Given a block, x[i], of M samples.

Calculating abs(fft(x)).^2 returns the power spectrum of that block through the use of a M-point FFT.

I can calculate the same using Goertzel's algorithm.

At which M will it be more efficient to use an FFT instead of Goertzel?

Given a block, $x[n]$, of M samples.

Calculating abs(fft(x)).^2 returns the power spectrum of that block through the use of a $M$-point FFT.

I can calculate the same using Goertzel's algorithm.

At which $M$ will it be more efficient to use an FFT instead of Goertzel?

Let's say I have a sample block of M samples and I want to figure out which frequencies are present in the sample block.

Let's say I want to run a frequency analysis that returns the power of N equally spaced frequencies.

At which N is it more efficient to use an FFT than Goertzel to calculate the power of said N frequencies based on M time-domain samples?

Given a block, x[i], of M samples.

Calculating abs(fft(x)).^2 returns the power spectrum of that block through the use of a M-point FFT.

I can calculate the same using Goertzel's algorithm.

At which M will it be more efficient to use an FFT instead of Goertzel?