CALCULATORS / SIGNALS, SAMPLING AND DATA

Waveform period, frequency and phase calculator

Window duration/bin spacing tradeoff for a uniform finite record.

signals-time-frequency.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	durations	binSpacingHz
	0.256	3.90625
	0.32	3.125

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

time window budget0.26 s✓ passes

BASELINE INPUTS

sampleRate1000 Hzsamples256

CALCULATED

duration0.256 s

binSpacing3.9063 Hz

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Waveform period, frequency and phase
# Scope: Window duration/bin spacing tradeoff for a uniform finite record.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

sampleRate = 1000 Hz
samples = 256

duration := samples/sampleRate [s]
binSpacing := 1/duration [Hz]

check time window budget: duration <= 0.3 s

scenario alternative: sampleRate = 800 Hz

Calculated from your source · not saved

Baseline · Baseline

time window budget0.26 s ✓ passes

alternative · alternative

time window budget0.32 s × fails

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

duration: duration = samples/sampleRate [s]
bin spacing: binSpacing = 1/duration [Hz]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

sample rate: 1000 Hz
samples: 256

Calculated

duration: 0.256 s
bin spacing: 3.90625 Hz

Assumptions and limits

Window duration/bin spacing tradeoff for a uniform finite record.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Waveform period, frequency and phase. Inputs: period or frequency; time offset. Outputs: frequency/period; phase offset. Model scope: Sampled-data models with stated bandwidth and noise assumptions. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: period or frequency, time offset
Outputs: frequency/period, phase offset
Modes: calculate, compare, sweep
Drawing: Signal, samples and spectrum

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS