A New Related Site!
The post announces the launch of MLRelated, a new Related site dedicated to machine learning and deep learning. It positions MLRelated as complementary to existing Related sites by highlighting cross-cutting interests: TinyML for embedded developers, machine/deep learning applications in signal processing, and FPGA-based AI/ML implementations. The new site debuts with a modest amount of content and is expected to expand rapidly through contributions from the Related community in the form of blogs, forum threads, and webinars. The author invites readers to report navigation errors, share feedback, and propose ideas to help steer MLRelated into a practical, community-driven resource for researchers and practitioners in ML and adjacent domains.
Filtering Noise: The Basics (Part 1)
How do you pull signals out of random noise? This post builds intuition from first principles for discrete-time white Gaussian noise and shows how simple linear FIR filtering (averaging) reduces noise. You’ll get derivations for the output mean, variance and autocorrelation, learn why the uniform moving-average minimizes noise under a unity-DC constraint, and why its sinc spectrum can be problematic. Part 1 of a short series.
Book Recommendation "What is Mathematics?"
Richard Courant and Herbert Robbins' What is Mathematics? is a lucid, classic survey that still rewards engineers who want a concept-first refresher. The author praises the book's calculus chapters as concise and readable, recommending specific sections on complex numbers, functions and limits, and calculus for practical study. Note that linear algebra is not covered and the 1996 edition adds a short Ian Stewart chapter on recent developments.
Evaluate Noise Performance of Discrete-Time Differentiators
Differentiators can be wildly different at rejecting noise, even when they share the same usable bandwidth. Neil Robertson introduces the Differentiator Noise Power Ratio, a practical Gaussian-noise metric and a compact formula that uses the filter coefficients to quantify output noise and SNR loss. The post also gives MATLAB guidance for designing and comparing FIR differentiators so you can pick or build filters with much better noise performance.
Off-Topic: A Fluidic Model of the Universe
Cedron Dawg develops a Newtonian, fluidic model where space is a compressible "fluff" and particle motion is governed by a simple refractive steering equation. He shows how rho = ln n links index, permittivity and permeability to a gravity-like potential, derives a massive-particle steering law, and works through orbit and disk solutions that produce MOND-like effects while conflicting with General Relativity. The paper highlights concrete formulas and numerics to test the hypothesis.
Learn About Transmission Lines Using a Discrete-Time Model
A simple discrete-time approach makes lossless transmission-line behavior easy to simulate and visualize. The post introduces MATLAB functions tline and wave_movie to model uniform lossless lines with resistive terminations, compute time and frequency responses, and animate travelling waves. A microstrip pulse example shows how reflections produce ringing and how source matching nearly eliminates it, making this a practical learning tool.
Determination of the transfer function of passive networks with MATLAB Functions
Starting the calculation from the output makes deriving a passive network transfer function simple, and this post shows how to do it in MATLAB using a sixth-order low-pass example. The walkthrough uses tf('s') to build a symbolic H(s), extracts coefficients with tfdata, and shows numerical frequency-response plotting via freqs or direct j*omega evaluation, with code and component values to reproduce the results.
A DSP Quiz Question
A short visual puzzle from Rick Lyons shows how a common plotting trick can fool even experienced DSP engineers. He presents a 3D circular plot that looks like a triangular window but is actually a 32-point hann window, then explains why the circular projection distorts the view. The post highlights the importance of checking equations and 2D plots before naming a window by sight.
The Discrete Fourier Transform and the Need for Window Functions
The FFT alone can mislead: capturing a finite-length signal with a rectangular window smears energy across frequency, producing spectral leakage that hides real components. This post explains the origin of leakage, shows how tapered windows such as the Hanning window suppress sidelobes, and demonstrates the tradeoff between sidelobe suppression and mainlobe widening while covering practical tips on zero-padding and record length.
