Discrete Fourier Transform Bin Calculator
Compute the frequency of a DFT bin and check whether a sinusoidal signal lands exactly on that bin from the sample rate, number of samples, signal frequency and target bin index.
How to Use the Discrete Fourier Transform Bin Calculator
- Enter the signal amplitude and frequency.
- Enter the sample rate and number of samples.
- Enter the target bin index k.
- Click Calculate to see the bin frequency and alignment.
使用场景
- •DSP homework.
- •Audio and vibration spectrum setup.
- •Teaching the discrete Fourier transform.
公式
X[k] = Σ x[n] · exp(−2π·i·k·n / N). The k-th bin has centre frequency f_k = f_s · k / N. A signal aligns on a bin when round(f · N / f_s) equals k.
常见问题
What is spectral leakage?
If the signal frequency does not coincide with a bin centre, its energy spreads into neighbouring bins. Windowing (Hann, Hamming, Blackman) attenuates but does not eliminate leakage.
How do I pick N?
Larger N gives finer frequency resolution f_s/N but longer acquisition. Choose N such that (f · N) / f_s is an integer for your test frequencies.
Why is amplitude an input?
It is carried through for completeness in later magnitude-spectrum calculators; this specific tool reports bin frequency and alignment only.