Stochastic Signal Processing vs TokenMax

Speech, music, seismic vibrations, oil prices, and climate measurements are all examples of stochastic (random) signals. In this textbook—intended for individuals with prior training in introductory signal processing and introductory probability theory—we develop techniques to process such signals to extract useful information. We present case studies ranging from music to photographic images to oil prices to climate data to the motion of individual biomolecules. This textbook, as an interactive textbook ("iBook"), makes use of your device's ability to display dynamic information through films and animations and to hear the results of the techniques applied to music. At the end of every chapter there are homework problems ranging from easy to "olympic". We make use of your device's interactive capabilities to offer 59 laboratory experiments in signal processing. The experiments use the camera, the microphone, the speakers, and the graphical user interface. These experiments are not simulations; they are examples of real digital processing of signals in your device. In this time of at-home and online learning, this is the way to learn signal processing through study and experimentation.

TokenMax is an AI learning lab for your iPhone, built by Vellora AI: a full computer-science curriculum, a real Python environment with auto-graded problem sets, a sandboxed terminal, and a tutor powered by a language model that runs on the phone itself. No accounts, no servers, no telemetry. LEARN AI, CS & PYTHON — 14 FULL COURSES, OFFLINE - Sidebar → Courses bundles 14 university-level open-courseware classes, readable offline, including: • 6.S191 Intro to Deep Learning — transformers, attention, RLHF, generative AI • 6.5940 TinyML & Efficient Deep Learning — quantization, pruning, the methods behind on-device models • 6.0001 + 6.0002 Intro to CS and Data Science in Python • 6.034 Artificial Intelligence, 6.864 Advanced NLP • 18.06 Linear Algebra, 18.065 Matrix Methods, 18.05 Probability & Statistics • 6.006 + 6.046 Algorithms, 6.S081 Operating Systems, 6.824 Distributed Systems - Course materials from MIT OpenCourseWare, used under CC BY-NC-SA 4.0. TokenMax is free and is not affiliated with or endorsed by MIT. Lecture videos link out to ocw.mit.edu. A REAL PYTHON LAB IN YOUR POCKET - Embedded Python 3.13 — write code and run it without leaving the app. - Auto-graded problem sets check your work line by line, with results in seconds. - Built for learning: the interpreter runs only the bundled lessons and the code you type. It never downloads or executes code from the internet, and network access inside the Python sandbox is disabled. - "Python Tutor (OCW 6.0001)" persona — a Socratic tutor that asks leading questions, runs your code through Python before commenting, and refuses to just hand you the answer. TERMINAL & SSH - A real sandboxed shell with twenty-something built-ins (ls, cd, cat, head, tail, grep, find, mkdir, mv, cp, rm, touch, …) operating only on the app's own writable directories. - SSH client in pure Swift. Save hosts in Settings, connect with password or ED25519 / RSA private keys, host-key fingerprint pinning on first connect. - Per-conversation Plan / Execute mode lets the model drive the terminal. Plan mode allows read-only commands; Execute mode requires per-command approval for anything destructive. AN AI THAT NEVER PHONES HOME - A language model ships inside the app — start chatting on first launch, even in Airplane Mode. - Streaming responses, regenerate, edit and re-roll, copy, pin, folders, in-conversation search, export to PDF / Markdown / JSON, share extension. - Sees photos, hears your voice, reads PDFs. Vision-language models run natively on Apple Silicon via mlx-swift: Qwen2.5-VL 7B on iPhone 15 Pro / 16 Pro / 17 Pro, Qwen2-VL 2B on iPhone 13+. Attach a photo while a text-only model is active and TokenMax reads it on-device with OCR instead. - Drop a PDF, .docx, .md or .txt and ask questions about it — retrieval runs locally with Apple's NLEmbedding. - Web search with real source citations, only when you ask for it. - Slash commands: /summarize, /explain, /code, /tldr, /translate, /improve. PRIVACY YOU CAN AUDIT - Your work stays on your iPhone. The only network calls TokenMax can make are optional model downloads, web search you trigger, and SSH connections to servers you've added — and Settings → Privacy & Data lists every one of them: the host, what data leaves, and what triggers it. - Sealed mode hard-blocks all network traffic with one switch. - Versioned in-app Terms and Privacy Policy. REQUIREMENTS - iPhone 13 or newer recommended. Runs on iPad too. iPhone 15 Pro / 16 Pro / 17 Pro for the 7B vision model. - Falcon 3 1B ships pre-installed — no download needed to start. Larger open-weight models are optional downloads that always show their exact size first (Qwen 2-VL / 2.5-VL under Tongyi Qianwen License, Falcon 3 under TII Falcon-LLM License 2.0, Bonsai 8B under Apache 2.0). TokenMax is built by Vellora AI. We don't run a server. We can't read your work because it never reaches us.