Goertzel algorithm for frequency detection

1. How does Goertzel algorithm work?
2. Why is Goertzel algorithm used?
3. How does Goertzel algorithm gives DFT?
4. How do you calculate DFT frequency?

How does Goertzel algorithm work?

Like the DFT, the Goertzel algorithm analyses one selectable frequency component from a discrete signal. Unlike direct DFT calculations, the Goertzel algorithm applies a single real-valued coefficient at each iteration, using real-valued arithmetic for real-valued input sequences.

Why is Goertzel algorithm used?

The Goertzel algorithm is typically used for frequency detection in the telephone tone dialing (dual-tone multi-frequency, DTMF), where the meaning of the signaling is determined by two out of a total of eight frequencies being simultaneously present [5].

How does Goertzel algorithm gives DFT?

Goertzel's algorithm is another methods that calculates the DFT by converting it into a digital filtering problem. The method looks at the calculation of the DFT as the evaluation of a polynomial on the unit circle in the complex plane.

How do you calculate DFT frequency?

calculate the magnitude of each DFT output bin: magnitude = sqrt(re*re+im*im) find the bin with the largest magnitude, call its index i_max . calculate the equivalent frequency of this bin: freq = i_max * Fs / N , here Fs = sample rate (Hz) and N = no of points in FFT.