The Real Star of Star Trek
Rick Lyons argues the real star of Star Trek is not an actor but the USS Enterprise, whose image drove much of the franchise's power. He traces the ship from two 1966 scale models through Smithsonian restoration, NASA naming influence, global architecture, and magazine art to show how an engineered prop became a worldwide cultural icon. The piece mixes nostalgia with concrete examples and a hands-on modeler lesson.
An s-Plane to z-Plane Mapping Example
A misleading online diagram prompted Rick Lyons to reexamine how s-plane points map to the z-plane. He spotted apparent errors in the original figure, drew a corrected mapping, and invites readers to inspect both diagrams and point out any remaining mistakes. The short post is a quick visual primer for engineers who rely on accurate s-plane to z-plane mappings in analysis and design.
Should DSP Undergraduate Students Study z-Transform Regions of Convergence?
Rick Lyons argues z-transform regions of convergence are mostly a classroom abstraction with little practical use for real-world DSP engineers. For all stable LTI impulse responses encountered in practice the ROC includes the unit circle, so DTFT and DFT exist and ROC analysis rarely affects implementation. He notes digital oscillators are a notable exception, and suggests reallocating classroom time to more practical engineering topics.
Implementing Impractical Digital Filters
Some published IIR block diagrams are impossible to implement because they contain delay-less feedback paths, and Rick Lyons shows how simple algebra fixes that. He works through two concrete examples—a bandpass built from a FIR notch and a narrowband notch using a feedback loop—and derives equivalent, implementable second-order IIR transfer functions. The post emphasizes spotting problematic loops and replacing them with practical block diagrams.
An Astounding Digital Filter Design Application
Rick Lyons was astonished by the ASN Filter Designer, a hands-on filter design tool that makes tweaking frequency responses as simple as dragging markers with your mouse. The software updates magnitude plots, z-plane pole/zero locations, and filter coefficients in real time, and it also includes a signal analyzer plus a MATLAB-like scripting language for custom coefficient generation. The post links to a demo and user guides so you can try it yourself.
The Swiss Army Knife of Digital Networks
A single discrete-signal network can masquerade as a comb filter, a recursive section, or something much more versatile. Rick Lyons shows how this seven-coefficient structure can be reconfigured to realize a wide range of DSP functions, with tables of impulse responses, pole-zero plots, and frequency responses to illustrate each case. The full explanations live in the downloadable PDF, but the post gives a strong feel for why this is such a handy building block.
Digital Envelope Detection: The Good, the Bad, and the Ugly
Envelope detection sounds simple, but implementation choices change everything. Rick Lyons gathers common digital detectors, including half-wave, full-wave, square-law, Hilbert-based complex, and synchronous coherent designs, and explains how harmonics, filtering, and carrier recovery change results. He ranks detectors by output SNR from a representative simulation and offers practical tips on filter cutoff, Hilbert transformer bandwidth, and when a simple detector is good enough.
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.
Optimizing the Half-band Filters in Multistage Decimation and Interpolation
Multistage decimation and interpolation by powers of two get a lot cheaper if you size each half-band filter differently. Rick Lyons walks through spectra for three-stage examples that show why early stages can use narrower filters for decimation while interpolation reverses the order, and how aliasing and images are handled by later stages. Learn a simple rule to cut multipliers without sacrificing performance.
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.
Correcting an Important Goertzel Filter Misconception
A common claim says the Goertzel algorithm is marginally stable and prone to numerical errors. Rick Lyons shows that the usual second-order Goertzel filter has conjugate poles exactly on the unit circle, so pole placement alone does not make it unstable. The practical limits are coefficient quantization, which reduces frequency precision, and accumulator overflow for very large N.
Improved Narrowband Lowpass IIR Filters
Rick Lyons presents a practical trick from his DSP book that makes narrowband lowpass IIR filters usable in fixed-point systems. By replacing unit delays with M-length delay lines to form an interpolated-IIR, pole radii and angles are transformed so desired poles fall into quantizer-friendly locations without wider coefficient words or extra multiplies. A following CIC image-reject stage removes replicated passbands to meet tight stopband specs.
A Differentiator With a Difference
Rick Lyons presents a compact, practical FIR differentiator that combines central-difference noise attenuation with a much wider linear range. The proposed ydif(n) doubles the usable frequency range to about 0.34π (0.17fs), uses ±1/16 coefficients so multiplications become simple 4-bit right shifts, and has an exact three-sample group delay for easy synchronization with other signals.
A Simpler Goertzel Algorithm
Rick Lyons presents a streamlined Goertzel algorithm that simplifies computing a single DFT bin by removing the textbook method's extra shift and zero-input steps. The proposed network changes the numerator so you run the main stage N times then perform one final output stage, making the implementation cleaner and slightly cheaper computationally. Rick also points out that common textbook forms differ from Gerald Goertzel's 1958 original.
Should DSP Undergraduate Students Study z-Transform Regions of Convergence?
Rick Lyons argues z-transform regions of convergence are mostly a classroom abstraction with little practical use for real-world DSP engineers. For all stable LTI impulse responses encountered in practice the ROC includes the unit circle, so DTFT and DFT exist and ROC analysis rarely affects implementation. He notes digital oscillators are a notable exception, and suggests reallocating classroom time to more practical engineering topics.
