Computing Large DFTs Using Small FFTs
Rick Lyons demonstrates a practical trick for computing large N-point DFTs by combining multiple smaller radix-2 FFTs when only limited FFT sizes are available. He walks through 16-point and 24-point examples using two and three 8-point FFTs, shows how to assemble outputs with twiddle factors, and explains a symmetry that reduces twiddle storage to N/4 values. The method supports non-power-of-two DFT lengths.
Frequency Dependence in Free Space Propagation
Free-space propagation of electromagnetic waves is essentially independent of frequency, a counterintuitive conclusion Eric Jacobsen demonstrates step by step. He shows the λ^2 factor in the Friis transmission equation comes from antenna effective area and gain, not from the space between antennas, explaining why dipoles favor lower bands while dishes improve with frequency. The post also reminds engineers that material penetration and atmospheric absorption remain genuine frequency dependent concerns.
Pulse Shaping in Single-Carrier Communication Systems
Eric Jacobsen clears up common confusion around pulse shaping in single-carrier communications, focusing on matched filtering, Nyquist filtering, and related terminology. He uses the NRZ rectangular pulse as a concrete example to show how the transmit spectrum becomes a sinc envelope when the bitstream has enough randomness, and he highlights how bit patterns and context-sensitive terms can change the observed behavior.
Linear-phase DC Removal Filter
Rick Lyons presents a practical, multiplier-free way to remove DC while preserving linear phase by cascading D-point moving-average filters. He shows how choosing D as a power of two gives bit-shift scaling, how a dual-MA yields a narrow transition band with modest ripple, and how a quad-MA drives ripple down to near inaudible levels while noting the fixed-point accumulator sizing required.
New Papers / Theses Section
Stephane Boucher launched a Papers & Theses section on DSPRelated to gather DSP dissertations and papers in one spot. Authors can submit already-hosted documents or upload PDFs for optional hosting, provided they have sharing rights, and help is available for PDF conversion. Listing your work boosts visibility and opportunities, and non-English documents are welcomed while the section is in beta.
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.
Free DSP Books on the Internet
Finding reliable DSP textbooks online is hit-or-miss. Rick Lyons assembled a curated list of over forty legally downloadable signal processing books, organized by topic from theory and communications to audio, image processing, and implementation. The post points to vendor manuals, MATLAB and algorithm resources, and clear copyright guidance so engineers can grab useful references without breaking licensing rules.
Benford's law solved with DSP
Steve Smith shows that standard DSP tools give a clean, intuitive explanation of Benford's law by treating leading-digit counts as signals on the number line and using convolution and Fourier analysis. He publishes the full derivation as an online chapter after traditional journals showed little interest. The result highlights how time- and spatial-domain DSP techniques can be applied to numeric distributions.
Correlation without pre-whitening is often misleading
White Lies
Correlation, as one of the first tools DSP users add to their tool box, can automate locating a known signal within a second (usually larger) signal. The expected result of a correlation is a nice sharp peak at the location of the known signal and few, if any, extraneous peaks.
A little thought will show this to be incorrect: correlating a signal with itself is only guaranteed to give a sharp peak if the signal's samples are uncorrelated --- for example if the signal is composed...
Handling Spectral Inversion in Baseband Processing
Spectral inversion often sneaks in during RF and IF mixing chains and can break downstream demodulation. Eric Jacobsen shows that at baseband you can correct inversion with three trivial, equivalent operations: invert Q, swap I and Q, or invert I, and he explains the math and geometric intuition behind each. The fixes work in modulators or demodulators and tolerate arbitrary phase offsets.
Constrained Integer Behavior
Overflow and underflow are not always bugs, they can be useful in DSP when fixed-width integers wrap during processing. Christopher Felton demonstrates with moving-average (recursive-windowed-averager) and CIC filter examples how 2's complement wraparound in MyHDL's modbv cancels between an integrator and a comb via pole-zero cancellation. He also covers fixed-point resizing choices, saturation versus wrap, and how rounding error can accumulate.
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.
New Code Sharing Section & Reward Program for Contributors!
UPDATE (11/02/2010): The code section is now live.
UPDATE 2 (01/31/2011): The reward program has changed. A flat fee of $20 per code snippet submitted will now be paid.
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I am very happy to finally announce the imminent launch of the new code sharing section. My vision for this new section is a rich library of high quality code snippets for the DSP community, from processor specific functions to Matlab or Scilab routines, from the simplest filter...
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.
Digital Filter Instructions from IKEA?
This is a wordless example of a folded FIR filter. Swedish “Bygglek” = build and play.
