DFT Calculator

DFT Formula

Worked Example

The 4-point sequence x[n] = {1, 2, 3, 4}:

1. X[k] = Σₙ x[n] e^(−j2πkn/4), k = 0 … 3
2. X[0] = 1 + 2 + 3 + 4 = 10
3. For N = 4 the twiddle factors are 1, −j, −1, j

Energy Σ|x[n]|²: 30 · Parseval check Σ|X[k]|²/N: 30

GATE tip

For N = 4 the twiddle factors are 1, −j, −1, j, so X[1] = x₀ − jx₁ − x₂ + jx₃. Writing the 4 × 4 DFT matrix once saves time on every 4-point question.

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Frequently asked questions

Sources

• The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.