https://your-domain.com/https://your-domain.com/posts/audio/stft_audio/https://your-domain.com/posts/audio/stft_audio/How modifying the brightness and gain of a spectrogram changes what you hear — without ever touching the phase. A step-by-step journey through STFT, C++20, and the foundations of DeepFilterNet.Sat, 16 May 2026 12:00:00 GMThttps://your-domain.com/posts/audio/noise-cancelator/phase1/https://your-domain.com/posts/audio/noise-cancelator/phase1/How to capture and play back audio in real time using PortAudio in C++, as the foundation of a noise cancellation engine.Wed, 29 Apr 2026 22:00:00 GMThttps://your-domain.com/posts/audio/noise-cancelator/phase2/https://your-domain.com/posts/audio/noise-cancelator/phase2/How to set up DeepFilterNet in Python to remove background noise from audio files, as the AI layer of a C++ and Python noise cancellation engine.Wed, 29 Apr 2026 21:00:00 GMThttps://your-domain.com/posts/audio/noise-cancelator/phase3/https://your-domain.com/posts/audio/noise-cancelator/phase3/How to connect a real-time C++ audio engine to a Python AI model using ZeroMQ, including the challenges of sample rates, audio APIs, and real-time constraints.Wed, 29 Apr 2026 20:00:00 GMThttps://your-domain.com/posts/audio/noise-cancelator/phase4/https://your-domain.com/posts/audio/noise-cancelator/phase4/How a single integer truncation caused 47% packet loss, how microsecond sleep precision fixed it, and what happened when we replaced Python with a Rust ONNX server.Wed, 29 Apr 2026 19:00:00 GMThttps://your-domain.com/posts/audio/noise-cancelator/phase5/https://your-domain.com/posts/audio/noise-cancelator/phase5/Orchestrating the three official DeepFilterNet3 ONNX models through a Rust server with full DSP pipeline, resampling, and stateful GRU inference.Wed, 29 Apr 2026 18:00:00 GMThttps://your-domain.com/posts/audio/noise-cancelator/phase6/https://your-domain.com/posts/audio/noise-cancelator/phase6/Replacing the per-chunk processing architecture with continuous ring buffers, eliminating chunk boundary glitches and voice loss from Phase 5.Wed, 29 Apr 2026 17:00:00 GMThttps://your-domain.com/posts/audio/noise-cancelator/resume/https://your-domain.com/posts/audio/noise-cancelator/resume/A Resume file that describes each one of the seven phases of the projectWed, 29 Apr 2026 16:00:00 GMThttps://your-domain.com/posts/audio/noise-cancelator/phase7/https://your-domain.com/posts/audio/noise-cancelator/phase7/Using the encoder's lsnr output as a Voice Activity Detection gate to eliminate residual background noise when no voice is present.Wed, 29 Apr 2026 16:00:00 GMThttps://your-domain.com/posts/cpp/opaque_pointer/https://your-domain.com/posts/cpp/opaque_pointer/How C and C++ share objects across a language boundary using void* pointers and a bridge layer, as seen in FFmpeg.Fri, 24 Apr 2026 14:30:00 GMThttps://your-domain.com/posts/audio/chordonomicon/https://your-domain.com/posts/audio/chordonomicon/An intuitive exploration of the Chordonomicon dataset, how chord progressions are stored as graphs, and how that representation opens the door to chord prediction and key detection.Thu, 23 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/cpp/linked_list/https://your-domain.com/posts/cpp/linked_list/An intuitive look at how linked lists work in C++, why they are slower than std::vector in practice, and what cache locality has to do with it.Thu, 23 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/cpp/data_race/https://your-domain.com/posts/cpp/data_race/An intuitive exploration of the bounds of a shared counter under a data race, and the surprising worst-case thread schedule that yields the minimum value of 2.Thu, 23 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/cpp/dynamic_allocation/https://your-domain.com/posts/cpp/dynamic_allocation/An intuitive demonstration of how dynamic memory allocation increases latency in C++, measured with a simple benchmark using std::chrono.Thu, 23 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/audio/juce_threads/https://your-domain.com/posts/audio/juce_threads/An intuitive exploration of the Message Thread and the Audio Thread in JUCE, why they exist, and why the Audio Thread must never allocate memory.Thu, 23 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/cpp/copy_elision/https://your-domain.com/posts/cpp/copy_elision/An intuitive exploration of why modern C++ compilers skip the copy constructor in certain initializations, and what Copy Elision actually means.Thu, 23 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/cpp/concepts/https://your-domain.com/posts/cpp/concepts/An intuitive exploration of C++20 Concepts, why they matter, and how they turn silent wrong behavior into clear, informative compile-time errors.Thu, 23 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/cpp/semaphore/https://your-domain.com/posts/cpp/semaphore/An intuitive breakdown of how a Semaphore is implemented in C++, and why Acquire and Release use different locking