The 2021 DSP Online Conference
Packed with practical talks and hands-on workshops, the 2021 DSP Online Conference gives DSP engineers a quick way to refresh skills and learn new techniques. Registering grants full access to talks, workshops, and Q&A at this year's event plus instant access to last year's videos. Highlights include FIR filter design with Python, software-defined radio, convolution reviews, and DSP/ML tools for IoT, with registration discounts on request.
ADC Clock Jitter Model, Part 1 -- Deterministic Jitter
Clock jitter on ADC sample clocks corrupts high-frequency signals, and this post builds a practical MATLAB model to show exactly how deterministic (periodic) jitter maps into phase modulation and discrete sidebands. The author explains a parabolic-interpolation approach using twice-rate samples, demonstrates examples from single tones to pulses, and matches simulation spectra to closed-form sideband formulas so engineers can predict jitter effects.
Adventures in Signal Processing with Python
Jason Sachs shows how PyLab (numpy, scipy, matplotlib) can handle many signal-processing and visualization tasks engineers usually reach for MATLAB to do. He walks through practical examples including PWM ripple, two pole RC filters, and symbolic math with SymPy, and shares real-world installation tips and trade-offs. The post closes with pointers to IPython and pandas to speed interactive analysis and data handling.
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.
Padé Delay is Okay Today
High-order Padé approximations for time delays break in surprising ways, but the failure is not magic. Jason Sachs walks through why coefficient-based transfer functions and companion-form state-space are numerically fragile, shows how to compute poles and zeros directly from the hypergeometric form with Newton iteration, and demonstrates building modal or block-diagonal state-space realizations to make high-order Padé delays practical while noting remaining limits.
Frequency Dependence in Free Space Propagation
Free-space propagation of electromagnetic waves is essentially independent of frequency, a counterintuitive conclusion Eric Jacobsen demonstrates step by step. He shows the λ^2 factor in the Friis transmission equation comes from antenna effective area and gain, not from the space between antennas, explaining why dipoles favor lower bands while dishes improve with frequency. The post also reminds engineers that material penetration and atmospheric absorption remain genuine frequency dependent concerns.
Going back to Germany!
A couple of blog posts ago, I wrote that the decision to go to ESC Boston ended up being a great one for many different reasons. I came back from the conference energized and really happy that I went.
These feelings were amplified a few days after my return when I received an email from Rolf Segger, the founder of SEGGER Microcontroller (check out their very new website), asking if I would be interested in visiting their headquarters...
Fractional Delay FIR Filters
You can realize arbitrary fractional-sample delays with standard FIR filters by shifting a sinc impulse response and removing symmetry, then windowing the result. This post shows a practical window-method implementation using Chebyshev windows, gives Matlab functions (frac_delay_fir.m and frac_delay_lpf.m) in the appendix, and walks through examples that demonstrate the delay, magnitude trade-offs, and how increasing taps widens the flat-delay bandwidth.
5G NR QC-LDPC Encoding Algorithm
Lyons Zhang breaks down the 5G NR QC-LDPC encoding structure, emphasizing the circulant permutation matrices and why QC-LDPC suits simple hardware. The post defines the Q(P) and Q(-1) notation, summarizes BG1 and BG2 dimensions and selection rules, and shows how the parity-check matrix is partitioned for practical encoder implementations.
Return of the Delta-Sigma Modulators, Part 1: Modulation
Jason Sachs returns to delta-sigma modulators with a hands-on, code-first treatment that focuses on the DAC side of things. Part 1 walks through first- and second-order kernels, linearized analysis, spectra, and practical coefficient choices while illustrating results with Python simulations. Expect clear rules of thumb for A, R, and B, a derivation of noise shaping behavior, and a useful error bound for RC filtering.
Second Order Discrete-Time System Demonstration
Want a hands-on way to see how continuous second-order dynamics appear in discrete time? Neil Robertson converts a canonical H(s) to H(z), shows z-plane pole mapping for different damping ratios, and walks through impulse-invariance scaling and zero placement. The post includes a MATLAB function so_demo.m that computes numerator and denominator coefficients, plots poles, and compares impulse and frequency responses so you can experiment with sampling effects.
