Bank-switched Farrow resampler
Markus Nentwig proposes a bank-switched variant of the Farrow resampler that breaks each impulse-response segment into multiple sub-segments, enabling accurate interpolation with lower-order polynomials and fewer multiplications per output. This trades increased total coefficient storage for computational savings. The post explains the concept, connects it to polyphase FIR interpolation, and provides Matlab/Octave and C example code for practical evaluation.
Impulse Response Approximation
A stepped-triangular impulse approximation represents an FIR low-pass using a cascade of recursive running-sum filters, offering big savings in computation. Christopher Felton outlines the quantization step that maps a true impulse into three stepped-triangular types and shows how the approximation is built from recursive running-sum and sparse-sum blocks. Inspect the frequency tradeoffs and decide if the efficiency gain is worth the approximation error.
Orfanidis Textbooks are Available Online
Two classic signal processing textbooks by Sophocles J. Orfanidis are now available for download from his Rutgers webpages. The first, Introduction to Signal Processing, includes errata and a homework solutions manual. The second, Optimum Signal Processing, includes a solutions manual plus MATLAB, C and Fortran code. Note that Prof. Orfanidis retains copyright on both books, All Rights Reserved.
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.
Do Multirate Systems Have Transfer Functions?
Multirate systems can fool you into thinking standard z-domain analysis always applies. Rick Lyons shows why CIC decimation and Hogenauer implementations do not have a single z-domain transfer function from the input to the downsampled output, because downsampling breaks the one-to-one frequency mapping of LTI systems. Use the cascaded-subfilter H(z) up to the decimation point, then explicitly account for aliasing when predicting the decimated spectrum.
FREE Peer-reviewed IEEE signal processing courses
IEEE Signal Processing Society is offering a small set of free, peer-reviewed courses covering topics like wavelets, speech analysis, and statistical detection. The post points to these endorsed materials as a useful way to browse vetted DSP learning resources without paying for formal coursework.
A Fixed-Point Introduction by Example
Christopher Felton walks through binary fixed-point representation with clear examples and a simple W=(wl,iwl,fwl) notation. He argues for designing to range and resolution rather than bit counts, then shows how multiplication and addition affect bit growth and alignment. These concrete examples make it easy to see why rounding, resizing, and radix-point bookkeeping are essential in DSP implementations.
DSP Algorithm Implementation: A Comprehensive Approach
This post lays out a practical pathway for taking DSP algorithms from high level simulation to production hardware, comparing GPP, DSP, FPGA and ASIC platforms. It presents a stepwise methodology starting with nested loop programs, then exposing parallelism with data flow graphs, using SystemC transaction level modeling to bridge to Verilog or VHDL, and explains why that flow speeds design and simulation.
DSP Papers, Articles, Theses, etc
Stephane Boucher invites the DSP community to help expand DSPRelated's Papers and Theses repository, which currently lists just over 100 documents. He asks contributors to find and submit recent DSP PDFs, ideally from the last ten years, and notes that each approved submission enters the submitter into a draw for Michael Parker's Digital Signal Processing 101; the draw is planned for early April.
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.
An Alternative Form of the Pure Real Tone DFT Bin Value Formula
Cedron Dawg derives an alternative exact formula for DFT bin values of a pure real tone, sacrificing algebraic simplicity for better numerical behavior near integer-valued frequencies. By rewriting cosine differences as products of sines and shifting to a delta frame of reference, the derivation avoids catastrophic cancellation and preserves precision for near-integer tones. The analysis also shows the integer-frequency case is a degenerate limit that yields the familiar M/2 e^{iφ} bin value.
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.
How to Find a Fast Floating-Point atan2 Approximation
This post shows how a compact, fast atan2 can be built from a Remez-derived arctangent approximation and a matching 3rd-order polynomial. It walks through using Boost's remez_minimax to recover coefficients 0.97239411 and -0.19194795, integrating the polynomial into an atan2 with quadrant reduction, and applying branch reduction, bit tricks, and SSE2 SIMD to cut runtime while keeping max error under about 0.005 radians.
Algebra's Laws of Powers and Roots: Handle With Care
Rick Lyons shows that familiar power and root rules from algebra can break down when exponents are complex. He tests common identities for two scenarios, real and fully complex exponents, with positive and negative mantissas, and compiles a table of cases that sometimes fail. The post includes MATLAB examples that reproduce counterexamples and a clear warning to numerically verify algebraic steps involving complex powers.
More free Ebooks
A handy roundup of free engineering ebooks and journals, with a focus on where DSPRelated readers might actually find useful material. The post points to InTechOpen, highlights several MATLAB books, and even calls out a numerical methods title plus some sensor fusion content. If you like browsing for practical references, this is a good place to start.