strategies.Thu, 23 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/cpp/static_cast/https://your-domain.com/posts/cpp/static_cast/An intuitive exploration of static_cast in C++, how it handles type conversions in class hierarchies, and why casting a Base pointer to Derived when the object is truly Base leads to unexpected behavior.Thu, 23 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/cpp/struc_class/https://your-domain.com/posts/cpp/struc_class/An intuitive exploration of the real difference between struct and class in C++, and why structs are more capable than most people think.Thu, 23 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/audio/tremolo/https://your-domain.com/posts/audio/tremolo/An intuitive explanation of why sudden parameter changes create audible clicks in a Tremolo effect, and how a one-pole smoother makes them vanish.Wed, 22 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/cpp/interleaving_threads/https://your-domain.com/posts/cpp/interleaving_threads/An intuitive exploration of how to synchronize two threads to produce ordered output using a mutex, a condition variable, and a shared boolean.Fri, 17 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/cpp/remez_algorithm/https://your-domain.com/posts/cpp/remez_algorithm/Exploring the Remez algorithm for minimax polynomial approximation, including its intuition, core components, and a step-by-step modular implementation in C++.Sun, 12 Apr 2026 11:30:00 GMThttps://your-domain.com/posts/dsp/alternation_minimax/https://your-domain.com/posts/dsp/alternation_minimax/An analysis of phase response and group delay, distinguishing between strict and generalized linear phase to ensure waveform preservation.Sat, 11 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/dsp/lti_impulse_response/https://your-domain.com/posts/dsp/lti_impulse_response/A formal exploration of how linearity, time-invariance, stability, and causality allow the impulse response to uniquely define a system's behavior.Sat, 11 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/dsp/linear_phase/https://your-domain.com/posts/dsp/linear_phase/A mathematical analysis of ideal lowpass filters, FIR approximations via truncation, and why the Gibbs phenomenon persists in L2 convergence.Sat, 11 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/abstract-algebra/groups/group_orbit_stabilizer/https://your-domain.com/posts/abstract-algebra/groups/group_orbit_stabilizer/A comprehensive guide to group actions, orbits, stabilizers, and their applications in geometric symmetry and group structure.Sat, 11 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/abstract-algebra/groups/idempotent/https://your-domain.com/posts/abstract-algebra/groups/idempotent/Exploring the equivalence between idempotent maps, retraction-section pairs, and direct product decompositions in abelian groups.Sat, 11 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/abstract-algebra/groups/quotient_groups/https://your-domain.com/posts/abstract-algebra/groups/quotient_groups/An intuitive journey through the First Isomorphism Theorem, product groups, inner automorphisms, and the dynamics of group actions.Sat, 11 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/analysis/exponential_series/https://your-domain.com/posts/analysis/exponential_series/Rapidly Decaying Exponential Series ExplanantionFri, 10 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/dsp/dft/https://your-domain.com/posts/dsp/dft/A comprehensive analysis of the Discrete Fourier Transform, covering function mapping, orthogonal basis representation, matrix computations, and physical significance.Fri, 10 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/dsp/discrete_time_fourier_transform/https://your-domain.com/posts/dsp/discrete_time_fourier_transform/Bridging the gap between periodic sequences and infinite-length aperiodic signals through DFS and DTFT analysis.Fri, 10 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/dsp/fourier-expansion-of-cosine/https://your-domain.com/posts/dsp/fourier-expansion-of-cosine/A detailed trigonometric analysis and step-by-step computation of the real Fourier series for the cosine function with a non-integer parameter.Fri, 10 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/dsp/fft/https://your-domain.com/posts/dsp/fft/A comprehensive analysis of the FFT's efficiency, its mathematical foundations in the Cooley-Tukey algorithm, and its impact on modern digital technology.Fri, 10 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/dsp/hilbert_spaces/https://your-domain.com/posts/dsp/hilbert_spaces/An exploration of Hilbert spaces as the mathematical foundation for Digital Signal Processing, focusing on infinite-dimensional vectors and completeness.Fri, 10 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/dsp/lsi/https://your-domain.com/posts/dsp/lsi/A formal analysis of Linear Shift-Invariant systems, focusing on stability, norm conditions, and the mathematical