Calculate amplitude and phase of a given harmonic

[escherstair]

I can use Real FFT Functions to calculate the amplitude and phase of all the harmonics in the signal represented by the input buffer.
And this is ok.
But sometimes I need to calculate only one specific harmonic (known in advance) and so using the FFT Functions (of 4096 samples, as an example) to keep only one FFT line (amplitude + phase) is far for optmized.

Can I use some internal FFT function (calling it directly) to get this result (using the same twiddle tables already available for FFT)?
Or should I implement the calculation from scratch, with the formula below?
X = sum(x.*exp(-i*2*pi*k*[0:N-1]/N));
and then

amplitude = mag(X)
phase = arg(X)

Thanks

[christophe0606]

@escherstair You need the Goertzel algorithm which is not provided by the library.