FFT Interpolation Based on FFT Samples: A Detective Story With a Surprise Ending
Rick Lyons follows a numerical mismatch from a published astronomy paper into a short detective story about FFT interpolation. He shows a commonly published interpolation formula produces large errors, explains why the algebraic approximations fail, and presents several correct alternatives with algebraic simplifications that greatly reduce computation. Engineers get both the debugging lesson and practical, lower‑cost formulas for evaluating X(k) between FFT bins.
Polyphase filter / Farrows interpolation
Markus Nentwig shows how polyphase filtering and the Farrow interpolator provide a practical, computation‑efficient way to realize sub-sample delays and variable resampling. He starts from the upsample-filter-decimate view, explains how polyphase decomposition reduces per-phase work, then describes how the Farrow structure fits polynomials to coefficient banks for continuous fractional-delay control. The post includes warnings about filter choices and links to code and references.
Pulse Shaping in Single-Carrier Communication Systems
Eric Jacobsen clears up common confusion around pulse shaping in single-carrier communications, focusing on matched filtering, Nyquist filtering, and related terminology. He uses the NRZ rectangular pulse as a concrete example to show how the transmit spectrum becomes a sinc envelope when the bitstream has enough randomness, and he highlights how bit patterns and context-sensitive terms can change the observed behavior.
Generating pink noise
This post implements a stochastic Voss-McCartney pink-noise generator in Python, tackling why incremental per-sample algorithms do not map well to NumPy batch operations. It presents a practical NumPy/Pandas approach that uses geometric-distributed update events and pandas' fillna for column-wise zero-order hold to make batch generation efficient. The generated noise shows a power-spectrum slope near -1, matching expected 1/f behavior.
Free Goodies from Embedded World - Full Inventory and Upcoming Draw Live-Streaming Date
Stephane came back from Embedded World with a massive haul of development kits, tools and swag and decided to give it away to multiple winners. Read the full inventory, learn how to enter by liking or sharing the LinkedIn and Twitter posts, and tune in Friday March 29 at 1pm EST on EmbeddedRelated.tv for the live draw where winners will pick their prizes.
The Number 9, Not So Magic After All
Rick Lyons dismantles the mystique around the number 9 by showing its 'magic' stems from our base-10 system rather than any unique numeral power. He walks through classic 9 tricks, including digit-sum divisibility, digital-root behavior, and division patterns, then generalizes them to base-B where digit B-1 plays the same role. The post is a short, playful link between recreational arithmetic and radix thinking.
Frequency Dependence in Free Space Propagation
Free-space propagation of electromagnetic waves is essentially independent of frequency, a counterintuitive conclusion Eric Jacobsen demonstrates step by step. He shows the λ^2 factor in the Friis transmission equation comes from antenna effective area and gain, not from the space between antennas, explaining why dipoles favor lower bands while dishes improve with frequency. The post also reminds engineers that material penetration and atmospheric absorption remain genuine frequency dependent concerns.
Linear-phase DC Removal Filter
Rick Lyons presents a practical, multiplier-free way to remove DC while preserving linear phase by cascading D-point moving-average filters. He shows how choosing D as a power of two gives bit-shift scaling, how a dual-MA yields a narrow transition band with modest ripple, and how a quad-MA drives ripple down to near inaudible levels while noting the fixed-point accumulator sizing required.
Optimizing the Half-band Filters in Multistage Decimation and Interpolation
Multistage decimation and interpolation by powers of two get a lot cheaper if you size each half-band filter differently. Rick Lyons walks through spectra for three-stage examples that show why early stages can use narrower filters for decimation while interpolation reverses the order, and how aliasing and images are handled by later stages. Learn a simple rule to cut multipliers without sacrificing performance.
