Advanced Signal Processing Techniques

High-Frequency Enveloping, Modulation, and Their Role in Vibration Analysis: High-frequency enveloping and modulation are advanced techniques in vibration analysis used to detect and diagnose faults in machinery, particularly in rolling element bearings, gears, and similar components. These methods help identify subtle fault signatures that might be masked by other vibration signals. 1. High-Frequency Vibration Analysis: High-frequency vibrations occur in the ultrasonic range, typically above the audible frequency range (>20 kHz). These signals are often generated by: Rolling element bearings under load. Impacts from pitting, spalling, or cracking. Gear tooth defects. High-frequency analysis involves capturing these ultrasonic vibrations and interpreting them to diagnose faults. 2. Enveloping Technique: Enveloping is a signal processing technique used to extract fault-related signatures from high-frequency vibration signals. It works by isolating the modulation pattern caused by impacts or irregularities in the system. How Enveloping Works: --Demodulation --Filtering --Rectification --Envelope Detection --Frequency Spectrum Analysis The envelope is subjected to Fast Fourier Transform (FFT) to identify characteristic fault frequencies, such as: Ball Pass Frequency Outer Race (BPFO) Ball Pass Frequency Inner Race (BPFI) Ball Spin Frequency (BSF) Fundamental Train Frequency (FTF) 3. Modulation in Vibration Analysis: Modulation refers to the alteration of a carrier signal's amplitude, frequency, or phase due to an underlying fault. In the context of vibration analysis: Faults like bearing defects, gear tooth wear, or misalignment create periodic impacts or variations in force, which modulate the vibration signal. Amplitude Modulation (AM) and Frequency Modulation (FM) are common in machinery diagnostics. 4. Applications of Enveloping and Modulation Analysis --Bearing Fault Diagnosis: Identifying characteristic frequencies like BPFO, BPFI, BSF, and FTF. Gearbox Analysis: Diagnosing gear tooth wear, cracks, or broken teeth. Isolating gear mesh frequencies and their harmonics, modulated by defects. Detection of Lubrication Issues: High-frequency enveloping can reveal lubrication starvation or contamination in rolling element bearings. Rotating Machinery Faults: Detecting misalignment, imbalance, or looseness, especially when these faults cause modulated vibration patterns.

My primary passion for the last six years, which is AI/ML, and my primary passion for the first two decades of my career, which was digital signal processing (DSP), have finally found a common point of intersection in the form of Fourier Analysis Networks (FAN). I have discussed in the past (I wrote a post on Komogorov-Arnold Network or KAN about six months ago) that as the input functions increase in complexity, the "universal approximation" foundation of multi-layer neural networks start hitting their limits. Result is too many hidden layers and somewhat unwieldy models. The Komogorov-Arnold Network, based on the Komogorov Representation, is a different approach, that can represent any continuous multi-variate function as a summation of multiple continuous univariate functions. This was quite a breakthrough, and it will continue to serve this field well. One aspect that is so far neglected, which is actually one of the primary objectives in DSP, is to discover, and utilize, the periodicity of data. One of the key benefits is that if there is a periodicity, a time domain input can be represented in a more compact way in the frequency domain. To do this, we use Fourier Analysis, which decomposes a signal into a sum of sinusoidal components, which are fundamental to understanding the periodicity and frequency components of the input. A Fourier Analysis Network (FAN) is a type of neural network that uses the principles of Fourier analysis to model, analyze, and process signals or data. The FANs incorporate sinusoidal functions into their architecture to capture periodic or frequency-domain features of data. Such networks can encode data in the frequency domain, which is particularly useful in scenarios where periodicity is present (such as audio signals and image textures). There are many types of FANs! Here are a few examples. The Fourier Neural Operator (FNO) uses the Fourier Transform to learn mappings between functional spaces, and it is very useful n solving partial differential equations. The Fourier Feature Networks use Fourier feature embeddings to transform input data into a high-dimensional space using sinusoidal functions, and Neural Radiance Fields (NeRF) is a useful application. Finally, Spectral Neural Networks operate entirely in the frequency domain instead of time or spatial domain, and can be used for image compression, denoising and other applications. We like to learn new things in our area of work all the time. But if a "ghost from the past" becomes useful in a new and different way, somehow that becomes even more interesting!

