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.
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.
Crowdfunding Articles?
Technical writers in the embedded world often have the expertise, but not always the time or incentive to turn it into a post. Stephane Boucher explores a crowdfunding model for technical articles, where readers would pledge small amounts to back promising abstracts before the writing begins. It is an interesting attempt to create more high quality EE content by paying authors upfront.
How precise is my measurement?
Precision is quantifiable, not guesswork. This post walks through practical, measurement-oriented statistics you can apply to static or dynamic signals to answer the question, "How precise is my measurement?" It focuses on using multiple samples, checking distribution assumptions, and constructing confidence intervals and levels so you can trade measurement time for a desired precision.
Embedded World 2018 - More Videos!
Two cinematic videos from Embedded World 2018 turn the show floor into slow-motion, stabilized footage using a Zhiyun Crane gimbal and a Sony a6300. One is a SEGGER booth highlights piece featuring Rolf Segger and Axel Wolf, the other is a roaming montage with appearances from Jacob Beningo, Micheal Barr, and Alan Hawse. Stephane asks viewers to enable audio and share feedback.
Phase or Frequency Shifter Using a Hilbert Transformer
A Hilbert transformer converts a real input into an analytic I+jQ pair, enabling phase shifts and frequency shifts while keeping real inputs and outputs. This article shows Matlab implementations (31-tap FIR with Hamming or Blackman windows), derives y = I cosθ - Q sinθ for phase and frequency shifting, and highlights practical limits from finite taps and coefficient/NCO quantization.
Feedback Controllers - Making Hardware with Firmware. Part 8. Control Loop Test-bed
Built around modest FPGA hardware, this post presents a practical test-bed for evaluating high-speed, low-latency feedback controllers. It covers ADC/DAC specifications, basic and arbitrary test signals, and an IFFT-based generator that can produce thousands of simultaneous tones for rapid Bode, phase, and latency measurements. The article also compares two IFFT strategies, explains turbo sampling, and shows open- and closed-loop test configurations.
Embedded World 2018 - The Interviews
Stephane Boucher brought video gear to Embedded World 2018 and teamed up with Jacob Beningo to capture concise vendor interviews that focus on real product news. The videos showcase Percepio's new Tracealyzer with a drone demo, Intrinsic ID's method for creating device-unique IDs from manufacturing variations, and SEGGER's broader toolset including embOS now certified by TÜV SÜD. Watch for short demos and expert explanations.
Phase and Amplitude Calculation for a Pure Complex Tone in a DFT using Multiple Bins
Cedron presents exact, closed-form formulas to extract the phase and amplitude of a pure complex tone from multiple DFT bin values, using a compact vector formulation. The derivation introduces a delta variable to simplify the sinusoidal bin expression, stacks neighboring bins into a basis vector, and solves for the complex amplitude q by projection. The phase and magnitude follow directly from q, and extra bins reduce leakage when the tone falls between bins.
Linear Feedback Shift Registers for the Uninitiated, Part XIII: System Identification
Jason Sachs shows how the output of a linear feedback shift register can be used for active system identification, not just spread-spectrum testing. The article compares traditional sine-wave probing with LFSR-based PRBS methods, demonstrates a worked Ra-Rb-C example, and unpacks practical issues such as reflected pseudonoise, ADC quantization, sample counts, and noise-shaping tricks to improve estimates.
State Space Representation and the State of Engineering Thinking
State space is common in control, but it shows up much less often in signal processing. This post argues that the difference is really about engineering priorities: for many DSP problems, transfer functions are enough, while state space becomes valuable when internal behavior matters, like filter scaling or Kalman filtering. It is a short, practical look at why engineers choose one model over the other.
Exact Near Instantaneous Frequency Formulas Best at Peaks (Part 1)
Cedron Dawg presents a new family of exact time-domain formulas to estimate the instantaneous frequency of a single pure tone. The methods generalize a known one-sample formula into k-degree neighbor-pair sums with spacing d, giving exact results in the noiseless case and tunable robustness in noise. The paper explains why real-tone estimates must be taken at peaks and shows the formulas also work for complex tones.
A multiuser waterfilling algorithm
Markus Nentwig shares a compact, heuristic multiuser waterfilling algorithm with ready-to-run C code, designed for practical radio resource allocation. The approach uses round-robin user handling, per-user power budgets and a mode switch between fixed-power and waterfilling distributions, and it is easy to extend for constraints or QoS tweaks. The implementation is suboptimal by design, fast, and requires verification before production use.
Some Observations on Comparing Efficiency in Communication Systems
Efficiency in wireless communications is a multidimensional tradeoff, not a single metric. Eric Jacobsen walks through how transmit power, channel bandwidth, and FEC choices interact, showing when to judge systems by Eb/No versus SNR and how to read bandwidth-efficiency plots. The piece highlights a practical "sweet spot" of FEC code rates where power, spectrum, and decoder complexity are balanced, helping engineers choose MCS sets wisely.
Accurate Measurement of a Sinusoid's Peak Amplitude Based on FFT Data
Measuring a sinewave's peak from FFT data can be severely biased by scalloping loss, producing errors up to 36.3 percent. Rick Lyons demonstrates how to apply a flat-top window via frequency-domain convolution to the FFT bins, cutting maximum amplitude error to about 0.02 dB compared with 3.9 dB for rectangular windows. The post includes Matlab code and practical caveats for reliable use.
