// multi-utility computation suite · offline · instant · precise
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sci.Goertzel-DFT-single-tone Calculator
Calculates the Goertzel algorithm DFT coefficient for a single frequency bin, using only N+1 multiplications versus N log N for FFT. The Goertzel algorithm is optimal when detecting only a few specific frequencies — it is used in DTMF tone decoding and industrial vibration monitoring.
Inputs
Fs Hz
Amount per unit of time or per unit quantity. Check the denominator before interpreting.
F Target Hz
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
N Samples
Linear measurement. Ensure consistent units: 1 m = 1,000 mm = 3.281 ft.
Results
Goertzel coefficient 2cos(2πk/N)
Sample size or count used in the calculation.
DFT bin k
Sample size or count used in the calculation.
actual frequency resolved (Hz)
Sample size or count used in the calculation.
frequency resolution (Hz/bin)
Sample size or count used in the calculation.
Goertzel complexity
Algorithmic complexity class (e.g. O(n), O(n log n), O(n^2)). Determines how runtime or memory scales with input size.
application
Recommended use case or application for this configuration or result.