Project update-1 : Digital Filter Blocks in MyHDL and their integration in pyFDA
By week 5 the project delivered parameterized MyHDL implementations of multiple digital filter topologies and started integration with PyFDA. The post walks through a behavioral direct-form I FIR, cascaded second-order-section implementations for FIR and IIR using structural modeling, and a parallel IIR design that concatenates per-section outputs for final summation. All designs infer order and coefficients from PyFDA, with examples in the filter-blocks repository.
Linear Feedback Shift Registers for the Uninitiated, Part XVI: Reed-Solomon Error Correction
Jason Sachs demystifies Reed-Solomon codes with hands-on examples and pragmatic tips for embedded engineers. The article shows why RS encoding is just polynomial division in GF(2^m), why decoding is mathematically heavier, and how to implement encoders in Python and in C-friendly form using LFSRs and table-driven methods. Read this for working code, generator-polynomial examples, and an embedded-minded view of RS practicalities.
Linear Feedback Shift Registers for the Uninitiated, Part XV: Error Detection and Correction
CRCs and Hamming codes look a lot less magical when you view them as redundancy with a purpose. Jason Sachs walks from parity bits and checksums into finite-field polynomial arithmetic, then shows how CRCs map cleanly onto LFSRs and how Hamming codes use syndromes to locate single-bit errors. It is a practical tour of error detection and correction, with enough worked examples to make the theory feel usable.
Who else is going to Sensors Expo in San Jose? Looking for roommate(s)!
Stephane Boucher is heading to Sensors Expo in San Jose for the first time, and he is bringing cameras to capture demos and build a highlights video. He is also looking for roommates for a roomy Airbnb near the convention center, plus local tips for making the most of a free day in the Bay Area. If you are attending, there is also a registration discount code and a VIP pass giveaway in the mix.
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.
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.
Two Easy Ways To Test Multistage CIC Decimation Filters
Rick Lyons shows that you can validate multistage CIC decimation filters with just two obvious tests, no elaborate spectral setup required. Apply a unit-sample impulse to check a combinatorial yout(1) value when D ≥ S, or feed an all-ones step to confirm an S-sample transient followed by a DS steady state; the Appendix ties both checks to Pascal's triangle and binomial math.
ADC Clock Jitter Model, Part 2 – Random Jitter
Neil Robertson shows how to simulate ADC sample-clock random jitter in Matlab, moving from band-limited Gaussian noise to wideband and close-in phase noise. The post highlights practical artifacts such as aliasing of wideband clock noise, the 20*log10 dependence of jitter sidebands on input frequency, and why cubic interpolation plus a custom noise_filter produces accurate rms and spectral results engineers can trust.
Take Control of Noise with Spectral Averaging
Spectral averaging turns noisy FFT outputs into repeatable, measurable spectra by trading time for noise control. This post explains the practical difference between RMS averaging, which reduces variance without changing the noise floor, and vector averaging, which can lower the noise floor but requires phase-coherent, triggered inputs. It also shows how linear and exponential weighting affect reaction time for live displays and measurement accuracy.
Linear Feedback Shift Registers for the Uninitiated, Part XIV: Gold Codes
Gold codes solve a practical spread-spectrum problem, sharing one PRBS across many transmitters eventually runs into ugly synchronization and correlation issues. Jason Sachs walks through why shifted copies of a single LFSR sequence are not enough, then shows how preferred pairs of m-sequences create a family of Gold codes with bounded cross-correlation. The post wraps with Python experiments and a UART DSSS demo that decodes multiple overlapping messages cleanly.
The Most Interesting FIR Filter Equation in the World: Why FIR Filters Can Be Linear Phase
Rick Lyons pulls back the curtain on a little-known coefficient constraint that makes complex-coefficient FIR filters exhibit linear phase. Rather than simple symmetry of real coefficients, the key is a conjugate-reflection relation involving the filter phase at DC, which collapses to ordinary symmetry for real taps. The post includes derivations, intuition using the inverse DTFT, and a Matlab example to verify the result.
OpenCV for DSP/GPU, MSDN equivalent for CCS, and more
Porting OpenCV to DSPs could be a real business opportunity, but it is far from trivial, writes Shehrzad Qureshi. He highlights major obstacles: the engineering scale, mixed open-source licenses, and hard-to-parallelize primitives like connected components. He also criticizes Code Composer Studio's help system compared with MSDN, notes an ATI Stream talk, and announces a CUDA walkthrough on FFT-based image filtering.
Python number crunching faster? Part I
Christopher Felton walks through simple benchmarks comparing raw Python, numpy, and PyPy for numeric workloads, and shares what surprised him about performance. He shows that idiomatic Python optimizations such as list comprehensions and built-ins plus the PyPy JIT can sometimes beat a numpy approach for small tests, and explains why native PyPy numpy progress matters for scientific users.
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.
Time Machine, Anyone?
Causal filters can look like time machines, but they do not break physics. Andor Bariska reproduces a classic electronic experiment in MATLAB, showing how a minimum-phase peaking filter and its FDLS biquad approximation produce negative group delay bands that make predictable, bandlimited signals appear to emerge early. The post walks through group delay, discretization, pulse and random-signal tests, and why unpredictability restores causality.
