Calculator Inputs
Use comma, space, semicolon, or new lines between values. This page uses a direct DFT, so very large lengths are intentionally limited.
Example Data Table
| Example | Real Samples | Imaginary Samples | Sample Rate | Window | Expected Observation |
|---|---|---|---|---|---|
| Alternating wave | 0, 1, 0, -1, 0, 1, 0, -1 | 0, 0, 0, 0, 0, 0, 0, 0 | 800 Hz | Hann | Strong energy near one-quarter of the sampling rate. |
| Impulse-like input | 1, 0, 0, 0, 0, 0, 0, 0 | Blank | 1000 Hz | Rectangular | Nearly flat magnitude across all bins. |
| Complex rotating signal | 1, 0, -1, 0 | 0, 1, 0, -1 | 400 Hz | Rectangular | Energy concentrates in a single positive-frequency bin. |
Formula Used
The calculator evaluates the forward discrete Fourier transform directly. For a sequence of length N, each frequency bin is computed from every time-domain sample.
X[k] = Σ x[n] · e^(-j·2π·k·n/N), for n = 0 to N-1
e^(-jθ) = cos(θ) - j·sin(θ)
Magnitude = √(Real² + Imaginary²)
Phase = atan2(Imaginary, Real)
Power = Magnitude²
Frequency at bin k = k · Fs / N
When normalization is enabled, the final complex sum is scaled by either 1/N or 1/√N. Windowing multiplies each input sample before the transform to reduce leakage.
How to Use This Calculator
- Enter the real sample sequence in order of acquisition.
- Optionally enter matching imaginary samples for complex signals.
- Set the sample rate to define the frequency axis in hertz.
- Choose zero padding, window type, normalization, and spectrum view.
- Submit the form to display the result above the calculator.
- Inspect the summary cards, peak table, graphs, and bin table.
- Use the CSV or PDF buttons to export the computed output.
Frequently Asked Questions
1. What does this calculator actually compute?
It computes the forward discrete Fourier transform of your entered samples. The output includes complex bin values, magnitude, phase, power, peak frequencies, and exportable result tables.
2. Why would I use zero padding?
Zero padding increases the number of displayed bins and makes the spectrum look smoother. It improves frequency sampling density, but it does not create new physical information.
3. What is the purpose of a window?
A window reduces spectral leakage when the captured record does not contain an integer number of cycles. Different windows trade peak width against sidelobe suppression.
4. When should I remove DC?
Remove DC when your signal contains an unwanted offset that hides smaller frequency components. Keeping DC is better when the offset itself is meaningful to your analysis.
5. Why are there one-sided and full spectrum views?
One-sided spectra are convenient for real signals because the negative side mirrors the positive side. Full spectra are helpful for complex signals and complete bin inspection.
6. What does normalization change?
Normalization rescales the transform output. It helps match academic conventions, compare transforms across different lengths, or preserve energy relationships in unitary form.
7. Why can two bins have similar magnitudes?
This can happen when the signal contains multiple tones, leakage spreads energy into nearby bins, or a real-valued sequence produces mirrored spectral content in the full view.
8. Is this page using FFT acceleration?
No. This page uses a direct DFT for clarity and transparency. That makes it ideal for learning, smaller datasets, and checking the transform formula step by step.