foundations of estimation error convergence.Fri, 10 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/dsp/poles_and_zeros/https://your-domain.com/posts/dsp/poles_and_zeros/An analysis of transfer functions in the Z-domain, the role of poles in defining the ROC, and the criteria for system stability and frequency response existence.Fri, 10 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/dsp/time_frequency_duality/https://your-domain.com/posts/dsp/time_frequency_duality/Exploring the fundamental dual relationships between convolution and multiplication in the time and frequency domains.Fri, 10 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/dsp/orthonormal_bases_and_vector_spaces/https://your-domain.com/posts/dsp/orthonormal_bases_and_vector_spaces/A formal introduction to the structure of N-dimensional Euclidean space, covering inner products, norms, and the properties of bases.Fri, 10 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/analysis/uniform-vs-pointwise/https://your-domain.com/posts/analysis/uniform-vs-pointwise/An intuitive journey through pointwise and uniform convergence, illustrated by a concrete sequence of functions and the role of compactness.Thu, 09 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/abstract-algebra/rings-and-fields/ring-extension/https://your-domain.com/posts/abstract-algebra/rings-and-fields/ring-extension/An intuitive journey through the construction, field transformation, and decomposition of polynomial quotient rings.Thu, 09 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/abstract-algebra/rings-and-fields/field_of_fractions/https://your-domain.com/posts/abstract-algebra/rings-and-fields/field_of_fractions/An intuitive exploration of why the field of fractions is 'smallest' using universal properties and category theory.Wed, 01 Apr 2026 12:00:00 GMThttps://your-domain.com/posts/algebraic-topology/alg_topo_1/https://your-domain.com/posts/algebraic-topology/alg_topo_1/An intuitive exploration of how spaces transform and the concepts that define their equivalence.Tue, 17 Mar 2026 12:00:00 GMThttps://your-domain.com/posts/general-topology/connectedness/https://your-domain.com/posts/general-topology/connectedness/An intuitive introduction to connectedness in topology.Mon, 16 Mar 2026 11:30:00 GMThttps://your-domain.com/posts/abstract-algebra/rings-and-fields/universal_property/https://your-domain.com/posts/abstract-algebra/rings-and-fields/universal_property/An intuitive explanation of what the Universal Properties from Category Theory areSun, 01 Mar 2026 12:00:00 GMThttps://your-domain.com/posts/cpp/simd/https://your-domain.com/posts/cpp/simd/Exploring CPU optimization techniques for Digital Signal Processing using SSE and AVX intrinsics.Tue, 17 Feb 2026 14:30:00 GMThttps://your-domain.com/posts/cpp/lowparallel/https://your-domain.com/posts/cpp/lowparallel/A simple way to make a program faster by letting many threads work independently without constant waiting.Tue, 17 Feb 2026 12:00:00 GMThttps://your-domain.com/posts/general-topology/topospace/https://your-domain.com/posts/general-topology/topospace/The formal definition of a topological space and two fundamental examples.Tue, 17 Feb 2026 11:30:00 GMThttps://your-domain.com/posts/general-topology/norm/https://your-domain.com/posts/general-topology/norm/My first post with equations.Tue, 17 Feb 2026 11:30:00 GMThttps://your-domain.com/posts/general-topology/uniquelimit/https://your-domain.com/posts/general-topology/uniquelimit/A rigorous proof that a subsequence of a convergent sequence in a metric space converges to the same limit.Tue, 17 Feb 2026 11:30:00 GMThttps://your-domain.com/posts/cpp/cache_thread/https://your-domain.com/posts/cpp/cache_thread/Exploring the mechanics of thread-safe caching and its potential applications in high-performance audio engines.Tue, 17 Feb 2026 11:30:00 GMThttps://your-domain.com/posts/general-topology/compacttoseq/https://your-domain.com/posts/general-topology/compacttoseq/A constructive proof that every compact metric space is sequentially compact.Tue, 17 Feb 2026 11:30:00 GMThttps://your-domain.com/posts/abstract-algebra/groups/normal_subgroups/https://your-domain.com/posts/abstract-algebra/groups/normal_subgroups/An intuitive journey through normal subgroups, quotient groups, the quaternion group, homomorphisms, and inner automorphisms.Wed, 10 Dec 2025 12:00:00 GMThttps://your-domain.com/posts/abstract-algebra/groups/subgroups_product_groups/https://your-domain.com/posts/abstract-algebra/groups/subgroups_product_groups/An intuitive journey through generated subgroups, the dihedral group, direct products, and some fundamental isomorphisms in group theory.Mon, 01 Dec 2025 12:00:00 GMThttps://your-domain.com/posts/dsp/zero_padding/https://your-domain.com/posts/dsp/zero_padding/A detailed analysis of zero padding in discrete-time sequences, its mathematical definition, and its impact on spectral visualization and computation.Fri, 24 May 2024 12:00:00 GMT