Real-Time Peak Detection System on FPGA | DRDO Internship As part of my DRDO internship, I designed and implemented an adaptive peak detection algorithm for real-time signal analysis on FPGA. The goal was to detect transient peaks in noisy signals with minimal latency and high reliability. 🧠 Algorithm Overview: The system maintains a sliding window of recent signal samples. It continuously calculates the mean and standard deviation over this window to adapt to signal baseline shifts. A new sample is compared against a dynamic threshold, defined as a multiple of the standard deviation above the mean. When the signal exceeds this threshold, it is marked as part of a peak region. A finite state machine (FSM) tracks entry into and exit from peak regions, using a hysteresis margin to ensure stable detection and avoid false triggers. Upon exit from a peak region, the system registers a valid peak along with its location, amplitude, and width. 🛠️ The design is optimized for FPGA implementation with fixed-point arithmetic, ensuring resource efficiency and real-time operation. It is suitable for applications like: Anomaly detection in sensor signals Vibration/event monitoring Embedded signal analytics This was a great opportunity to apply statistical signal processing in hardware and optimize it for defense-grade embedded systems. #FPGA #SignalProcessing #Verilog #PeakDetection #RealTimeSystems #AdaptiveThreshold #HardwareDesign #DRDO #DigitalSignalProcessing #VLSI

Everyone in the EE and signal processing field has heard of the Fourier transform and hopefully the ubiquitous Fast Fourier Transform (FFT). One of the cornerstones of signal processing we know today. You may have even dealt with the Hilbert transform - which is useful when dealing with complex-valued signals leveraged in digital comms, adaptive beamforming, phase/freq estimation, demodulation, channelization, etc, etc. These signals take on many different names in literature: I/Q, quadrature phase, analytic, etc. - where the basis is derived from the Hilbert transform. But have you heard of the Fast Hilbert Transform (FHT)? Probably not. It is something I discovered years back when developing an efficient digital down-converter (DDC) scheme. The serendipitous and incredible outcome is that you can compute the Hilbert transform of a signal without any multiplies or adds. Basically just sign changes. It is the most efficient way to compute a Hilbert transform I have seen, and the encompassing DDC architecture is the most efficient topology to convert a real-valued signal into an analytic (complex-valued) signal I have come across in my experience. You get a 2-4x speedup in compute efficiency over the current state of the art. I discovered this topology while researching ways to improve throughput on a low power multi-channel RF board. If interested I am finishing up a white paper outlining all of this, seeing as I havent made this very well publicized in the past. If you are working on high speed signal processing in FPGAs or processors, or are an ADC chip architect - this might be of worth to you. I can easily envision this filtering structure used in new ADCs designs (that also have onboard digital down conversion blocks) to further reduce power draw in those types of chips while not sacrificing performance. In any event, it was a real eye opener to me in terms of innovating in DSP, when you thought there was nothing new left to figure out or discover. There is still hope to uncover new things...

