# Calculating spectral coherence coefficient (scc) - implementation help

I am trying to calculate the SCC of a cyclostationary signal. I have estimated the Spectral Correlation Function (scf) of the signal using FFT Accumulation Method (FAM). I implemented the following pseudocode in matlab:

function [Sx, alphao, f] = scf(x, fs, d_f, d_alpha)
Compute N' = pow2(nextpow2(fs/df))
L = N'/4
P=pow2(nextpow2(fs/dalpha/L));
N = P*L;    %total no of datat points to process
x = x(1:N)
Divide x into chunks of length N' with L overlapping points
Apply Hamming window across each chunk
Perform FFT
Perform the downshift to baseband
Multiply the baseband with it's complex conjugate
Execute smoothing by means of P-points FFT.
end


where fs is sampling frequency, d_f is frequency resolution and d_alpha is cyclic frequency resolution

Now I have three matrices : $S_x^\alpha$, which is the SCF, $alphao$, which is a 1D vector the cyclic frequencies and $f$, which is a 1D vector the spectral frequencies. I need to calculate the Spectral Coherence Coefficient which is given by the following equation: $C_x^\alpha(f) = \frac{S_x^\alpha(f)}{\sqrt{S_x^0(f-\alpha/2)S_x^0(f+\alpha/2)}} \forall f$

My questions are:

1. If I put $S_x^0(f-\alpha/2)$ in the denominator then won't the denominator essentially becomes $S_x^0(f)$ since $\alpha = 0$?

2. Will $C_x^\alpha$ be of the same size as $S^\alpha_x$?

1. If I put $S_x^0(f-\alpha/2)$ in the denominator then won't the denominator essentially become $S_x^0(f)$, since $\alpha = 0$?
It will become $|S_x^0(f)|$ at $\alpha = 0$, but at other values of $\alpha$, you would need the conjugate multiply at offsets of $f$.
1. Will $C_x^\alpha$ be of the same size as $S^\alpha_x$?
I am struggling with the FAM, it appears to output data on a tilted spectral plane, where $\alpha=0$ lies on the matrix diagonal.