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math-reasoning-mcp

by TeleEng

compute_fft

Compute the Fast Fourier Transform of a discrete numerical sequence to convert time-domain samples into complex frequency-domain bins for spectral analysis.

Instructions

Computes the Fast Fourier Transform (FFT) of a discrete numerical sequence using numpy. Returns complex-valued frequency bins.

Input Schema

TableJSON Schema
NameRequiredDescriptionDefault
sequenceYes

Output Schema

TableJSON Schema
NameRequiredDescriptionDefault
resultYes

Schema Changelog

Changes observed during successful MCP inspections.

  1. First observedv0.1.0

TDQS

B3.4/5.0
Behavior3/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

With no annotations, the description carries the full burden. It does add useful behavior: the implementation uses numpy and the output consists of complex-valued frequency bins. However, it does not disclose constraints like input length handling, normalization, or behavior on empty/non-finite sequences.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is two concise sentences with no filler. It front-loads the main operation in the first sentence and adds a directly relevant output detail in the second.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness4/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a single-parameter FFT utility with an output schema present, the description covers the core input and output semantics adequately. It would be more complete with an example or a brief note on normalization, but the tool is simple enough that an agent can likely invoke it correctly with the given information.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 0%, so the description partially compensates by identifying `sequence` as a discrete numerical sequence and implying numpy-compatible input. It does not elaborate on required formatting, length constraints, or whether complex input is allowed, but the single parameter is fairly self-explanatory from its name and type.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose4/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description clearly states the tool computes the Fast Fourier Transform of a discrete numerical sequence and returns complex-valued frequency bins. It partially distinguishes itself from sibling symbolic/continuous transform tools via 'discrete numerical sequence' and 'using numpy', but it does not explicitly name alternatives or contrast with them.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines2/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

No usage guidance is provided. The description does not mention when to prefer compute_fft over sibling tools like fourier_transform_signal or dtft_signal, and it gives no exclusions or alternative tool recommendations.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.