𝗙𝗿𝗼𝗺 𝘁𝗵𝗲𝗼𝗿𝘆 𝘁𝗼 𝘄𝗮𝘃𝗲𝗳𝗼𝗿𝗺: 𝗴𝗲𝗻𝗲𝗿𝗮𝘁𝗶𝗻𝗴 𝟯𝟮𝗔𝗣𝗦𝗞 𝘃𝗶𝗮 𝗮𝗿𝗯𝗶𝘁𝗿𝗮𝗿𝘆 𝗜/𝗤 Most modern signal generators come equipped with standard modulation formats—QPSK, 16QAM, even 256QAM. But when it comes to more advanced or less common schemes like 𝗔𝗣𝗦𝗞 (Amplitude and Phase Shift Keying) or 𝗙𝗤𝗣𝗦𝗞 (Feher’s Quadrature Phase Shift Keying), you’re often on your own. Let’s take 𝟯𝟮𝗔𝗣𝗦𝗞, a constellation used in high-data-rate satellite telemetry and defined in the 𝗖𝗖𝗦𝗗𝗦 𝟭𝟯𝟭.𝟮-𝗕-𝟮 standard. While critical for modern space communications, it’s often not available as a built-in option on commercial signal generators. The solution? 𝗔𝗿𝗯𝗶𝘁𝗿𝗮𝗿𝘆 𝘄𝗮𝘃𝗲𝗳𝗼𝗿𝗺 𝗴𝗲𝗻𝗲𝗿𝗮𝘁𝗶𝗼𝗻 (AWG). Using MathWorks MATLAB, it’s possible to generate the baseband I and Q waveforms defined by the 32APSK constellation. These are then loaded into the 𝘁𝘄𝗼 𝗶𝗻𝗱𝗲𝗽𝗲𝗻𝗱𝗲𝗻𝘁 𝗰𝗵𝗮𝗻𝗻𝗲𝗹𝘀 of an arbitrary waveform generator—one for I, one for Q. However, generating arbitrary I/Q signals this way requires precise 𝘀𝘆𝗻𝗰𝗵𝗿𝗼𝗻𝗶𝘇𝗮𝘁𝗶𝗼𝗻. Any phase or timing mismatch between the I and Q channels can distort the resulting constellation. With dense schemes like 32APSK, 𝗽𝗵𝗮𝘀𝗲 𝗮𝗹𝗶𝗴𝗻𝗺𝗲𝗻𝘁 is critical for maintaining signal integrity. To bring this approach to life, we leveraged a 𝗠𝘂𝗹𝘁𝗶𝗰𝗼𝗺𝗽 𝗮𝗿𝗯𝗶𝘁𝗿𝗮𝗿𝘆 𝘄𝗮𝘃𝗲𝗳𝗼𝗿𝗺 𝗴𝗲𝗻𝗲𝗿𝗮𝘁𝗼𝗿 to implement and visualize a 32APSK signal in a lab environment. Starting with MATLAB-generated I/Q baseband waveforms aligned to the CCSDS 131.2-B-2 standard, we carefully loaded the signal into the AWG’s independent channels. This hands-on demonstration provided a powerful validation of how flexible hardware and software tools—when precisely configured—can seamlessly translate theoretical constellations into real-time signals. It’s a tangible reminder that with the right setup, simulation doesn’t have to stay confined to the screen—it can drive practical, measurable outcomes in complex signal generation tasks. If you want to learn more about the 32APSK waveform and its definition, you can find the CCSDS 131.2-B-2 standard here: https://lnkd.in/d4Aftc2e Special thanks to Miguel Garcia Gutierrez and Ángel Roldán Martín from Farnell Electronics for kindly providing the Multicomp generator used in this demonstration. #DSP #RF #MATLAB #CCSDS #SATCOM

Turning Noise Into Atomic-Scale Insight: A Breakthrough in Super-Resolution X-Ray Imaging Overview Researchers have demonstrated a novel X-ray spectroscopy technique that converts statistical noise into high-value signal, enabling unprecedented, super-resolution views of electronic motion inside atoms. Using the world-leading capabilities of the European XFEL, the team achieved femtosecond-scale snapshots of excited electronic states—an advance long sought in chemistry and materials science. The Core Innovation The method, stochastic Stimulated X-ray Raman Scattering (s-SXRS), leverages the inherent fluctuations in ultrafast X-ray pulses. Instead of suppressing noise, the approach applies covariance analysis to correlate incoming X-ray pulses with emitted Raman signals. This statistical treatment extracts fine electronic details far beyond conventional spectral limits, akin to super-resolution microscopy concepts recognized by the 2014 Nobel Prize in Chemistry. The work is reported in Nature, underscoring its foundational significance. How It Works Intense X-ray pulses pass through neon gas, amplifying Raman signals by nearly a billion-fold. Thousands of stochastic micro-interactions per pulse are averaged to pinpoint energy levels with extreme precision—well below the apparent width of spectral features. High-performance simulations at Argonne’s leadership computing facilities validated the experimental data and refined interpretation. Why It Matters Directly visualizes excited-state electron dynamics, the drivers of chemical reactions and material properties. Accelerates data collection by eliminating slow energy-scanning methods. Enables atomic-level insight critical for catalysis, nanotechnology, and advanced materials design. Positions s-SXRS as a platform technology for next-generation X-ray laboratories worldwide. Bottom Line This work reframes “noise” from a liability into a strategic asset. By marrying ultrafast X-ray sources with sophisticated statistical analysis, researchers have opened a new operational frontier in atomic-scale imaging—one that promises sharper predictions, faster discovery cycles, and deeper control over the electronic processes that underpin modern chemistry and materials science.