Fast Fourier Transform (FFT) Calculator
MiniWebtool’s Fast Fourier Transform (FFT) Calculator converts real or complex samples into frequency bins. Sample rate, windowing, and padding choices shape magnitude, phase, frequency labels, and peak summaries for interpreting the signal’s spectrum.
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Enter samples and a sample rate below to get the spectrum's magnitude, phase, frequency bins and dominant peaks.
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.
At a Glance
The Fast Fourier Transform (FFT) Calculator converts real or complex samples into frequency bins. It reports frequency, real and imaginary parts, magnitude, normalized magnitude and phase, with window and padding options and a waveform and spectrum plot.
| Feature | What you get | Good for |
|---|---|---|
| Real or complex input | Paste samples such as 0, 1, 0, -1 or complex values such as 1+0i, 0+1i, -1+0i, 0-1i. | Checking textbook FFT examples |
| Test signal builder | Enter tones as Hz:amplitude pairs, a sample rate, a sample count and optional noise, then fill the samples automatically. | Generating a test signal to experiment with |
| Window functions | Choose Rectangular, Hann, Hamming or Blackman to reduce spectral leakage before the transform. | Measured signals that do not hold a whole number of cycles |
| FFT length | Choose the next power of 2, the input length, or double the power of 2 for a denser frequency grid. | Controlling padding and bin spacing |
| Spectrum output | A bin table gives frequency, real, imaginary, magnitude, normalized magnitude and phase in degrees, in one-sided or full view. | Locating tones and comparing phase |
| Peaks and export | Dominant peaks and frequency resolution (sample rate divided by FFT length) are listed. Copy the spectrum as CSV or a complex vector. | Moving results into a spreadsheet or code |
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.
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.
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
- Paste a sequence of real or complex samples. Use values like
0, 1, 0, -1or1+0i, 0+1i, -1+0i, 0-1i. - Enter the sample rate. Use
1if you only need normalized cycles per sample. - Choose a window. Start with Rectangular for exact synthetic examples and Hann for measured signals.
- Choose the FFT length. Next power of 2 is the fastest default; Double power of 2 gives a denser display grid.
- 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.
Can an FFT detect a 60 Hz tone sampled at 1,000 samples per second?
Yes. The Nyquist frequency is half the sample rate, so at 1,000 samples per second it is 500 Hz; a 60 Hz tone is below that limit and can be represented. The FFT bin spacing depends on the transform length: with 1,000 samples and no padding, bins are 1 Hz apart. If the tone does not complete a whole number of cycles in the sampled segment, its energy can spread across nearby bins.
What is the Nyquist frequency for my FFT sample rate?
The Nyquist frequency is half the sample rate. If you sample at 800 Hz, the Nyquist frequency is 400 Hz, so frequencies above 400 Hz cannot be uniquely distinguished from lower-frequency aliases using those samples alone. This limit assumes evenly spaced samples and proper signal sampling. Increasing the FFT length by zero padding makes the frequency grid denser, but it does not raise the Nyquist frequency or recover information that was not sampled.
Why does an FFT show energy at frequencies beside a clean tone?
A finite sample window can cut through a tone before it completes an exact whole number of cycles. The abrupt start and end then spread the tone's energy across neighboring frequency bins, a pattern called spectral leakage. A Hann, Hamming, or Blackman window can reduce that spread, though each changes the spectrum's peak width and amplitude. Check the sample length and window choice when a tone appears across several nearby bins.
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
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