Compressive Sensing - Recovery of Sparse Signals (Part 1)
The amount of data that is generated has been increasing at a substantial rate since the beginning of the digital revolution. The constraints on the sampling and reconstruction of digital signals are derived from the well-known Nyquist-Shannon sampling theorem...
Spline interpolation
Markus Nentwig provides a cookbook for segmented cubic spline interpolation that turns scattered or noisy data into efficient fixed-point functions. The article shows how to build third-order polynomial segments with explicit value and slope control via basis functions, solve scaling factors by least-squares in Octave/Matlab, and export coefficients for Verilog RTL evaluation using the Horner scheme and practical fixed-point tips.
Compute Modulation Error Ratio (MER) for QAM
Neil Robertson shows how to define and compute Modulation Error Ratio (MER) for QAM using a simplified baseband model and decision-slice errors. The post derives per-symbol and averaged MER formulas, explains when MER tracks carrier-to-noise ratio under AWGN and matched root-Nyquist filters, and provides example Pav values for QAM-16 and QAM-64 plus a Matlab script and practical tips.
A Fast Guaranteed-Stable Sliding DFT Algorithm
Rick Lyons presents a compact, computationally efficient sliding DFT that computes a single N-point DFT bin output for each input sample in real time. The design replaces the traditional complex resonator with a 2nd-order real resonator and uses pole/zero cancellation to match the DFT bin response. Crucially, the resonator poles remain on the z-plane unit circle even with quantized coefficients, guaranteeing numerical stability.
Simulink-Simulation of SSB demodulation
This post walks through Simulink models that implement SSB demodulation and modulation, using Richard Lyons' phasing method as a foundation. It shows practical models for simple carrier multiplication and for the phasing method with cosine and -sin paths plus Hilbert filtering, and it highlights sampling, decimation, filter choices, and delay alignment to make the techniques work in simulation.
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.
Design IIR Band-Reject Filters
This post walks through designing IIR Butterworth band-reject filters and provides two MATLAB synthesis functions, br_synth1.m and br_synth2.m. br_synth1 accepts a null frequency plus an upper -3 dB frequency, while br_synth2 takes lower and upper -3 dB frequencies. The author demonstrates an example where a 2nd-order prototype yields a 4th-order H(z), prints b and a coefficients, and plots the response using freqz.
Linear Feedback Shift Registers for the Uninitiated, Part XII: Spread-Spectrum Fundamentals
Jason Sachs shows why LFSR-generated pseudonoise is a natural fit for direct-sequence spread spectrum, then walks through Fourier basics, spectral plots, and runnable Python examples. The article demonstrates how DSSS multiplies a UART bitstream with a chipping sequence to spread energy, how despreading concentrates the desired signal while scrambling narrowband interference, and how multiple transmitters can share bandwidth when using uncorrelated sequences.
Finally got a drone!
Stephane Boucher finally bought a DJI Phantom 4 and found it does more than boost his video production value, it’s also hugely fun to fly. He used the drone for an aerial shot at SEGGER’s anniversary and for a beach project where kids drew a turtle while a separate camera captured a side timelapse. The post highlights creative shot combinations and a reminder to fly where it is legal.
DFT Bin Value Formulas for Pure Real Tones
Cedron Dawg derives a closed-form expression for the DFT bin values produced by a pure real sinusoid, then uses that formula to explain well known DFT behaviors. The post walks through the algebra from Euler identities to a compact computational form, highlights the integer versus non-integer frequency cases, and verifies the result with C code and printed numeric output.
DFT Graphical Interpretation: Centroids of Weighted Roots of Unity
DFT bin values can be seen as centroids of weighted roots of unity, a geometric picture that makes many DFT properties immediate. Cedron Dawg uses the geometric-series identity and polar plots of integer and fractional tones to show why constants appear only at DC, how wrapping relates to bin index, and how phase, scaling, offsets, and real-signal symmetry affect bin magnitudes and angles.
Coupled-Form 2nd-Order IIR Resonators: A Contradiction Resolved
Rick Lyons resolves a long-standing confusion about the coupled-form 2nd-order IIR resonator by deriving its correct z-domain transfer function and explaining why textbooks can appear to contradict pole plots. He shows that with infinite precision the coupled and standard denominators match, but finite-bit quantization of rcos(Θ) and rsin(Θ) changes the z^-2 coefficient and shifts pole positions. Read to learn the correct H(z) to predict quantized behavior and when the coupled form outperforms the standard design.
Some Observations on Comparing Efficiency in Communication Systems
Efficiency in wireless communications is a multidimensional tradeoff, not a single metric. Eric Jacobsen walks through how transmit power, channel bandwidth, and FEC choices interact, showing when to judge systems by Eb/No versus SNR and how to read bandwidth-efficiency plots. The piece highlights a practical "sweet spot" of FEC code rates where power, spectrum, and decoder complexity are balanced, helping engineers choose MCS sets wisely.
Frequency Translation by Way of Lowpass FIR Filtering
Rick Lyons shows how you can translate a signal down in frequency and lowpass filter it in a single operation by embedding cosine mixing values into FIR coefficients. The post explains how to build the translating FIR, how to choose the number of coefficient sets, and how decimation can dramatically reduce storage needs while noting practical constraints like the requirement that ft be an integer submultiple of fs.
Is It True That j is Equal to the Square Root of -1 ?
A viral YouTube video claimed that saying j equals the square root of negative one is wrong. Rick Lyons shows the apparent paradox comes from misusing square-root identities with negative arguments, not from the usual definition of j. He argues it is safer to define j by j^2 = -1 and illustrates how careless root operations produce contradictions in two appendices.
