FFT Calculator

Purpose & User Intent: The FFT Online Calculator converts time-domain samples into a frequency-domain representation. It targets engineers, researchers, data scientists, and students who need quick spectral insights for signals such as audio, vibration, or sensor data. Users typically identify dominant frequencies, verify harmonics, or compare spectral content across windows and sampling configurations.\n\nCore Logic & Features: The tool uses a discrete Fourier transform via FFT with configurable windowing and transform length. Required inputs are time-domain samples, sampling_rate, and N. Optional features include window_type (Rectangular, Hann, Hamming, Blackman), DC removal, zero-padding, and normalization. Outputs include magnitude_spectrum, frequency_bins (Hz), and optional phase_spectrum; one-sided spectra are available for real inputs.\n\nInputs & Outputs: Inputs: samples, sampling_rate, N, window_type, remove_dc, normalize. Outputs: magnitude, frequencies, optional phase, optional power.\n\nAlgorithms & Calculations: Core is the Cooley–Tukey FFT. If windowing is used, samples are multiplied by the window. Zero-padding extends to N. Magnitude = sqrt(real^2+imag^2); one-sided scaling is applied for real signals. Frequency_bins = k*Fs/N for k=0..N-1.\n\nError & Edge Cases: Validate sampling_rate (>0) and numeric samples. Handle NaN, non-integer N, or unknown window_type with explicit errors. If inputs are missing or inconsistent, results are undefined until data is provided.\n\nIndustry/Region & Localization: Frequencies in Hz; sampling_rate in Hz; units follow SI conventions. Output formatting can respect locale for decimals; no currency or region-specific data is required.\n\nAssumptions & Exclusions: Assumes stationary signals in the analysis window. Not a time-frequency tool; excludes STFT, wavelets, real-time streaming, or external data fetches unless explicitly enabled.