"Neat" Rectangular to Polar Conversion Algorithm
Rick Lyons revisits a clever slide-rule era trick for estimating the magnitude of a complex number without computing a square root. He highlights a neat identity, prompted by a Jerry Avins post, that converts the sqrt problem into forward and inverse trigonometric operations plus ratios. The post invites readers to derive Eq. (2) and see why a seemingly complex idea is actually simple and practical.
Code Snippets Suggestions
Despite being only a couple of months old, the Code Snippet section ( DSPRelated.com/code.php ) already contains tens of snippets, thanks to the contributors who have taken the time to share their code.
But let's not stop here - there is room for several hundreds more snippets before the database can be said to cover a decent portion of the DSP field.
To keep the momentum going, I will do two things:
First, I am modifying the rewards program. Instead of...
'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.
A Useful Source of Signal Processing Information
I just discovered a useful web-based source of signal processing information that was new to me. I thought I'd share what I learned with the subscribers here on DSPRelated.com.
The Home page of the web site that I found doesn't look at all like it would be useful to us DSP fanatics. But if you enter some signal processing topic of interest, say, "FM demodulation" (without the quotation marks) into the 'Search' box at the top of the web page
and click the red 'SEARCH...
Microprocessor Family Tree
Rick Lyons shares a compact, nostalgic microprocessor family tree that highlights early integrated circuits and his fondness for the Intel 8080. The post invites engineers to spot classic chips they remember, pairing brief commentary with a scanned image from Creative Computing, June 1985, copied without permission. It’s a short historical snapshot for anyone interested in vintage CPU lineage.
ICASSP 2011 conference lectures online (for free)
For the first time, the oral sessions of ICASSP 2011 were recorded and posted online for free, giving engineers worldwide easy access to the conference. The talks span speech and communication signal processing, plus eclectic topics like bio-inspired methods, where Prof. Sayed uses a distributed LMS model to reproduce group predator and prey behavior. Expect some theoretical material, but many presentations are practical and inspiring for DSP practitioners.
Update To: A Wide-Notch Comb Filter
This blog presents alternatives to the wide-notch comb filter described in Reference [1]. That comb filter, which for notational reasons I now call a 2-RRS wide notch comb filter, is shown in Figure 1. I use the "2-RRS" moniker because the comb filter uses two recursive running sum (RRS) networks.
The z-domain transfer function of the 2-RRS wide-notch comb filter, H2-RRS(z), is:
References
[1] R. Lyons, "A Wide-Notch Comb Filter", dsprelated.com Blogs, Nov. 24, 2019, Available...
Call for Speakers for the Inaugural Signal Processing Summit
Announcing the Call for Speakers for the inaugural Signal Processing Summit, happening October 14-16, 2025 in Silicon Valley. If you have practical, real-world DSP experience, including communications, audio, AI/ML, or core techniques, organizers want talks that are actionable and engineer-focused. Four tracks plus an open call for radar, imaging, biomedical, and sensor-system applications are listed; submit proposals by August 8, 2025.
GPS - some terminology!
Hi!
For my first post, I will share some information about GPS - Global Positioning System. I will delve one step deeper than a basic explanation of how a GPS system works and introduce some terminology.
GPS, like we all know is the system useful for identifying one's position, velocity, & time using signals from satellites (referred to as SV or space vehicle in literature). It uses the principle of trilateration (not triangulation which is misused frequently) for...
FREE Peer-reviewed IEEE signal processing courses
The IEEE signal processing society is offereing FREE peer reviewed courses, though not many, they are peer reviewed and span differenet topics like; wavelets, speech analysis, and statistical detection.
Enjoy
http://cnx.org/lenses/ieeesps/endorsements?b_start:int=0&-C=
Components in Audio recognition - Part 1
This post introduces the core components of an audio recognition system, framed against how the human auditory system naturally familiarizes and retrieves tunes. Prabindh Sundareson outlines the three building blocks: an archive store, an analysis and fingerprinting engine that groups tracks, and a front-end that accepts queries and places samples into groups. He previews upcoming posts that will dig into implementations and tradeoffs.
Roll Your Own Differentiation Filters
Practical guide to constructing differentiation filters from sampled signals using interpolation rather than messy Taylor expansions. It shows how Lagrange polynomials produce forward, backward and central derivative formulas, and how the pseudospectral differentiation matrix D = X'X^{-1} maps sample vectors to derivative estimates. Includes a compact MATLAB snippet and a discussion of node-choice tradeoffs and ill-conditioning for large N.
50,000th Member Announced!
In my last post, I wrote that DSPRelated.com was about to reach the 50,000 members mark. Well, I am very happy to announce that it happened during the holidays, and the lucky person is Charlie Tsai from Taiwan. Charlie is an assistant professor in the Department of Electrical Engineering at the National Central University in Taiwan where he teaches the "Biomedical Signal Processing" class. He is also the advisor of the
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.
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.
