Sonos, Shut Up and Take My Money! - Is Spatial Audio Finally Here?
Stephane bought a Sonos ERA 300 and discovered that spatial audio can finally feel convincing from a single wireless speaker, provided you set it up correctly. The trick is using Dolby Atmos tracks played inside the Sonos app, plus Sonos' calibration and a close listening position. The post shares setup tips, vivid listening impressions, and encouragement for more spatial mixes to come.
Simple Discrete-Time Modeling of Lossy LC Filters
Converting a lossy LC filter into a discrete-time impulse response lets you analyze mixed analog and DSP systems in one time domain. This post walks through computing the LC frequency response via chain (ABCD) parameters including resistive losses, enforcing the Hermitian symmetry required for a real IDFT, and using the IDFT to produce an asymmetrical FIR impulse response. A 5th-order Butterworth example illustrates insertion loss and impulse-shape effects.
The Discrete Fourier Transform as a Frequency Response
Neil Robertson shows that the discrete frequency response H(k) of an FIR filter is exactly the DFT of its impulse response h(n). He derives the continuous H(ω) and discrete H(k) using complex exponentials for a four-tap FIR, then replaces h(n) with x(n) to recover the general DFT formula. The post keeps the math simple and calls out topics left for separate treatment, such as windowing and phase.
Simple Concepts Explained: Fixed-Point
Fixed-point is the bridge between real-world values and integer arithmetic, and this post makes that bridge tangible with a hands-on ADC-to-gain example. It walks through mapping voltages to Q-format integers, choosing gain resolution in bits, and how multiplication adds bit growth and produces quantization error. Read it to build intuition for practical fixed-point choices when implementing DSP on FPGA or ASIC.
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.
Add the Hilbert Transformer to Your DSP Toolkit, Part 2
This post shows a simple practical route to a Hilbert transformer by starting from a half-band FIR filter and tweaking its symmetry. It walks through a 19-tap example synthesized with Matlab's firpm (Parks-McClellan), explains the required frequency scaling, and shows how even-numbered taps become (or can be forced) zero through symmetry and coefficient quantization. Useful design rules are summarized for choosing ntaps.
Add the Hilbert Transformer to Your DSP Toolkit, Part 1
Learn how the Hilbert transformer creates a 90-degree phase-shifted quadrature component without down-conversion, and why it is simply a special FIR filter. Part 1 defines the transformer, derives its ideal frequency response H(ω)=j for ω<0 and -j for ω≥0, and walks through Matlab examples that demonstrate phase shifting and image attenuation for bandpass signals.
Candan's Tweaks of Jacobsen's Frequency Approximation
Cedron Dawg shows how small tweaks to Jacobsen's three-bin frequency estimator turn a popular approximation into an exact formula, and how a modest cubic correction yields a near-exact, low-cost alternative. The article derives an arctan/tan exact recovery, relates it to Candan's 2011/2013 tweaks, and supplies reference C code and numerical tables so engineers can see when each formula is sufficient.
A Recipe for a Basic Trigonometry Table
Cedron Dawg walks through building a degree-based sine and cosine table from first principles, showing both recursive and multiplicative complex-tone generators. The article highlights simple drift-correction tricks such as mitigated squaring and compact normalization, gives series methods to compute one-degree and half-degree values, and includes practical C code that ties the table to DFT usage and frequency estimation.
A New Contender in the Quadrature Oscillator Race
Rick Lyons highlights a compact quadrature oscillator introduced by A. David Levine and Martin Vicanek, offering guaranteed stability, accurate low-frequency tuning, and modest computational cost. The post walks through the simple u, v, w recurrences used for software implementation. Appendices provide transfer functions and an algebraic stability proof for engineers who want formal verification before deployment.
Delay estimation by FFT
Markus Nentwig presents a practical FFT-based algorithm to estimate and correct integer and fractional sample delays between two signals, returning a scaled, aligned replica and delay estimate. The method combines coarse cross-correlation with a phase-slope linear regression on weighted spectra to achieve subsample timing accuracy. The article also discusses accuracy limits, phase-unwrapping pitfalls, and how to use the error-vector spectrum to reveal distortion in lab measurements.
Understanding and Relating Eb/No, SNR, and other Power Efficiency Metrics
Eric Jacobsen untangles the common confusion around Eb/N0, SNR, Es/No and related power-efficiency metrics, showing when each metric applies and how to convert between them. He covers practical measurement techniques including spectrum-analyzer and slicer-based estimates, the impact of symbol rate, modulation order and FEC code rate, and offers simple sanity checks to catch common dB and factor-of-two errors. Engineers get a concise toolkit for accurate comparisons.