Sinusoidal Frequency Estimation Based on Time-Domain Samples
Rick Lyons presents three time-domain algorithms for estimating the frequency of real and complex sinusoids from samples. He shows that the Real 3-Sample and Real 4-Sample estimators, while mathematically exact, fail in the presence of noise and can produce biased or invalid outputs. The Complex 2-Sample (Lank-Reed-Pollon) estimator is more robust but can be biased at low SNR and near 0 or Fs/2, so narrowband filtering is recommended.
Somewhat Off Topic: Deciphering Transistor Terminology
Rick Lyons unpacks a small linguistic mystery in electronics, revealing why the transistor's middle terminal is called the "base". He traces the name to the 1949 Bell Labs "semiconductor triode", where the device sat on a metal base plate described as a large-area low-resistance contact, and notes that later transistor sandwich designs kept the name for historical reasons. The post includes original references and a few trivia nuggets.
Why Time-Domain Zero Stuffing Produces Multiple Frequency-Domain Spectral Images
Zero stuffing in the time domain creates spectral copies, and Rick Lyons walks through why that happens using DFT and DFS viewpoints. He shows that inserting L-1 zeros between samples yields a longer DFT with replicated spectral blocks, and that true interpolation requires lowpass filtering to remove those images. The post uses a concrete L=3 example and an inverse-DFT summation proof to make the effect intuitive.
60-Hz Noise and Baseline Drift Reduction in ECG Signal Processing
Rick Lyons shows a very efficient way to clean up ECGs when both baseline drift and 60 Hz power-line interference are getting in the way. He starts from a linear-phase DC removal filter, reshapes it into a notch filter that hits both 0 Hz and 60 Hz, and then tests it on a noisy real-world ECG. The payoff is a practical design that uses only two multiplications and five additions per sample.
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.
Why Time-Domain Zero Stuffing Produces Multiple Frequency-Domain Spectral Images
Zero stuffing in the time domain creates spectral copies, and Rick Lyons walks through why that happens using DFT and DFS viewpoints. He shows that inserting L-1 zeros between samples yields a longer DFT with replicated spectral blocks, and that true interpolation requires lowpass filtering to remove those images. The post uses a concrete L=3 example and an inverse-DFT summation proof to make the effect intuitive.
An Astounding Digital Filter Design Application
Rick Lyons was astonished by the ASN Filter Designer, a hands-on filter design tool that makes tweaking frequency responses as simple as dragging markers with your mouse. The software updates magnitude plots, z-plane pole/zero locations, and filter coefficients in real time, and it also includes a signal analyzer plus a MATLAB-like scripting language for custom coefficient generation. The post links to a demo and user guides so you can try it yourself.
Correcting an Important Goertzel Filter Misconception
A common claim says the Goertzel algorithm is marginally stable and prone to numerical errors. Rick Lyons shows that the usual second-order Goertzel filter has conjugate poles exactly on the unit circle, so pole placement alone does not make it unstable. The practical limits are coefficient quantization, which reduces frequency precision, and accumulator overflow for very large N.
Should DSP Undergraduate Students Study z-Transform Regions of Convergence?
Rick Lyons argues z-transform regions of convergence are mostly a classroom abstraction with little practical use for real-world DSP engineers. For all stable LTI impulse responses encountered in practice the ROC includes the unit circle, so DTFT and DFT exist and ROC analysis rarely affects implementation. He notes digital oscillators are a notable exception, and suggests reallocating classroom time to more practical engineering topics.
A Simple Complex Down-conversion Scheme
Rick Lyons shows a compact way to turn a real bandpass signal centered at ±fs/4 into a complex, zero-centered analytic signal. The trick uses a delay, a Hilbert transform filter, and a 4:1 downsample, with a small compensation filter to widen the usable passband. He also points out a no-multiplier implementation using shift-and-add coefficients, or a higher-attenuation version with two multiplies per output sample.
The DFT of Finite-Length Time-Reversed Sequences
Rick Lyons digs into a surprisingly under-documented corner of DSP, showing how finite-length time reversal changes a sequence's DFT. The post distinguishes flip and circular time-reversal, gives closed-form DFT relationships, and explains why modulo N arithmetic matters. Engineers get ready-to-use tables and derivations that clarify when and how time reversal affects spectral analysis.
Coupled-Form 2nd-Order IIR Resonators: A Contradiction Resolved
Rick Lyons resolves a long-standing confusion about the coupled-form 2nd-order IIR resonator by deriving its correct z-domain transfer function and explaining why textbooks can appear to contradict pole plots. He shows that with infinite precision the coupled and standard denominators match, but finite-bit quantization of rcos(Θ) and rsin(Θ) changes the z^-2 coefficient and shifts pole positions. Read to learn the correct H(z) to predict quantized behavior and when the coupled form outperforms the standard design.
Frequency Translation by Way of Lowpass FIR Filtering
Rick Lyons shows how you can translate a signal down in frequency and lowpass filter it in a single operation by embedding cosine mixing values into FIR coefficients. The post explains how to build the translating FIR, how to choose the number of coefficient sets, and how decimation can dramatically reduce storage needs while noting practical constraints like the requirement that ft be an integer submultiple of fs.
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.
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.
