Goertzel derivation

1. How does Goertzel algorithm gives DFT?
2. Why is Goertzel algorithm used?
3. How does Goertzel algorithm work?
4. What is radix 2 FFT algorithm?

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 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 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.

What is radix 2 FFT algorithm?

Radix-2 algorithm is a member of the family of so called Fast Fourier transform (FFT) algorithms. It computes separately the DFTs of the even-indexed inputs (x0,x2,...,xN−2) and of the odd-indexed inputs (x1,x3,...,xN−1), and then combines those two results to produce the DFT of the whole sequence.