Adventures in Signal Processing with Python
Jason Sachs shows how PyLab (numpy, scipy, matplotlib) can handle many signal-processing and visualization tasks engineers usually reach for MATLAB to do. He walks through practical examples including PWM ripple, two pole RC filters, and symbolic math with SymPy, and shares real-world installation tips and trade-offs. The post closes with pointers to IPython and pandas to speed interactive analysis and data handling.
Collaborative Writing Experiment: Your Favorite DSP Websites
Stephane Boucher invites the DSPRelated community to a live Google Docs experiment to crowdsource the best DSP websites. After a successful run with EmbeddedRelated, he opens a shared document where members can add, edit, and curate links in real time. The post explains the simple rules, notes revision rollback protection, and asks readers to refresh and help keep the list useful and spam-free while watching it evolve.
Python scipy.signal IIR Filtering: An Example
Christopher Felton walks through using scipy.signal IIR filters to demodulate PWM signals, using spectrum and spectrogram analysis to show what works and what does not. He demonstrates using filtfilt to avoid phase delay, compares a single narrow IIR to a very high order FIR, and shows how staged IIR filtering and multirate ideas give much better attenuation. Includes an FPGA-ready MyHDL PWM model.
A Quadrature Signals Tutorial: Complex, But Not Complicated
Quadrature signals are essential in modern communications, yet complex numbers and the j operator intimidate many engineers. In this tutorial Rick Lyons uses phasor geometry, three-dimensional time and frequency plots, and practical I/Q sampling examples to demystify complex exponentials, negative frequency, and how to generate baseband complex signals. Read to get physical intuition and hands-on rules you can apply to modulation, demodulation, and DSP implementations.
Polyphase Filters and Filterbanks
Kyle walks through practical polyphase filtering and analysis filterbanks, complete with Python code using numpy, scipy and matplotlib. The post shows how splitting an FIR into M polyphase legs gives identical, more efficient decimation while avoiding aliasing, and it flags the subtle reordering, zero padding and FFT versus IDFT ordering issues that trip many implementers. Includes runnable reference code and links for deeper theory.
Beat Notes: An Interesting Observation
Rick Lyons overturns a common intuition about beat notes, showing that adding two nearby audio tones yields an average-frequency tone whose amplitude fluctuates, rather than a separate low-frequency sinusoid. He contrasts multiplication and summation of sines, provides simple trigonometric insight, and includes Matlab audio demos to explain why aircraft engine "whump" sounds are amplitude fluctuations of the average engine frequency.
DSPRelated Finally on Twitter!
After resisting social networks, Stephane Boucher announces DSPRelated's move to Twitter and a few site improvements. Users can now sign in once to access DSPRelated, FPGARelated and EmbeddedRelated with the same account, and the site will post updates from @dsprelated, @embeddedrelated and @fpgarelated. To encourage followers, Boucher will occasionally tweet links that award prizes to the first visitors.
Using the DFT as a Filter: Correcting a Misconception
Some sources claim the DFT, when used as a filter, shifts spectral energy down to DC. Rick Lyons shows that this is not true for consecutive DFT-bin outputs and explains the cause of the confusion: the FIR interpretation requires reversing the usual twiddle-factor order. He derives the DFT-bin frequency response, shows the bandpass center at 2πm/N, and explains when decimation does produce a translation to zero Hz.
The Little Fruit Market: The Beginning of the Digital Explosion
A small fruit market in Mountain View became an unlikely cradle for the modern electronics era. Rick Lyons recounts how William Shockley’s lab at 391 San Antonio prompted the Traitorous Eight to form Fairchild, seeding Silicon Valley and spawning an industry whose transistor production quickly dwarfed grains of rice. The post ties that history to the everyday ubiquity of semiconductor devices.
Noise shaping
Markus Nentwig presents a compact, practical introduction to noise shaping by treating quantization error as the first sample of a designed impulse response. He shows how to derive a noise shaper from a target spectrum, demonstrates the tradeoff between in-band noise reduction and total noise increase, and includes a Matlab example while highlighting clipping and stability caveats for sigma-delta contexts.
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.
Differentiating and integrating discrete signals
Think DSP's new chapter digs into discrete differentiation and integration, using first differences, convolution, and FFTs to compare time and frequency domain views. The author reproduces diff via convolution then explores cumsum as its inverse and runs into two puzzling mismatches: noisy FFT amplitude ratios for nonperiodic data, and a time-domain convolution that does not reproduce cumsum for a sawtooth despite matching frequency responses. The post includes IPython notebooks and invites troubleshooting.
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.
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.
Modeling a Continuous-Time System with Matlab
Neil Robertson demonstrates a practical workflow for converting a continuous-time transfer function H(s) into an exact discrete-time H(z) using Matlab's impinvar. He walks through a 3rd-order Butterworth example, shows how to match impulse and step responses, and compares frequency response and group delay so engineers can see where the discrete model stays accurate and when sampling-rate limits cause departure.