Design IIR Butterworth Filters Using 12 Lines of Code
Build a working lowpass IIR Butterworth filter from first principles in just 12 lines of Matlab using Neil Robertson's butter_synth.m. The post walks through the analog prototype poles, frequency pre-warping, bilinear transform pole mapping, adding N zeros at z = -1, and gain normalization so the result matches Matlab's built-in butter function. It's a compact, hands-on guide with clear formulas and code.
Sum of Two Equal-Frequency Sinusoids
Rick Lyons exposes a frequent trig mistake and delivers complete closed-form expressions for collapsing two equal-frequency sinusoids into a single sinusoid. Using complex-exponential phasor addition and equating real and imaginary parts, he compiles easy-to-use tables for cosine+cosine, sine+sine, and cosine+sine cases and shows how to derive each form. Engineers get corrected identities and compact derivations useful for analysis and communications.
PID Without a PhD
You do not need control theory to implement useful PID loops in embedded projects. Tim Wescott walks through simple, ready-to-use C code, clear explanations of P, I and D terms, and a practical tuning recipe you can apply to motors, precision actuators, and heaters. The article highlights anti-windup, sampling-rate guidance, and when to call in a control expert.
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.
Interpolation Basics
Neil Robertson demonstrates interpolation by an integer factor using a frequency-domain approach, showing how zero-insertion followed by an FIR low-pass filter reconstructs a higher-rate signal. The article walks through spectra, passband and stopband selection, and a 41-tap Parks-McClellan filter example applied to a Chebyshev-window test signal. Matlab code and percent-error plots are included so engineers can reproduce and evaluate the method.
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.
The Exponential Nature of the Complex Unit Circle
Euler's equation links exponential scaling and rotation by translating a distance along the unit-circle circumference into a complex value. Cedron Dawg develops an intuitive geometric view, using integer and fractional powers of i to show how points, roots of unity, and multiplication behave as additive moves along that circumference. The article also connects this picture to radians and the conventional Taylor-series proof for broader perspective.
Simple but Effective Spectrum Averaging
In this article, I provide a Matlab function that performs exponential PSD averaging, using first-order infinite impulse response (IIR) filtering to continuously average the PSD bins. This approach works well for computing the spectrum of a long-duration signal over time, because the spectrum is constantly updated as new PSD’s are computed. Conveniently, the time constant of the PSD averaging is determined by the single adjustable parameter α. I also provide a Matlab function for conventional (unweighted) PSD averaging. Neither function requires any canned code other than the Fast Fourier Transform (FFT), although I do use the Matlab hann window function for convenience.
Python scipy.signal IIR Filter Design
Christopher Felton walks through designing infinite impulse response filters using scipy.signal in Python, focusing on practical specs and functions rather than theoretical derivations. He explains normalized passband and stopband definitions, gpass and gstop, and shows how iirdesign and iirfilter differ. Plots compare elliptic, Chebyshev, Butterworth and Bessel responses, highlighting steep transitions versus near-linear phase tradeoffs.
How to Find a Fast Floating-Point atan2 Approximation
This post shows how a compact, fast atan2 can be built from a Remez-derived arctangent approximation and a matching 3rd-order polynomial. It walks through using Boost's remez_minimax to recover coefficients 0.97239411 and -0.19194795, integrating the polynomial into an atan2 with quadrant reduction, and applying branch reduction, bit tricks, and SSE2 SIMD to cut runtime while keeping max error under about 0.005 radians.
Simplest Calculation of Half-band Filter Coefficients
Half-band FIR filters put the cutoff at one-quarter of the sampling rate, and nearly half their coefficients are exactly zero, which makes them highly efficient for decimation-by-2 and interpolation-by-2. This post shows the straightforward window-method derivation of half-band coefficients from the ideal sinc impulse response, providing a clear, hands-on explanation for engineers learning filter design. It also points to equiripple options such as Matlab's firhalfband and a later Parks-McClellan implementation.
Interpolation Basics
Neil Robertson demonstrates interpolation by an integer factor using a frequency-domain approach, showing how zero-insertion followed by an FIR low-pass filter reconstructs a higher-rate signal. The article walks through spectra, passband and stopband selection, and a 41-tap Parks-McClellan filter example applied to a Chebyshev-window test signal. Matlab code and percent-error plots are included so engineers can reproduce and evaluate the method.
Music/Audio Signal Processing
Julius Orion Smith III traces his journey from musician to music/audio DSP researcher, sharing the choices that shaped his career and research focus. He recounts work on violin modeling and waveguide synthesis, then highlights modern prototyping tools like Faust and Octave that accelerate experimentation. Read for practical career advice on coursework, publishing, and why free open-source tools matter for rapid audio research.