An s-Plane to z-Plane Mapping Example
A misleading online diagram prompted Rick Lyons to reexamine how s-plane points map to the z-plane. He spotted apparent errors in the original figure, drew a corrected mapping, and invites readers to inspect both diagrams and point out any remaining mistakes. The short post is a quick visual primer for engineers who rely on accurate s-plane to z-plane mappings in analysis and design.
DSP Related Math: Nice Animated GIFs
Stephane Boucher collected a compact set of animated GIFs that make common DSP math click visually. He spotted popular posts on the ECE subreddit and aggregated DSP-focused GIFs in one place to speed intuition and teaching. Examples include the relationship between sin and cos with right triangles, constructing a square wave from an infinite series, and the continuous Fourier transform pair of the rect and sinc functions.
DSPRelated and EmbeddedRelated now on Facebook & I will be at EE Live!
Stephane Boucher announces two practical updates for DSPRelated readers. He launched Facebook pages for DSPRelated and EmbeddedRelated so members can get faster updates, and he will be attending EE Live in San Jose from March 30 to April 3 with a $100-off promo code for early registration. He also asks the community for ideas on how to make his conference coverage most useful.
Collaborative Writing Experiment: Your Favorite DSP Websites
Stephane Boucher invites the DSPRelated community to a live Google Docs experiment to crowdsource the best DSP websites. After a successful run with EmbeddedRelated, he opens a shared document where members can add, edit, and curate links in real time. The post explains the simple rules, notes revision rollback protection, and asks readers to refresh and help keep the list useful and spam-free while watching it evolve.
DSPRelated Finally on Twitter!
After resisting social networks, Stephane Boucher announces DSPRelated's move to Twitter and a few site improvements. Users can now sign in once to access DSPRelated, FPGARelated and EmbeddedRelated with the same account, and the site will post updates from @dsprelated, @embeddedrelated and @fpgarelated. To encourage followers, Boucher will occasionally tweet links that award prizes to the first visitors.
Two jobs
Stephane Boucher explains why EmbeddedRelated went quiet for a few months after a volunteer project demanded more of his time. He and his wife organized a clown-gymnastics show with 15 kids, sold more than 700 of 800 tickets, and raised $2,700 for the Tree of Hope. Now the shows are done and he plans to resume regular posting with new site features.
Do you like the new Comments System?
I have just finished implementing a new comments system for the blogs. Do you like it?
Please share your thoughts with me by adding a comment.
I'll wait a few days and make sure it works properly and then I'll port it to the code snippets and papers section.
Thanks!
DSP Papers, Articles, Theses, etc
Stephane Boucher invites the DSP community to help expand DSPRelated's Papers and Theses repository, which currently lists just over 100 documents. He asks contributors to find and submit recent DSP PDFs, ideally from the last ten years, and notes that each approved submission enters the submitter into a draw for Michael Parker's Digital Signal Processing 101; the draw is planned for early April.
Code Snippets Suggestions
Despite being only a couple of months old, the Code Snippet section ( DSPRelated.com/code.php ) already contains tens of snippets, thanks to the contributors who have taken the time to share their code.
But let's not stop here - there is room for several hundreds more snippets before the database can be said to cover a decent portion of the DSP field.
To keep the momentum going, I will do two things:
First, I am modifying the rewards program. Instead of...
Latest DSP Books
Rick Lyons' third edition of Understanding Digital Signal Processing has arrived, and Stephane Boucher says the new material justifies upgrading older copies. He also highlights a new title, C. Britton Rorabaugh's Notes On Digital Signal Processing, as another recent release to watch. In addition, dsprelated.com's books listing now sorts by publication date rather than database addition, making it easier to find newly published DSP titles.
Code Snippets Section Now LIVE
A new code-sharing section on DSPRelated is now live, giving engineers a central place to browse and share DSP code snippets. Take a few minutes to rate and comment on snippets you can judge, or apply to become a contributor and upload your own examples. You can also learn about the contributor reward program and send feedback to help the community grow, says Stephane Boucher.