Feedback Controllers - Making Hardware with Firmware. Part 9. Closing the low-latency loop
This article demonstrates combining DSP and feedback-control on an Intel Cyclone floating-point FPGA to build low-latency closed-loop circuit emulators and controllers. Using a single floating-point biquad at 1.6 Msps, an IFFT multi-tone 4.096 ms capture for wideband measurement, and MATLAB references for verification, the author achieves sub-nanosecond timing insight and applies DSP phase compensation to cancel about 100 pF of PCB parasitics.
50,000th Member Announced!
DSPRelated just crossed a major milestone, 50,000 registered members, and Stephane Boucher celebrates the anniversary by spotlighting the lucky winner, Charlie Tsai, an assistant professor in Taiwan. The post also looks back at more than a decade of community growth and thanks the contributors, authors, and sponsors who helped make the site a go-to DSP resource. It closes with a promise of big improvements ahead in 2010.
Reducing IIR Filter Computational Workload
Rick Lyons demonstrates a simple, practical way to cut the multiply count for IIR lowpass and highpass filters by converting them into dual-path allpass structures. The conversion preserves the original magnitude response while drastically reducing multiplies per input sample, for example turning a 5th-order IIR that needs 11 multiplies into an equivalent allpass form needing only five. The linked PDF includes theory, implementation notes, a design example, and MATLAB code.
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.
Feedback Controllers - Making Hardware with Firmware. Part 8. Control Loop Test-bed
Built around modest FPGA hardware, this post presents a practical test-bed for evaluating high-speed, low-latency feedback controllers. It covers ADC/DAC specifications, basic and arbitrary test signals, and an IFFT-based generator that can produce thousands of simultaneous tones for rapid Bode, phase, and latency measurements. The article also compares two IFFT strategies, explains turbo sampling, and shows open- and closed-loop test configurations.
The Beginning of a New Chapter
After years of hesitation, Stephane Boucher and Jacob Beningo finally turned their virtual events into an in-person reality with the inaugural Signal Processing Summit and Embedded Systems Summit at the Sonesta Silicon Valley. The post captures the logistics, a last-minute travel scare during a US government shutdown, the joy of meeting speakers like Fred Harris, and practical lessons for future technical events. It closes by inviting community feedback and venue suggestions.
A Wide-Notch Comb Filter
Traditional comb filters make very narrow stopband notches, which limits their ability to suppress broader interfering tones. Rick Lyons presents a linear-phase comb filter that produces wider stopband notches than the conventional design while preserving linear-phase behavior. The post also reviews the traditional cascaded recursive running-sum architecture, its co-located dual poles and zeros on the z-plane, and the placement of nulls at integer multiples of fs/D.
A Two Bin Solution
Cedron Dawg shows how a real sinusoid's frequency, amplitude and phase can be recovered from only two adjacent DFT bins. The article derives exact two-bin formulas, gives a clear Gambas reference implementation, and demonstrates that accurate parameters can be obtained with very few samples when the tone lies between the bins. It also explains when the method breaks down and how the real-valued unfurling improves robustness.
Phase and Amplitude Calculation for a Pure Complex Tone in a DFT
Cedron Dawg derives compact, exact formulas to recover the phase and amplitude of a single complex tone from a DFT bin when the tone frequency is known. The paper turns the complex bin value into closed-form expressions using a sine-fraction amplitude correction and a simple phase shift, and includes working code plus a numeric example for direct implementation.
Radio Frequency Distortion Part II: A power spectrum model
Markus Nentwig presents a power-spectrum model that predicts RF nonlinear distortion from spectral power values instead of time-domain signals. The model computes distortion as repeated convolutions with a frequency-reversed replica and uses an FFT/IFFT trick with real-valued arithmetic for very high efficiency, making it suitable for system-level simulations and interference-aware radios. It is accurate for OFDM-like, Gaussian-amplitude signals when spectral binning is sufficiently fine; narrowband cases require denser bins.
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.
Multi-Decimation Stage Filtering for Sigma Delta ADCs: Design and Optimization
A Matlab toolbox streamlines the design and optimization of multi-stage decimation filters for sigma-delta ADCs. MSD-toolbox automates stage-count and decimation-factor selection, generates Parks-McClellan equiripple FIR coefficients, and iteratively selects coefficient quantization to meet in-band noise constraints. It accepts sigma-delta bitstream stimuli for spectral and intra-stage analysis, includes cost estimation routines, and is published open-source on MathWorks with examples and a dissertation reference.
Filter a Rectangular Pulse with no Ringing
You can filter a rectangular pulse with no ringing simply by using an FIR whose coefficients are all positive, and make them symmetric to get identical leading and trailing edges. This post walks through a MATLAB example that convolves a normalized Hanning window with a 32-sample rectangular pulse, showing that window length controls edge duration and that shorter windows widen the spectrum. It also notes this is not a QAM pulse-shaping solution.
Polar Coding Notes: Channel Combining and Channel Splitting
Lyons Zhang walks through the core algebra of polar coding, showing how channel combining builds the vector channel W_N from N copies of a binary-input DMC using the polar transform G_N = B_N F^{⊗n}. The notes then define channel splitting, derive the coordinate-channel transition probabilities from the chain rule, and present the recursive formulas that let you compute W_{2N}^{(2i-1)} and W_{2N}^{(2i)} from W_N^{(i)}.
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.
