What is the difference between Goertzel algorithm and cross correlation in time

1. What is the difference between cross-correlation and convolution?
2. Why Goertzel algorithm is used?
3. How does Goertzel algorithm work?
4. Why use convolution instead of correlation?

What is the difference between cross-correlation and convolution?

Cross-correlation and convolution are both operations applied to images. Cross-correlation means sliding a kernel (filter) across an image. Convolution means sliding a flipped kernel across an image.

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].

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 use convolution instead of correlation?

Which one you use depends on the application. If you are performing a linear, time-invariant filtering operation, you convolve the signal with the system's impulse response. If you are "measuring the similarity" between two signals, then you cross-correlate them.