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.
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.
TCP/IP interface (Matlab/Octave)
Markus Nentwig supplies a compact set of mex C functions that let you control Ethernet-enabled measurement instruments directly from Matlab or Octave on Windows. The code opens raw TCP/IP sockets, sends SCPI commands, and handles ASCII and binary replies including binary-length headers. It intentionally avoids instrument-control toolboxes and timeouts for simplicity, and includes instrIf_socket, instrIf_write, instrIf_read and instrIf_close with simple usage examples.
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.
How Discrete Signal Interpolation Improves D/A Conversion
Digital interpolation can drastically simplify the analog filtering that follows a DAC, lowering cost and improving output quality. Rick Lyons explains how inserting zeros and applying a digital lowpass filter (interpolation-by-two) raises the effective sample rate, reduces the DAC sin(x)/x droop, and widens the analog filter transition band. The post gives practical intuition and spectral illustrations engineers can reuse in real designs.
Weighted least-squares FIR with shared coefficients
Markus Nentwig demonstrates how to design FIR filters that share coefficients across delay taps, allowing multiplier reuse and reduced implementation cost. He reimplements Lawson's iterative reweighted least-squares for complex-valued FIRs and provides Matlab/Octave code you can adapt for nonstandard constraints. The post explains iteration weight logic, the Toeplitz special-case with Levinson-Durbin, and practical trade-offs between multiplier count and stopband performance.
How Not to Reduce DFT Leakage
Rick Lyons debunks a proposed 'data-flipping' fix for DFT spectral leakage, demonstrating with MATLAB that it can produce higher sidelobes and a troubling mainlobe dip for some input frequencies. He explains that windowing's goal is to reduce amplitude discontinuities in a periodic extension, not merely to force end samples to zero, and concludes the method is frequency-dependent and not recommended.
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.
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.
Curse you, iPython Notebook!
Christopher Felton shares a cautionary tale about losing an ipython 0.12 notebook session after assuming the browser would save his interactive edits. He explains that notebooks at the time required clicking the top Save button to persist sessions, and autosave was not yet available. He recommends basing interactive work on scripts, saving often, and testing export behavior to avoid redoing text, LaTeX, and plots.
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.
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.
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.
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.
Implementing Simultaneous Digital Differentiation, Hilbert Transformation, and Half-Band Filtering
Recently I've been thinking about digital differentiator and Hilbert transformer implementations and I've developed a processing scheme that may be of interest to the readers here on dsprelated.com.
ESC Boston's Videos are Now Up
Stephane Boucher shares the videos he produced from ESC Boston, including a short highlight montage, a booth video for DLOGIC, and full talk clips from the conference. He also reflects on what he learned shooting on the show floor, especially the challenge of getting engineers on camera. It’s a quick behind-the-scenes look at technical event videography, with a preview of his next stop in Germany.
Design Square-Root Nyquist Filters
A multirate signal processing textbook presents a neat method for designing square-root Nyquist FIR filters that combine zero ISI with strong stopband attenuation. This post walks through the principle that matched transmit and receive filters need square-root Nyquist responses, gives the key design relations for excess bandwidth and stopband edge, and includes a Matlab implementation to produce practical FIR matched filters for QAM-style systems.
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.
A Useful Source of Signal Processing Information
A surprisingly handy web tool turned up for finding signal processing material in PDF and PowerPoint form. Rick Lyons shows how a plain-looking site can surface lots of topic-specific documents, using FM demodulation as the example. If you often hunt for reference slides and papers, this is a quick source worth bookmarking.
Curse you, iPython Notebook!
Christopher Felton shares a cautionary tale about losing an ipython 0.12 notebook session after assuming the browser would save his interactive edits. He explains that notebooks at the time required clicking the top Save button to persist sessions, and autosave was not yet available. He recommends basing interactive work on scripts, saving often, and testing export behavior to avoid redoing text, LaTeX, and plots.
Off Topic: Refraction in a Varying Medium
Cedron Dawg derives a compact vector differential equation for a point particle moving through a smoothly varying refractive medium using the Euler-Lagrange variational method. By introducing a log refractive index called "fluff density," the paper expresses acceleration purely in terms of the fluff gradient and velocity, then explores curvature, superposition, and point-source capture radii with simple closed-form results.
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.
Fibonacci trick
Tim Wescott shares a compact, surprising trick linking Fibonacci numbers and difference equations. Start with any two consecutive Fibonacci numbers, negate the larger-magnitude one, and iterate the usual recurrence; after a few steps you'll arrive at the standard Fibonacci sequence or its negative. This behavior is specific to the Fibonacci recurrence and makes a great illustrative example for teaching linear recurrences.
There's No End to It -- Matlab Code Plots Frequency Response above the Unit Circle
If you want a fresh way to inspect a digital filter, this post introduces plotfil3d, a compact MATLAB function that wraps the magnitude response around the unit circle in the Z-plane so you can view it in 3D. It uses freqz to compute H(z) in dB for N points and accepts an optional azimuth to change the viewing angle; the code is provided in the appendix.
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.
A Two Bin Exact Frequency Formula for a Pure Complex Tone in a DFT
Cedron Dawg derives an exact two-bin frequency formula for a pure complex tone in the DFT, eliminating amplitude and phase to isolate frequency via a complex quotient and the complex logarithm. He presents an adjacent-bin simplification that replaces a complex multiply with a bin offset plus an atan2 angle, and discusses integer-frequency handling and aliasing. C source and numerical examples show the formula working in practice.
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.
Three Bin Exact Frequency Formulas for a Pure Complex Tone in a DFT
Cedron Dawg derives closed-form three-bin frequency estimators for a pure complex tone in a DFT using a linear algebra view that treats three adjacent bins as a vector. He shows any vector K orthogonal to [1 1 1] yields a = (K·Z)/(K·D·Z) and derives practical K choices including a Von Hann (Pascal) kernel and a data-driven projection. The post compares estimators under noise and gives simple selection rules.
Book Recommendation "What is Mathematics?"
Richard Courant and Herbert Robbins' What is Mathematics? is a lucid, classic survey that still rewards engineers who want a concept-first refresher. The author praises the book's calculus chapters as concise and readable, recommending specific sections on complex numbers, functions and limits, and calculus for practical study. Note that linear algebra is not covered and the 1996 edition adds a short Ian Stewart chapter on recent developments.
DSPRelated and EmbeddedRelated now on Facebook & I will be at EE Live!
Stephane Boucher announces two practical updates for DSPRelated readers. He launched Facebook pages for DSPRelated and EmbeddedRelated so members can get faster updates, and he will be attending EE Live in San Jose from March 30 to April 3 with a $100-off promo code for early registration. He also asks the community for ideas on how to make his conference coverage most useful.
