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.
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.
Ancient History
Technology moves fast, and the tools, platforms, and assumptions you rely on can become outdated almost overnight. In this reflective post, the author contrasts the rapid evolution of embedded development with the much slower pace of social change, from programming turnaround times to the underrepresentation of women in engineering. It is a reminder to keep learning, but also to think about how we work and who gets included.
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.
Autocorrelation and the case of the missing fundamental
A short hands-on exploration shows why we perceive the fundamental pitch even when it's absent from the spectrum. Using saxophone recordings, high-pass filtering, and autocorrelation plots, the post demonstrates that the highest ACF peak often predicts perceived pitch rather than the strongest spectral line. The experiments also show that removing high harmonics eliminates the effect, and that autocorrelation is a useful but incomplete model of pitch perception.
Summary of ROC Rules
This is a very short guide on how to find all possible outcomes of a system where Region of Convergence (ROC) and the original signal is not known.
Signal Processing Summit - Cancellation Policy
The post announces a flexible cancellation policy for the inaugural Signal Processing Summit, an intimate DSP event limited to 70 seats and scheduled in Silicon Valley this October. It explains refundable options designed to give attendees confidence when registering early: a full refund minus a $95 processing fee for cancellations before the end of September, a 50% refund for cancellations in October before October 6, and no refunds after that date. The policy is positioned to help prospective attendees lock in the Early Bird rate, secure discounted hotel accommodations, and plan travel with reduced risk. The announcement frames the policy as a way to remove barriers to commitment and encourages readers who have been undecided to register now and attend the Summit.
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.
DFT Graphical Interpretation: Centroids of Weighted Roots of Unity
DFT bin values can be seen as centroids of weighted roots of unity, a geometric picture that makes many DFT properties immediate. Cedron Dawg uses the geometric-series identity and polar plots of integer and fractional tones to show why constants appear only at DC, how wrapping relates to bin index, and how phase, scaling, offsets, and real-signal symmetry affect bin magnitudes and angles.
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.
Polar Coding Notes: A Simple Proof
Lyons Zhang presents a compact, elementary derivation of channel polarization for binary-input discrete memoryless channels. The note leverages Mrs. Gerber's Lemma to bound conditional entropies and follows the Alsan-Telatar averaging argument to show mediocre channels vanish. The proof sidesteps martingale convergence and recovers the standard result that the fraction of good channels approaches the channel capacity.
Add a Power Marker to a Power Spectral Density (PSD) Plot
Read absolute power directly from a PSD plot with a simple MATLAB helper. The author presents psd_mkr, a function that computes the PSD with pwelch and overlays a power marker in three modes: normal for narrowband tones, band-power for integrated power over a specified bandwidth, and 1 Hz for noise density readings. Examples show how bin summing, window loss, and scalloping are handled for accurate measurements.
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.
The Discrete Fourier Transform of Symmetric Sequences
Symmetric sequences arise often in digital signal processing. Examples include symmetric pulses, window functions, and the coefficients of most finite-impulse response (FIR) filters, not to mention the cosine function. Examining symmetric sequences can give us some insights into the Discrete Fourier Transform (DFT). An even-symmetric sequence is centered at n = 0 and xeven(n) = xeven(-n). The DFT of xeven(n) is real. Most often, signals we encounter start at n = 0, so they are not strictly speaking even-symmetric. We’ll look at the relationship between the DFT’s of such sequences and those of true even-symmetric sequences.
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.
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.
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.
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.
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.
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.
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.
Overview of my Articles
Cedron presents a guided tour of his DSPRelated articles that teach the discrete Fourier transform through derivations, numerical examples, and sample code. The collection centers on novel "bin value" formulas and exact frequency estimators for complex and real tones, with methods for phase and amplitude recovery and iterative multitone resolution. The overview also points to a zeroing-sine window family and an integer pseudo-differentiator for efficient peak and zero-crossing detection.