'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.
The New Forum is LIVE!
The EmbeddedRelated forum just got a major interface refresh, and Stephane Boucher is rolling it out in beta. The new editor makes it easier to drop in images and files, add LaTeX equations with MathJax, and publish highlighted code snippets with highlight.js. Access is gated by approval for now, mainly to keep trolls, spammers, and bots out.
Exact Near Instantaneous Frequency Formulas Best at Zero Crossings
Cedron Dawg derives time-domain formulas that yield near-instantaneous frequency estimates optimized for zero crossings of pure tones. Complementing his earlier peak-optimized results, these difference-ratio formulas work for real and complex signals, produce four-sample estimators similar to Turners, and cancel amplitude terms, making them attractive low-latency options for clean tones while warning they degrade in noise and at peaks.
A Recipe for a Basic Trigonometry Table
Cedron Dawg walks through building a degree-based sine and cosine table from first principles, showing both recursive and multiplicative complex-tone generators. The article highlights simple drift-correction tricks such as mitigated squaring and compact normalization, gives series methods to compute one-degree and half-degree values, and includes practical C code that ties the table to DFT usage and frequency estimation.
Multimedia Processing with FFMPEG
FFMPEG is a set of libraries and a command line tool for encoding and decoding audio and video in many different formats. It is a free software project for manipulating/processing multimedia data. Many open source media players are based on FFMPEG libraries.
Evaluate Noise Performance of Discrete-Time Differentiators
Differentiators can be wildly different at rejecting noise, even when they share the same usable bandwidth. Neil Robertson introduces the Differentiator Noise Power Ratio, a practical Gaussian-noise metric and a compact formula that uses the filter coefficients to quantify output noise and SNR loss. The post also gives MATLAB guidance for designing and comparing FIR differentiators so you can pick or build filters with much better noise performance.
Correlation without pre-whitening is often misleading
Correlation sounds like the obvious way to find a known pattern, but Peter Kootsookos shows why it can go badly wrong on real, nonwhite data. Using an image example with overlapping blobs, he demonstrates that pre-whitening, here done with a simple row difference, can turn a messy correlation result into a sharply localized peak.
The Sampling Theorem - An Intuitive Approach
Scott Kurtz from DSPSoundWare.com has put together a video presentation that aims to give DSP engineers an intuitive grasp of the Sampling Theorem. The short, approachable video focuses on conceptual understanding of sampling and aliasing rather than mathematical formality. Watch the presentation on DSPRelated and share your reactions in the post comments to join the discussion.
Frequency Formula for a Pure Complex Tone in a DTFT
The analytic formula for calculating the frequency of a pure complex tone from the bin values of a rectangularly windowed Discrete Time Fourier Transform (DTFT) is derived. Unlike the corresponding Discrete Fourier Transform (DFT) case, there is no extra degree of freedom and only one solution is possible.
Fitting Filters to Measured Amplitude Response Data Using invfreqz in Matlab
This post is a redirect notice for a code snippet now hosted elsewhere. If you were looking for the invfreqz example on fitting a filter to measured amplitude response data, this page simply points you to the new location and asks you to update your bookmark.
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.
Free DSP Books on the Internet - Part Deux
Rick Lyons updates his curated list of freely downloadable DSP textbooks, adding titles across communications, implementation, spectral analysis, audio restoration, mathematics and music theory. The post highlights readable introductions like Prandoni and Vetterli's Signal Processing for Communications and Vetterli and Kovacevic's Wavelets and Subband Coding, while reminding readers that these copyrighted books are free only for individual download and not for redistribution.
The Phase Vocoder Transform
Treating the phase vocoder as a continuous transform, this post frames PV(x,α,β) as a bijection on signal space and derives the domain constraints needed for an inverse mapping. It uses geometric intuition and group-theory analogies to explain negative and zero scalings, then brings the idea back to DSP to show how aliasing and phase artifacts appear. The Laroche and Dolson consistency measure D_M plus MATLAB experiments are used to compare classic and identity phase-locking reconstructions.
More free Ebooks
A handy roundup of free engineering ebooks and journals, with a focus on where DSPRelated readers might actually find useful material. The post points to InTechOpen, highlights several MATLAB books, and even calls out a numerical methods title plus some sensor fusion content. If you like browsing for practical references, this is a good place to start.
Project Report : Digital Filter Blocks in MyHDL and their integration in pyFDA
This Summer of Code project shows how to move from Python filter design to synthesizable HDL by building a MyHDL "filter-blocks" package and connecting it to PyFDA. The author implemented direct form I FIR and IIR blocks, added an API, tests, tutorials, and PyFDA export to VHDL and Verilog. The report also highlights practical fixed-point design choices and remaining work such as second-order sections.
