Discrete Fourier Transform Calculator
Calculate a real numeric record’s one-sided DFT amplitude spectrum, complex bins, phase, DC mean and dominant non-DC bin.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Directly evaluate the standard negative-exponent DFT of the rectangular finite record and scale a one-sided amplitude spectrum.
X[k]=Σx[n] exp(−i2πkn/N); non-edge one-sided amplitude=2|X[k]|/N
Worked example
Eight samples 0,1,0,−1,0,1,0,−1 at 8 Hz contain an exact 2 Hz bin with one-sided amplitude 1. DC is zero and time-domain RMS is √0.5.
Assumptions and input details
2–256 real numeric samples, not an audio upload. No window other than rectangular, detrending, zero padding or peak interpolation is applied. DC and even-length Nyquist amplitudes are not doubled; odd-length final bins are doubled. Phase is undefined near numerical zero. A dominant bin does not establish an analog tone frequency, significance or absence of aliasing.
References: NumPy: DFT conventions and real-input spectra
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
SI prefixes are explicit: for example, milli means one thousandth, micro one millionth and kilo one thousand. Changing a unit changes the interpretation of the entered number.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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