CALCULATORS / SIGNALS, SAMPLING AND DATA

FFT resolution and record length calculator

Uniform sampled FFT frequency-bin spacing; no spectral interpolation.

signals-fft-resolution.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	binWidthHz	recordLengths
	0.976563	1.024
	0.78125	1.28

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.

frequency resolution budget0.98 Hz✓ passes

BASELINE INPUTS

sampleRate1000 Hzsamples1024

CALCULATED

binWidth0.97656 Hz

recordLength1.024 s

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# FFT resolution and record length
# Scope: Uniform sampled FFT frequency-bin spacing; no spectral interpolation.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

sampleRate = 1000 Hz
samples = 1024

binWidth := sampleRate/samples [Hz]
recordLength := samples/sampleRate [s]

check frequency resolution budget: binWidth <= 1 Hz

scenario alternative: sampleRate = 800 Hz

Calculated from your source · not saved

Baseline · Baseline

frequency resolution budget0.98 Hz ✓ passes

alternative · alternative

frequency resolution budget0.78 Hz ✓ passes

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.

bin width: binWidth = sampleRate/samples [Hz]
record length: recordLength = samples/sampleRate [s]

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: 1024

Calculated

bin width: 0.976563 Hz
record length: 1.024 s

Assumptions and limits

Uniform sampled FFT frequency-bin spacing; no spectral interpolation.

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: FFT resolution and record length. Inputs: sample rate; sample count; window choice. Outputs: bin spacing; record duration; effective resolution context. 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: sample rate, sample count, window choice
Outputs: bin spacing, record duration, effective resolution context
Modes: calculate, compare, sweep
Drawing: Signal, samples and spectrum

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