Fast Fourier Transform Calculator

Transform samples into meaningful spectral insight quickly. Reveal tones, harmonics, energy spread, and phase shifts. Compare windows, inspect peaks, and export polished analysis tables.

Calculator Inputs

Enter real-valued samples separated by commas, spaces, or line breaks. The input area uses a responsive three-column layout on large screens, two columns on medium screens, and one column on mobile.

Example: 0, 1.2071, 1.0000, 0.2071, 0.0000, -0.2071, -1.0000, -1.2071
Reset

Example Data Table

This example uses 8 samples at 8 samples per second. It produces visible peaks near 1 and 2 cycles per second.

Index Time (s) Sample Value
00.00000.0000
10.12501.2071
20.25001.0000
30.37500.2071
40.50000.0000
50.6250-0.2071
60.7500-1.0000
70.8750-1.2071

Formula Used

Discrete Fourier Transform:

X[k] = Σ x[n] · e-j2πkn/N, for n = 0 to N-1

Fast Fourier Transform idea:

The FFT computes the same DFT values efficiently by splitting the signal into smaller even and odd parts, then combining them recursively or iteratively using butterfly operations.

Single-sided amplitude estimate:

Amplitude[k] = 2 · |X[k]| / (N · coherent gain), for interior bins. DC and Nyquist bins are not doubled.

Frequency bin spacing:

Δf = fs / N, where fs is the sampling rate and N is the FFT size.

How to Use This Calculator

  1. Enter the sampled signal values in the textarea.
  2. Set the sampling rate in samples per second.
  3. Choose a window function to reduce leakage when needed.
  4. Enable mean removal to reduce the DC component.
  5. Enable zero padding if your sample count is not a power of two.
  6. Choose how many dominant peaks you want highlighted.
  7. Click Compute FFT to display results above the form.
  8. Review charts, peak summaries, and the frequency table.
  9. Use the CSV or PDF buttons to export the analysis.

Frequently Asked Questions

1) What does this FFT calculator measure?

It converts time-domain samples into frequency-domain information. You can inspect frequency bins, amplitude, phase, power, dominant peaks, and charted spectra from real-valued sampled data.

2) Why do I need a sampling rate?

The sampling rate converts FFT bins into real frequency values. Without it, the transform still exists, but the horizontal axis cannot be labeled in meaningful frequency units.

3) What does zero padding change?

Zero padding increases the FFT length and creates finer frequency spacing between plotted bins. It does not add new physical information, but it can make peak locations easier to inspect visually.

4) When should I remove the mean?

Remove the mean when your signal has a large DC offset. This reduces the zero-frequency spike and helps reveal smaller periodic components more clearly.

5) Which window should I choose?

Rectangular is simplest. Hann is a strong general-purpose choice. Hamming preserves tone height well. Blackman offers stronger leakage suppression when nearby frequencies interfere.

6) Why are only positive frequencies shown?

For real-valued signals, negative-frequency content mirrors positive-frequency content. Showing the positive half-spectrum keeps the report compact while preserving the most useful interpretation.

7) Can this analyze non-power-of-two sample counts?

Yes, if padding is enabled. The calculator extends the data with zeros to the next power of two. If padding is disabled, the entered sample count must already be a power of two.

8) What do amplitude and phase mean here?

Amplitude indicates how strong a frequency component is. Phase indicates the angular shift of that component relative to the chosen sample origin in the time-domain input.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.