PID Without a PhD
You do not need control theory to implement useful PID loops in embedded projects. Tim Wescott walks through simple, ready-to-use C code, clear explanations of P, I and D terms, and a practical tuning recipe you can apply to motors, precision actuators, and heaters. The article highlights anti-windup, sampling-rate guidance, and when to call in a control expert.
Feedback Controllers - Making Hardware with Firmware. Part 10. DSP/FPGAs Behaving Irrationally
A practical approach to emulating lossy transmission lines in real time, using pole-zero approximations to replace irrational s-domain behaviors and enable FPGA implementation. The author shows 8-pole/zero fits for Zo(s) and a 6-pole/zero plus delay for P(s), validated against LTSpice and MATLAB. Conversion to sampled-data Zo(z) and biquad implementations is detailed, along with issues in single-precision arithmetic and mitigations such as mixed sample rates and partial-fraction decomposition.
Round Round Get Around: Why Fixed-Point Right-Shifts Are Just Fine
Jason Sachs explains why, in most embedded systems, simple bitwise right-shifts are an acceptable way to do fixed-point division rather than paying the runtime cost to round. He shows the cheap trick of adding 2^(N-1) to implement round-to-nearest, explains unbiased "round-to-even" issues, and compares arithmetic error to much larger ADC and sensor errors. The takeaway: save cycles unless your algorithm or inputs require extra precision.
Plotting Discrete-Time Signals
Neil Robertson demonstrates a practical interpolate-by-8 FIR approach to make sampled signals look like their continuous-time counterparts when plotted. The post explains a 121-tap filter designed for signals up to 0.4*fs, shows Matlab examples for a sinusoid and a filtered pulse, and highlights the transient and design trade-offs so you can reproduce clean plots with the supplied interp_by_8.m code.
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.
Back from ESC Boston
Stephane nearly skipped ESC Boston, but going turned into a productive mix of networking, informal meetups, and on-the-floor filming. He captures candid encounters with speakers and vendors, learns how small shows differ from larger expos, and outlines practical follow-ups like booth highlight videos and speaker hospitality suggestions. The post is an encouraging read for engineers weighing the value of regional conferences and DIY event coverage.
Launch of Youtube Channel: My First Videos - Embedded World 2017
Stephane Boucher turned his Embedded World 2017 trip into a debut YouTube series of short booth highlight videos. He walks through the steep learning curve of trade-show filming, the specific gear he bought and rented to cope with low light and noise, and the practical mistakes he plans to fix. The post lists filmed vendors and asks readers for feedback to improve future episodes.
New Comments System (please help me test it)
DSPRelated just got a practical upgrade, Stephane Boucher has released a new comments system built from his earlier forum work. It supports drag-and-drop or Insert Image uploads, MathML, TeX and ASCIImath rendered by MathJax, syntax-highlighted code via highlight.js, and in-place editing and deletion of comments. Improved email notifications alert authors and commenters to replies, and readers are invited to post test comments and report problems.
3 Good News
Stephane Boucher reports three quick wins for the EmbeddedRelated community: two sponsors have seeded a $1,000 rewards pool, the site now serves all pages over HTTPS, and the new forums have their first active discussions. If you want a share of the sponsor-funded rewards, jump into the forums and check the Vendors Directory for opportunities. Stay tuned for more updates.
The New Forum is LIVE!
After months of hard word, I am very excited to introduce to you the new forum interface.
Here are the key features:
1- Easily add images to a post by drag & dropping the images in the editor
2- Easily attach files to a post by drag & dropping the files in the editor
3- Add latex equations to a post and they will be rendered with Mathjax (tutorial)
4- Add a code snippet and surround the code with
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.
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.
Recruiting New Bloggers!
Previous calls for bloggers have been very successful in recruiting some great communicators - Rick Lyons, Jason Sachs, Victor Yurkovsky, Mike Silva, Markus Nentwig, Gene Breniman, Stephen Friederichs,
Premium Forum?
Stephane Boucher proposes a paid "premium" forum for DSPRelated that would redistribute membership fees to the community s top contributors via voting. The plan frames the $20/year fee as an incentive mechanism, not a revenue stream, with monthly payouts to the most appreciated posters. Boucher invites reader feedback to decide whether to implement the idea or pursue alternatives.
The Sampling Theorem - An Intuitive Approach
Scott Kurtz from DSPSoundWare.com has put together a video presentation that aims to give DSP engineers an intuitive grasp of the Sampling Theorem. The short, approachable video focuses on conceptual understanding of sampling and aliasing rather than mathematical formality. Watch the presentation on DSPRelated and share your reactions in the post comments to join the discussion.
