Computing FFT Twiddle Factors
Rick Lyons gives two compact algorithms to compute individual twiddle factors for radix-2 DIF and DIT FFTs, handy when you need only a subset of outputs such as in pruned FFTs. He explains stage indexing, provides closed-form formulas including the bit-reversal step for DIT, and walks through N=8 examples so you can implement the twiddle-angle calculations directly.
Knowledge Mine for Embedded Systems
A little-known interactive portal makes learning embedded systems surprisingly practical and visual. The site is organized into four main areas: embedded systems design, design lifecycle, design methods, and design tools. Each section uses clickable system block diagrams so you can jump from a block, for example a MAC unit, to a focused page with detailed explanations. It’s a handy, ready reference for DSP and embedded engineers.
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.
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.
Googling: a now-required skill
Finding the right DSP answer often starts with finding the right search term, not the right textbook. Seth Benton shares the web resources he leans on, from comp.dsp and the MATLAB File Exchange to Google tricks like related searches and the tilde operator. It is a practical reminder that better keywords can cut straight through the rabbit hole.
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.
Computing an FFT of Complex-Valued Data Using a Real-Only FFT Algorithm
Rick Lyons shows a compact trick to get an N-point complex FFT using only real-input FFT routines by transforming the real and imaginary parts separately and recombining their outputs. The post presents a one-line recombination formula, Xc(m) = real[Xr(m)] - imag[Xi(m)] + j{imag[Xr(m)] + real[Xi(m)]}, and an algebraic derivation based on the two-real-in-one-complex FFT identity. Useful for systems that only provide real-only FFTs.
Random GPGPU Musings
Shehrzad Qureshi argues that general-purpose GPU computing is poised to reshape engineering workloads, and contrasts Nvidia's CUDA ecosystem with ATI's Stream and OpenCL. He points out that GPU architectures and programming models are similar across vendors, but Nvidia's head start in sample code and developer community gives CUDA a practical advantage. Read for a concise industry perspective on choosing a GPGPU platform.
GPGPU DSP
Shehrzad Qureshi kicks off his DSP blog by championing GPGPU, focusing on Nvidia's CUDA and real-product experience. He argues that with CPU clock speeds stalled, large-scale parallelism on GPUs is the practical path forward for many signal-processing tasks. The post traces GPGPU history from shader 'hacks' to modern APIs and previews future posts comparing CUDA vs OpenCL, Intel's Larrabee, and Nvidia Fermi.
Some Thoughts on a German Mathematician
Rick Lyons revisits the remarkable career of Carl Friedrich Gauss, mixing memorable anecdotes with technical highlights. The post links Gauss’s work on the Gaussian curve, complex-plane representation, orbit prediction, and early telegraph experiments to ideas familiar to DSP engineers, and notes historical evidence that he developed trigonometric series before Fourier. It’s a short, engaging reminder of Gauss’s broad influence.
New Code Sharing Section & Reward Program for Contributors!
DSPRelated is launching a new code sharing section and looking for contributors to help seed it with useful DSP snippets. Stephane Boucher also introduces a pageview-based reward program, with payouts tied to unique visits so popular code can earn contributors up to $250. It is a practical push to build a high-quality library for the DSP community from the start.
Code Snippets Suggestions
The DSPRelated Code Snippet section is growing fast, but Stephane Boucher wants to accelerate it further with a new incentive. He is offering a one-time $20 payment for each of the next 100 submitted snippets, and he has also launched a page where readers can suggest the DSP code examples they want most. One lucky suggestion will win a copy of Notes on Digital Signal Processing.
Implementing a full-duplex UART using the TMS320VC33 serial port
You can convert the TMS320VC33's synchronous serial port into a full-duplex UART in software by using DR0/DX0, on-chip timers, and an external interrupt. Manuel Herrera walks through an interrupt-driven 9600 baud, 8N1 asynchronous receiver/transmitter, explains receiver gating by start bit detection, and includes a schematic plus a complete assembly listing with timer values tied to a 150 MHz clock. Adjust timing for different clock rates.
scipy.signal calling all developers
SciPy’s signal-processing toolbox is at a crossroads, and Christopher Felton is urging developers to jump in. He points to active discussion on scipy-dev, the possibility of a separate scikit-signal effort, and the broad set of functions already in scipy.signal. If you work in DSP and like open-source software, this is a good moment to look at the package, and maybe help shape it.
