# 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.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9350634813308716, "perplexity": 1653.075619590958}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027313501.0/warc/CC-MAIN-20190817222907-20190818004907-00521.warc.gz"}