Paper V: Polyphase Signal Calculus · Guided reading
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How can we split, filter, and reconstruct a signal while keeping track of every channel?
Residue projectors turn signals into exact polyphase channels and filters into transfer matrices. The same analysis–synthesis language describes perfect reconstruction, finite-depth Haar transforms, and edge-packet calculations.
These suggested paths use this edition’s available material. Infinite signal results retain their specified sequence space and norm. Exact known-edge reconstruction assumes the edge packet is supplied; estimated packets have separate error bounds.
Visual introduction
Vectors, matrices, linear maps, kernels and images, and reading a statement with hypotheses. Consult the selected paper for any additional algebra or analysis it uses.
- Separate averages and details
Paper V supplies signal background. Information Realization includes a finite Haar contract within its recorded formal core.
- Refine a signal
Read Paper II for refinement and Paper V for signal and polyphase constructions.
- Refine a signal
Follow the worked calculation, its expected output, and its source links.
- Visual guide in HTML
Explore the drawings and their accompanying explanations.
- Question, background, and scope
Use the work overview to identify the problem and required background.
Checkpoint: Explain the question and the model in your own words before continuing.
Full study
Keep the work’s definitions and hypotheses with each result.
- Begin the HTML reading edition
Start at the opening section, then use previous and next to continue in order.
- The signal realization of the seed calculus
Continue through the opening chapters in the edition’s order.
- Residue projectors and exact polyphase coordinates
Continue through the opening chapters in the edition’s order.
- Linear time-invariant operators as transfer matrices
Continue through the opening chapters in the edition’s order.
- Full contents
Choose any chapter or companion section from the complete contents.
- All reading files
Return to the edition’s full reading-file list.
Checkpoint: Choose a result or example and record its assumptions, conclusion, and source location.
Proof and evidence
Read the corresponding statement and its assumptions before inspecting an evidence record.
Recorded coverage. Publication 1.2.0 closes its stated scope. 20 finite formal core results and 225 theorem targets are inherited evidence, separate from the larger manuscript.
Lean: Inherited / related evidence · Evidence basis: Historical formal evidence
Remaining work. Replay the inherited formal core with the pinned runtime. Retain the documented E11.1 amendment and current reproduction entry point.
- Polyphase coordinates
Read the selected setup or definition before using the result.
- Polyphase projector theorem
Read the precise statement and its hypotheses.
- Read its written proof
Follow the recorded written argument for this statement.
- Lean guide (PDF)
Read the correspondence map or formal guide before interpreting formal coverage.
- Inspect retained Lean sources
Compare the full types with the written statements and recorded coverage.
- Code and reproduction files
Read the input limits, expected results, and reproduction instructions.
- Evidence and recorded limits
Check the edition and evidence behind the work’s status.
Checkpoint: Distinguish the written claim, what was checked, and what remains open.