Discrete Fourier Transform (DFT) Calculator

Compute DFT, magnitude/phase spectrum, and inverse reconstruction for sequences up to 8 samples.

Scratchpad (not saved)

Save to create a persistent, shareable workspace.

What This Calculator Does

Compute DFT, magnitude/phase spectrum, and inverse reconstruction for sequences up to 8 samples.

It combines Sequence Length N, x[0], x[1], x[2] to estimate DFT Spectrum X[k], Magnitude Bins, Phase Bins (rad).

Formula & Method

Core equations: X[k]=\sum_{n=0}^{N-1}x[n]e^{-i2\pi kn/N} and x[n]=\frac{1}{N}\sum_{k=0}^{N-1}X[k]e^{i2\pi kn/N}.

Notation used in the formulas: R = DFT Spectrum X[k]; x_{1} = Sequence Length N; x_{2} = x[0]; x_{3} = x[1]; x_{4} = x[2]; x_{5} = x[3]; x_{6} = x[4].

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Inputs Used

Sequence Length N: Used directly in the calculation.
x[0]: Used directly in the calculation.
x[1]: Used directly in the calculation.
x[2]: Used directly in the calculation.
x[3]: Used directly in the calculation.
x[4]: Used directly in the calculation.
x[5]: Used directly in the calculation.
x[6]: Used directly in the calculation.
x[7]: Used directly in the calculation.

Related Calculators

Percentage Calculator — Perform common percentage operations: find a percentage of a value, calculate what percentage one number is of another, and find percentage change.
Fraction Calculator — Add, subtract, multiply, or divide two fractions and simplify the result.
Ratio Calculator — Simplify a ratio and compute equivalent forms.
Proportion Calculator — Solve proportions of the form a / b = c / x.
Average Calculator — Compute mean, median, and mode from up to five values.
Standard Deviation Calculator — Compute population and sample standard deviation from up to five values.
Prime Factorization Calculator — Factor an integer and derive divisor-count, divisor-sum, Euler totient, and divisor list.
GCD / LCM Calculator — Compute greatest common divisor and least common multiple of two integers.