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.
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.
'z' as in 'Zorro': Frequency Masking FIR
Markus Nentwig shows an efficient way to build steep wideband FIR filters by combining upsampled and complementary stages, then masking their spectra. He provides a Matlab and Octave design program that uses a generic least-squares optimizer to place coefficients, letting you explore filter sizes and oversampling while cutting computational cost significantly compared to a conventional symmetric FIR.
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.
GPGPU DSP
Shehrzad Qureshi kicks off his DSP blog by championing GPGPU, focusing on Nvidia's CUDA and real-product experience. He argues that with CPU clock speeds stalled, large-scale parallelism on GPUs is the practical path forward for many signal-processing tasks. The post traces GPGPU history from shader 'hacks' to modern APIs and previews future posts comparing CUDA vs OpenCL, Intel's Larrabee, and Nvidia Fermi.
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.
Improved Three Bin Exact Frequency Formula for a Pure Real Tone in a DFT
Cedron Dawg extends his two-bin exact frequency formulas to a three-bin DFT estimator for a pure real tone, and presents the derivation in computational order for practical use. The method splits complex bin values into real and imaginary parts, forms vectors A, B, and C, applies a sqrt(2) variance rescaling, and computes frequency via a projection-based closed form. Numerical tests compare the new formula to prior work and show improved accuracy when the tone lies between bins.
Update to a Narrow Bandpass Filter in Octave or Matlab
Paul Lovell presents an updated, compact Octave/Matlab implementation of a narrow bandpass FIR that runs about four times faster and uses float32 to cut processing cost. The design combines a single matrix IFIR stage with three moving-sum (RRS) stages per baseband, auto-calculates the IFIR expansion factor, and adds easier parameter setup plus WAV I/O and FFT plots. A TensorFlow Colab demo is also provided.
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.
Exact Near Instantaneous Frequency Formulas Best at Peaks (Part 2)
Cedron Dawg derives a second family of exact time domain formulas for single-tone frequency estimation that trade a few extra calculations for improved noise robustness. Built from [1+cos]^k binomial weighting of neighbor-pair sums, the closed-form estimators are exact and are best evaluated at signal peaks for real tones, while complex tones do not share the zero-crossing limitation. Coefficients up to k=9 are provided.
Of Forests and Trees and DSP
Too often DSP engineers fixate on algorithms and miss the rest of the product. Tim Wescott uses the humble Korg CA-20 chromatic tuner to show that a great algorithm alone does not make a usable device, you also need good data acquisition, adequate processing, sensible precision, a usable UI, and appropriate casing and cost. The post gives practical do's and don'ts for system-level DSP design.
Why is Fourier transform broken
Many engineers know the Gibbs phenomenon without grasping its root cause. This post shows that the problem comes from using the incomplete metric space of continuous functions, C[a,b], for Fourier series, and explains how switching to Lp spaces resolves convergence in the mean but allows functions to differ on sets of measure zero. It also reminds readers that Fourier analysis gives no time localization, so be mindful of its limits.
Engineering the Statistics
Statistical analysis can get messy fast when theory and MATLAB simulations refuse to agree. This post shares a graduate student’s hard-earned shortcuts for taming random variables, from deriving a CDF or moments to using Gaussian or Gamma approximations, and falling back on Chernoff bounds when the exact PDF stays out of reach.
Project update-2 : Digital Filter Blocks in MyHDL and their integration in pyFDA
This update shows a working integration between Pyfda and MyHDL using a compact API that passes fixed-point coefficients, stimulus data, and returns simulated filter responses. It walks through two usage styles, constructor-based and setter-method-based, and demonstrates a Pyfda workflow from specs to MyHDL simulation and plotting. Future plans include HDL code generation and API extension as filters grow.
Digging into an Audio Signal and the DSP Process Pipeline
Zooming into an audio waveform can be misleading if you rely on only one view. This post compares Audacity with a simple C++ WAV reader and shows how the same samples can look like zero in a GUI, while the raw data reveals a small nonzero value. It is a practical reminder that multiple tools help you inspect and verify signal data more accurately.
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.
