conference. In future shows, I absolutely need to insert clips here and there of engineers saying a few words about the conference (why they...
The Freshers Interview Guide
Hiring managers see the same avoidable mistakes from new grads, so Jeff offers blunt, practical advice to fix them. This short guide explains why honesty, solid debugging skills, and clear resumes matter more than cramming technical facts, and shows how to demonstrate problem-solving, organization, and teamwork in an interview to stand out as a reliable entry-level DSP or EE candidate.
Do Multirate Systems Have Transfer Functions?
Multirate systems can fool you into thinking standard z-domain analysis always applies. Rick Lyons shows why CIC decimation and Hogenauer implementations do not have a single z-domain transfer function from the input to the downsampled output, because downsampling breaks the one-to-one frequency mapping of LTI systems. Use the cascaded-subfilter H(z) up to the decimation point, then explicitly account for aliasing when predicting the decimated spectrum.
Computing Translated Frequencies in Digitizing and Downsampling Analog Bandpass Signals
Textbooks rarely give ready formulas for tracking where individual spectral lines land after bandpass sampling or decimation. Rick Lyons provides three concise equations, with Matlab code, that compute translated frequencies for analog bandpass sampling, real digital downsampling, and complex downsampling. Practical examples show how to place the sampled image at fs/4 and how to translate a complex bandpass to baseband for efficient demodulation.
Errata for the book: 'Understanding Digital Signal Processing'
Rick Lyons collects all errata for every edition and printing of his book Understanding Digital Signal Processing into one centralized list, with downloadable PDFs for each variant. The post also shows how to identify your book's printing number for American 1st, 2nd, and 3rd editions and flags a few oddball versions that lack errata.
Online DSP Classes: Why Such a High Dropout Rate?
Rick Lyons digs into a startling statistic: online DSP courses reported a 97% dropout rate. He argues the main culprits are math-heavy curricula that overwhelm beginners and rigid, non-self-paced schedules that demand sustained 8-10+ hours per week. Rick urges course creators to rethink pacing and mathematical depth to improve completion rates and student engagement.
Feedback Controllers - Making Hardware with Firmware. Part 5. Some FPGA Aspects.
This installment digs into practical FPGA choices and board-level issues for a low-latency, floating-point feedback controller. It compares a Cyclone V implementation against an older SHARC-based design, quantifies the tradeoff between raw DSP resources and cycle latency, and calls out Gotchas found on the BeMicro CV A9 evaluation card. Engineers get concrete prompts for where to optimize: clocking, DSP-block use, I/O standards, and algorithm partitioning.
Reducing IIR Filter Computational Workload
Rick Lyons demonstrates a simple, practical way to cut the multiply count for IIR lowpass and highpass filters by converting them into dual-path allpass structures. The conversion preserves the original magnitude response while drastically reducing multiplies per input sample, for example turning a 5th-order IIR that needs 11 multiplies into an equivalent allpass form needing only five. The linked PDF includes theory, implementation notes, a design example, and MATLAB code.
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,...
Orfanidis Textbooks are Available Online
Two classic signal processing textbooks by Sophocles J. Orfanidis are now available for download from his Rutgers webpages. The first, Introduction to Signal Processing, includes errata and a homework solutions manual. The second, Optimum Signal Processing, includes a solutions manual plus MATLAB, C and Fortran code. Note that Prof. Orfanidis retains copyright on both books, All Rights Reserved.
Third-Order Distortion of a Digitally-Modulated Signal
Amplifier third-order distortion is a common limiter in RF and communications chains, and Neil Robertson walks through why it matters using hands-on MATLAB simulations. He shows how a cubic nonlinearity creates IMD3 tones, causes spectral regrowth and degrades QAM constellations, and gives practical notes on estimating k3, computing ACPR from PSDs, and sampling considerations.
Controlling a DSP Network's Gain: A Note For DSP Beginners
Rick Lyons calls out a simple but costly mistake beginners make when normalizing digital networks, scaling the input instead of the output. Using fixed-point examples he shows that pre-multiplying an A/D output by 1/8 throws away bits and costs about 18 dB of SQNR. The practical guidance is to place gain control as the final multiplication stage and beware a faulty Simpson's 1/3 integrator example.
Project introduction: Digital Filter Blocks in MyHDL and their integration in pyFDA
Sriyash Caculo is building a bridge between filter design and hardware by implementing digital filter blocks in MyHDL and integrating them with PyFDA as part of a Google Summer of Code project. The work aims to convert PyFDA floating point designs into fixed point MyHDL blocks that automatically generate VHDL or Verilog, with tests and tutorials to ensure correctness and usability.
Bank-switched Farrow resampler
Markus Nentwig proposes a bank-switched variant of the Farrow resampler that breaks each impulse-response segment into multiple sub-segments, enabling accurate interpolation with lower-order polynomials and fewer multiplications per output. This trades increased total coefficient storage for computational savings. The post explains the concept, connects it to polyphase FIR interpolation, and provides Matlab/Octave and C example code for practical evaluation.
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
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.
