Goertzel algorithm produces incorrect phase

1. How does Goertzel algorithm work?
2. How does Goertzel algorithm gives DFT?
3. Why Goertzel algorithm is used?

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.

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.

Why Goertzel algorithm is 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].