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.
Generating Partially Correlated Random Variables
Designing signals to match a target covariance is simpler than it sounds. This post shows how to build partially correlated complex signals by hand for the two-signal case, then generalizes to N signals using the Cholesky decomposition. Short MATLAB examples demonstrate the two-line implementation and the article highlights numerical caveats when a covariance is only positive semidefinite.
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.
Angle Addition Formulas from Euler's Formula
Complex numbers are rotations and scalings in the plane, and Cedron Dawg walks through polar and Cartesian representations to make that concrete. Using Euler's formula, the article shows how multiplying complex numbers multiplies magnitudes and adds angles, and how that directly yields the sine and cosine angle-addition formulas. Practical notes cover using atan2/arg and a brief Gambas example to verify results.
Demonstrating the Periodic Spectrum of a Sampled Signal Using the DFT
This post makes a basic DSP principle tangible by computing the DFT over an extended set of bins and plotting the results. It demonstrates that a sampled signal's spectrum repeats every sampling rate, explains the k-to-frequency mapping, and contrasts common bin ranges such as 0..N-1 and -N/2..N/2-1. The write-up also highlights symmetry for real sequences and recommends using the FFT for efficiency.
Free Goodies from Embedded World - What to Do Next?
Stephane Boucher went on a hunt for free stuff at Embedded World to assemble a giveaway bundle for a lucky reader. This short update shares that haul and asks the embedded community for ideas on what to do next. It is a conversational call for suggestions, aiming to turn conference swag into a useful prize.
Back from Embedded World 2019 - Funny Stories and Live-Streaming Woes
Stephane Boucher tried live-streaming multiple talks from Embedded World 2019 and turned a chaotic experiment into a useful set of lessons for embedded engineers. Between broken tripods, flaky venue WiFi, tricky German SIM purchases, and audio nightmares, he learned practical fixes for reliable streams and better video quality. Read this if you want candid, tactical advice on streaming hardware, connectivity, and on-site troubleshooting.
Spread the Word and Run a Chance to Win a Bundle of Goodies from Embedded World
EmbeddedRelated is turning Embedded World into a live-streaming experiment, and the more engineers help spread the word, the better the coverage could get. Stephane Boucher is asking readers to follow updates on Twitter and LinkedIn, where every like, share, or repost adds another chance to win a box of vendor goodies. The prize mix includes t-shirts, dev kits, gadgets, and plenty of pens.
Launch of EmbeddedRelated.tv
Stephane Boucher launches EmbeddedRelated.tv to host live broadcasts from Embedded World, starting next week. The site will show a constantly evolving schedule, a Live! tab to find ongoing streams, and ad-hoc demos added from the show floor. Expect schedule conflicts and small hiccups, and plan to refresh the page and join the forum thread for real-time updates and feedback.
Stereophonic Amplitude-Panning: A Derivation of the 'Tangent Law'
Rick Lyons presents a clear geometrical derivation of the stereophonic amplitude-panning Tangent Law, filling a gap left by common references. Using vector components and the equidistant speaker assumption to keep signals in phase, he arrives at the Tangent Law and isolates practical gain formulas gL and gR needed to place an apparent source at a desired panning angle. Engineers can apply Eqs. (12) and (14) directly.
RF in Slow Motion: Sonifying a Wi-Fi 7 Packet
What would a 160 MHz OFDM waveform up in the 5 GHz U-NII band sound like if scaled to audio frequencies to keep the same wavelength (acoustic vs RF)?
Model Signal Impairments at Complex Baseband
Neil Robertson presents compact complex-baseband channel models for common signal impairments, implemented as short Matlab functions of up to seven lines. Using QAM examples and constellation plots, he demonstrates how interfering carriers, two-path multipath, sinusoidal phase noise, and Gaussian noise distort constellations and affect MER. The examples are lightweight and practical, making it easy to test receiver diagnostics and prototype adaptive-equalizer scenarios.
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.
Setting the 3-dB Cutoff Frequency of an Exponential Averager
Many engineers use a simple exponential averager but need the correct α to achieve a specified 3-dB cutoff. Rick Lyons compares a common approximation with the exact closed-form solution, shows when the approximation is valid, and derives the exact α in the appendix. The approximation works well for fc < 0.1fs, but it becomes noticeably inaccurate as the normalized cutoff increases.
Fitting Filters to Measured Amplitude Response Data Using invfreqz in Matlab
This post is a redirect notice for a code snippet now hosted elsewhere. If you were looking for the invfreqz example on fitting a filter to measured amplitude response data, this page simply points you to the new location and asks you to update your bookmark.
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.
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.
