This setup models a clean, discretized 3-phase system with controlled quantization and physically meaningful signal delay.

sine-3phase-equal-sync.m

clear; clc;

%% PARAMETERS
N      = 144;               % samples per period
Nbins  = 18;                % 18 bins -> 9 per half cycle
L      = N / Nbins;         % samples per bin = 8
n      = 0:N-1;             % sample indices
w0     = 2*pi/N;            % sine frequency
shift  = N/3;               % 120° = 48 samples = 6 bins

delay_cap = L/2 + 1;        % requested delay = 5 samples

%% ---- Phase A base sine ----
xA = sin(w0 * n);

%% ---- Time quantization of Phase A into 18 bins ----
xA_blocks = reshape(xA, L, Nbins);   % 8 x 18, each column is a bin
xA_bin    = mean(xA_blocks, 1);      % 1 x 18 bin averages

%% ---- ENFORCE PERFECT SYMMETRY ON BIN LEVELS ----
% Positive half: bins 1..9
pos = xA_bin(1:9);                   % [a b c d ~1 d' c' b' a']

% Symmetrize around centre (index 5)
for k = 1:4
    j = 10 - k;                      % mirror index (9..6)
    v = 0.5 * (pos(k) + pos(j));     % average the pair
    pos(k) = v;
    pos(j) = v;
end

% Force centre bin to exactly 1 (optional but nice)
pos(5) = 1.0;

% Build full symmetric 18-bin pattern
xA_bin_sym        = zeros(1, Nbins);
xA_bin_sym(1:9)   = pos;             % + half
xA_bin_sym(10:18) = -pos;            % exact negative half

% Expand to staircase for Phase A
xA_q = repelem(xA_bin_sym, L);       % 1 x 144

%% ---- 3-phase quantized stairs (just shifts of the same pattern) ----
xB_q = circshift(xA_q,  shift);      % 120°
xC_q = circshift(xA_q,  2*shift);    % 240°

%% ---- 3-phase *true* sines (for contour) ----
xB = circshift(xA,  shift);
xC = circshift(xA,  2*shift);

%% ---- Causal delay (no wrap-around) for contours ----
delay_causal = @(x, init, D) [ repmat(init, 1, D), x(1:end-D) ];

xA_d = delay_causal(xA, xA_q(1), delay_cap);
xB_d = delay_causal(xB, xB_q(1), delay_cap);
xC_d = delay_causal(xC, xC_q(1), delay_cap);

%% ---- Quantization level lines (9 levels) ----
pos_levels = sort(unique(pos));          % a,b,c,d,1
all_levels = [-fliplr(pos_levels), 0, pos_levels];

%% ---- PLOT EVERYTHING ----
figure; hold on;

% Quantized stairs
stairs(n, xA_q, 'LineWidth', 2, 'Color', [1 0 0]);       % Phase A
stairs(n, xB_q, 'LineWidth', 2, 'Color', [0 0.6 0]);     % Phase B
stairs(n, xC_q, 'LineWidth', 2, 'Color', [0 0 1]);       % Phase C

% Delayed contour sines
plot(n, xA_d, 'o', 'Color', [1 0 0], 'MarkerSize', 4, 'LineStyle', 'none');
plot(n, xB_d, 's', 'Color', [0 0.6 0], 'MarkerSize', 4, 'LineStyle', 'none');
plot(n, xC_d, 'd', 'Color', [0 0 1], 'MarkerSize', 4, 'LineStyle', 'none');

% Level lines
for Lvl = all_levels
    yline(Lvl, '--', 'Color', [0.5 0.5 0.5 0.5], 'LineWidth', 1);
end

title('3-Phase Symmetric Stair Sine (N = 144, 18 bins) with Delayed Contours');
xlabel('Sample index n');
ylabel('Amplitude');
legend(...
    'Phase A quantized', 'Phase B quantized', 'Phase C quantized', ...
    'Phase A delayed',   'Phase B delayed',   'Phase C delayed' ...
);
grid on;