An Efficient Linear Interpolation Scheme
A simple trick slashes the cost of linear interpolation to at most one multiply per output sample, and often to none. The post shows a zero-order-hold based network that preserves input samples, has a short L-1 transient, and lets 1/L scaling be implemented as a binary shift when L is a power of two. It also gives a fixed-point layout that moves scaling to the end to reduce quantization distortion.
Accelerating Matlab DSP Code on the GPU
Seth Benton spent a few days testing Jacket to accelerate MATLAB on NVIDIA GPUs, and found it surprisingly easy to speed up DSP code. He ran 2D FFT and interp2 benchmarks on a MacBook Air with a GeForce 9400M, seeing impressive speedups for large images while hitting GPU memory and precision limits at high sizes. The post shares practical tips on casting to GPU types, minimizing CPU-GPU transfers, and when GPU acceleration is most useful.
Exact Frequency Formula for a Pure Real Tone in a DFT
Cedron Dawg derives an exact closed form formula to recover the frequency of a pure real sinusoid from three DFT bins, challenging the usual teaching that it is impossible. The derivation solves for cos(alpha) in a bilinear form and gives a computationally efficient implementation (eq.19), with practical notes on implicit Hann-like weighting and choosing the peak bin for robustness.
Instant CIC
Modeling CIC decimators in floating point is simpler than you might think, Markus Nentwig shows, if you treat the filter as a finite FIR by sampling its impulse response. The post compares a naive float time-domain implementation, an FFT-based frequency-domain approach, and the recommended method of computing the impulse response and using an off-the-shelf FIR filter, with code and plots.
Hidden Linear Algebra in DSP
Linear algebra is hiding in plain sight inside many DSP techniques, not just abstract theory. By treating linear systems as matrix operators y = A x you reveal Toeplitz structure in LTI systems, connect to covariance matrices, and gain geometric intuition via eigenvalues and eigenvectors. This matrix viewpoint complements convolution-based thinking and offers practical tools for filter and channel analysis.
Should DSP Undergraduate Students Study z-Transform Regions of Convergence?
Rick Lyons argues z-transform regions of convergence are mostly a classroom abstraction with little practical use for real-world DSP engineers. For all stable LTI impulse responses encountered in practice the ROC includes the unit circle, so DTFT and DFT exist and ROC analysis rarely affects implementation. He notes digital oscillators are a notable exception, and suggests reallocating classroom time to more practical engineering topics.
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.
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.
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.
Time-Domain Periodicity and the Discrete Fourier Transform
Finite-length observation windows change how tones appear in a DFT, and Eric Jacobsen shows how the convolution theorem explains the familiar sin(x)/x main lobe and sidelobes. He contrasts two consistent viewpoints: viewing the DFT as a windowed signal convolved with the window transform, or as the transform of a periodically repeated sequence. Practical tips on zero-padding, bin spacing, and phase effects help avoid common misinterpretations.
Instantaneous Frequency Measurement
Measuring carrier frequency quickly and with minimal data matters in radar and signal characterization. Parth Vakil explains the delay-and-multiply instantaneous frequency measurement technique, shows how analytic signals and multiple delays resolve the 2π ambiguity, and demonstrates noise, phase-wrapping, and interferer effects using MATLAB code. He also outlines practical mitigations like phase unwrapping and channelization.
The DFT of Finite-Length Time-Reversed Sequences
Rick Lyons digs into a surprisingly under-documented corner of DSP, showing how finite-length time reversal changes a sequence's DFT. The post distinguishes flip and circular time-reversal, gives closed-form DFT relationships, and explains why modulo N arithmetic matters. Engineers get ready-to-use tables and derivations that clarify when and how time reversal affects spectral analysis.
Half-band filter on Xilinx FPGA
Lyons Zhang shows a practical, high-throughput implementation of a symmetric systolic half-band FIR on Xilinx FPGAs using DSP48 slices. The post includes a two-channel interleaved downsample-by-2 Verilog module, pipeline mapping to DSP48, and a symmetric rounding trick to reduce the DC shift from truncation. It highlights performance-and-latency tradeoffs and gives working code you can drop into a Spartan-6 style flow.
Design study: 1:64 interpolating pulse shaping FIR
Markus Nentwig presents a practical 1:64 root-raised cosine interpolator built from cascaded FIR stages that slashes computational cost. By separating pulse shaping from rate conversion, designing each interpolator to suppress only known alias bands, and equalizing the pulse shape, the design achieves just 4.69 MACs per output, roughly 12 percent of a straight polyphase implementation while meeting EVM targets.
Sensors Expo - Trip Report & My Best Video Yet!
Stephane Boucher turns a first-time Sensors Expo visit into a fun travelogue and a polished conference highlights video. He mixes candid trip anecdotes from Moncton to San Jose, electric-scooter discoveries, Santa Cruz detours, Airbnb tips, and on-the-floor expo footage. The post culminates in what he calls his best highlights reel yet, plus a follow-up video focused on embedded and IoT.