Modeling Anti-Alias Filters
Modeling anti-alias filters brings textbook aliasing examples to life. This post shows how to build discrete-time models G(z) for analog Butterworth and Chebyshev lowpass anti-alias filters, compares bilinear transform and impulse invariance, and simulates ADC input/output including aliasing of sinusoids and Gaussian noise. It concludes that impulse invariance gives better stopband accuracy and includes Matlab helper functions.
Computing the Group Delay of a Filter
Rick Lyons presents a neat, practical way to get a filter's group delay directly from its impulse response using only DFTs. The method computes an N-point DFT of h(n) and of n·h(n), divides them in the frequency domain, and takes the real part to obtain group delay in samples, avoiding phase unwrapping. The post includes MATLAB code, a zero-division warning, and a caution that the method is reliable for FIR filters but not always for IIRs.
Waveforms that are their own Fourier Transform
Steve Smith admits a long-standing mistake and overturns the claim that only Gaussians are their own Fourier transform. He gives trivial and nontrivial examples, explains why infinitely many such waveforms exist, and shows a quick discrete construction using the DFT with a 1/sqrt(N) normalization. Engineers get an intuitive 30-second argument plus a practical recipe to build self-Fourier signals.
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.
Angle Addition Formulas from Euler's Formula
Complex numbers are rotations and scalings in the plane, and Cedron Dawg walks through polar and Cartesian representations to make that concrete. Using Euler's formula, the article shows how multiplying complex numbers multiplies magnitudes and adds angles, and how that directly yields the sine and cosine angle-addition formulas. Practical notes cover using atan2/arg and a brief Gambas example to verify results.
Digital PLL's, Part 3 -- Phase Lock an NCO to an External Clock
Phase-locking a numerically controlled oscillator to an external clock that is unrelated to system clocks is practical and largely unexplored. Neil Robertson presents a time-domain digital PLL that converts the ADC-sampled clock into I/Q with a Hilbert transformer and measures phase error with a compact complex phase detector. The post shows loop-filter coefficient formulas and simulations that reveal how ADC quantization and Gaussian clock noise map into NCO phase noise and how loop bandwidth shapes the result.
Using the DFT as a Filter: Correcting a Misconception
Some sources claim the DFT, when used as a filter, shifts spectral energy down to DC. Rick Lyons shows that this is not true for consecutive DFT-bin outputs and explains the cause of the confusion: the FIR interpretation requires reversing the usual twiddle-factor order. He derives the DFT-bin frequency response, shows the bandpass center at 2πm/N, and explains when decimation does produce a translation to zero Hz.
Shared-multiplier polyphase FIR filter
One multiplier and a dual-port RAM can implement an arbitrary m/n polyphase FIR resampler on an FPGA, Markus Nentwig demonstrates. The post focuses on practical implementation details, including a parametrized Verilog design, pipelined MAC control, and a Matlab testbench for verification. It shows how bank indexing and pipeline delay compensation let you multiplex many coefficient banks efficiently for resource-constrained FPGA designs.
Understanding Radio Frequency Distortion
Markus Nentwig breaks down how analog RF nonlinearities appear in a complex baseband model so you can simulate and predistort real transmitters. The article shows that even-order terms vanish in-band under narrowband assumptions, while odd-order products collapse to |BB(t)|^(n-1) BB(t) and do not depend on the carrier frequency. It also explains bandwidth scaling and includes a MATLAB example plus measured PA coefficients.
Why Time-Domain Zero Stuffing Produces Multiple Frequency-Domain Spectral Images
Zero stuffing in the time domain creates spectral copies, and Rick Lyons walks through why that happens using DFT and DFS viewpoints. He shows that inserting L-1 zeros between samples yields a longer DFT with replicated spectral blocks, and that true interpolation requires lowpass filtering to remove those images. The post uses a concrete L=3 example and an inverse-DFT summation proof to make the effect intuitive.
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.
Waveforms that are their own Fourier Transform
Steve Smith admits a long-standing mistake and overturns the claim that only Gaussians are their own Fourier transform. He gives trivial and nontrivial examples, explains why infinitely many such waveforms exist, and shows a quick discrete construction using the DFT with a 1/sqrt(N) normalization. Engineers get an intuitive 30-second argument plus a practical recipe to build self-Fourier signals.
Python scipy.signal IIR Filter Design Cont.
Christopher Felton continues his practical tour of SciPy's iirdesign, moving beyond lowpass examples to show highpass, bandpass, and stopband designs with concise, code-focused explanations. He highlights how ellip and cheby2 let you tighten specifications for sharper transitions, and shows that the iirdesign workflow is consistent across filter types. Read for clear, reusable examples to produce IIR filter coefficients with scipy.signal.
