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Fast Fourier Transform (FFT) Calculator

Compute the discrete FFT of a real or complex signal sequence. Apply common window functions, choose FFT length and zero padding, inspect magnitude, phase, frequency bins, dominant peaks, and copy the full complex spectrum.

Fast Fourier Transform (FFT) Calculator
Quick examples:
Sine-like 8 samples Windowed pulse Complex rotating phasor Clean sinusoid
Separate samples with commas, spaces, semicolons, or new lines. Complex values can use 3+4i, -2i, or 1.25-0.5i.
The default length pads to a power of two so the radix-2 FFT path is used.

Embed Fast Fourier Transform (FFT) Calculator Widget

About Fast Fourier Transform (FFT) Calculator

The Fast Fourier Transform (FFT) Calculator computes the discrete Fourier transform of a finite signal sequence and turns the result into practical frequency-bin output: real and imaginary components, magnitude, normalized magnitude, phase angle, frequency labels, dominant peaks, and copyable spectrum data. It accepts real or complex samples, supports common window functions, and uses power-of-two zero padding by default so the fast radix-2 algorithm can be used.

What the FFT Computes

For a sequence of N samples x[0], x[1], ..., x[N−1], the discrete Fourier transform produces N complex bins X[0], X[1], ..., X[N−1]. Each bin measures how strongly a sinusoidal component at that bin frequency appears in the signal.

X[k] = Σ x[n] · e^(−2πi·k·n/N), for k = 0, 1, ..., N−1

The FFT is an efficient way to compute the same DFT. When the transform length is a power of two, the radix-2 FFT reduces work from roughly N² complex operations to about N log₂ N operations, which is why zero padding to the next power of two is common in signal-processing workflows.

How to Read the Output

Column Meaning Typical use
Frequency Bin index converted to physical units using sample rate / FFT length. Locate tones, vibration frequencies, modulation bands, or periodic components.
Real / Imaginary The complex FFT coefficient for each bin. Preserve full phase-aware information for reconstruction or further math.
Magnitude The size of the complex coefficient, written as |X[k]|. Identify which frequencies are strongest.
Phase The angle of the complex coefficient in degrees. Compare timing offsets between components or channels.
Normalized magnitude Magnitude divided by FFT length. Compare spectra calculated with different padded lengths.

Sample Rate and Frequency Resolution

If your sample rate is Fs and the FFT length is N, adjacent FFT bins are spaced by Fs / N. A larger FFT length produces denser bin spacing, but zero padding does not create new information; it interpolates the frequency grid of the existing signal segment.

frequency of bin k = k · Fs / N and Δf = Fs / N

For real-valued input, the positive-frequency half is usually enough because the negative-frequency half is the complex conjugate mirror. For complex-valued input, the full spectrum is often meaningful and this calculator switches to the full view in the complex example.

Window Function Guide

A window changes the edges of the sampled segment before the FFT. This reduces spectral leakage when the segment does not contain a whole number of cycles. The tradeoff is that windows spread energy across a wider main lobe and change amplitude scaling.

Window Best for Tradeoff
Rectangular Signals that already line up cleanly with the sample window. Highest leakage when the captured segment cuts a waveform mid-cycle.
Hann General spectral inspection and smooth leakage reduction. Moderate amplitude loss and moderate main-lobe width.
Hamming Reducing nearby sidelobes while keeping a compact main lobe. Slightly less smooth at the boundaries than Hann.
Blackman Suppressing leakage from strong tones into weaker nearby bins. Wider main lobe, so close frequencies are harder to separate.

How to Use This Calculator

  1. Paste a sequence of real or complex samples. Use values like 0, 1, 0, -1 or 1+0i, 0+1i, -1+0i, 0-1i.
  2. Enter the sample rate. Use 1 if you only need normalized cycles per sample.
  3. Choose a window. Start with Rectangular for exact synthetic examples and Hann for measured signals.
  4. Choose the FFT length. Next power of 2 is the fastest default; Double power of 2 gives a denser display grid.
  5. Click Calculate FFT, then inspect the magnitude plot, peak list, phase column, and copyable CSV output.

Worked Example

For the sample sequence 0, 1, 0, -1, 0, 1, 0, -1 at a sample rate of 8, the signal completes two cycles over eight samples. The strongest non-DC FFT bins appear at the corresponding positive and negative frequency positions. In one-sided mode, the positive-frequency peak is the easiest to read.

FAQ

What does an FFT calculator compute?
An FFT calculator computes the discrete Fourier transform of a finite sequence. It rewrites time-domain samples as frequency bins with complex amplitudes, magnitudes, and phases.

Do I need a power-of-two number of samples?
A radix-2 FFT is fastest when the transform length is a power of two. This calculator can automatically zero-pad your input to the next power of two, and it uses a direct DFT fallback for small exact-length sequences that are not powers of two.

What is the FFT frequency resolution?
Frequency resolution is sample rate divided by FFT length. For example, a 1000 Hz sample rate and a 1024-point FFT give bins spaced by about 0.9766 Hz.

Should I use a Hann, Hamming, or Blackman window?
Use a window when your captured segment does not contain an integer number of cycles. Hann is a balanced general-purpose choice, Hamming reduces nearby sidelobes, and Blackman gives stronger sidelobe suppression with a wider main lobe.

Why are FFT results complex numbers?
Each frequency bin has both amplitude and phase. The real and imaginary parts are a compact way to store that phase-aware sinusoidal component.

Reference this content, page, or tool as:

"Fast Fourier Transform (FFT) Calculator" at https://MiniWebtool.com/fast-fourier-transform-fft-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Apr 24, 2026

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

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