Added frft functions towards codegen (c code on PS)

frft_codegen/frft_tb_lfm.m

@@ -0,0 +1,128 @@
+%% FrFT Validation Script (Reference vs Original)
+% Author: Canisio Barth
+
+clear; clc; close all;
+
+%% Parameters
+Fs = 512e6;          % Sampling rate
+T  = 1e-6;           % Signal duration
+N  = Fs*T;           % 512 samples
+
+n = (0:N-1).';
+t = (n - N/2)/ Fs;
+
+% Beta range (Hz/s)
+betas = (-32e12 : 8e12 : 32e12);
+
+% Order sweep (for heatmap)
+a_vec = linspace( 0.5,  1.5, 100);
+
+%% ============================================================
+%% A) HEATMAP (single chirp, order sweep)
+%% ============================================================
+
+beta0 = 16e12; % pick one chirp for visualization
+
+% Generate LFM chirp
+x = exp(1j*pi*beta0*t.^2);
+
+% External interpolation (IMPORTANT)
+x_interp = bizinter(x);
+
+N_interp = length(x_interp);
+N_out = N_interp/2; % after decimation
+
+% Allocate
+FrFT_map_ref = zeros(N_out, length(a_vec));
+FrFT_map_cmp = zeros(N_out, length(a_vec));
+
+for k = 1:length(a_vec)
+    a = a_vec(k);
+
+    % Reference
+    y_ref = fracF_ref(x_interp, a);
+
+    % Comparison (original / other implementation)
+    y_cmp = fracF_cg(x_interp, a);
+
+    FrFT_map_ref(:,k) = y_ref;
+    FrFT_map_cmp(:,k) = y_cmp;
+end
+
+% Plot - Reference
+figure;
+imagesc(a_vec, 1:N_out, abs(FrFT_map_ref) / sqrt(N));
+axis xy;
+xlabel('Order a');
+ylabel('Index');
+title('FrFT Magnitude (Reference)');
+colorbar;
+
+% Plot - Comparison
+figure;
+imagesc(a_vec, 1:N_out, abs(FrFT_map_cmp) / sqrt(N));
+axis xy;
+xlabel('Order a');
+ylabel('Index');
+title('FrFT Magnitude (Comparison)');
+colorbar;
+
+% Plot - Difference
+figure;
+rel_err_map = abs(FrFT_map_ref - FrFT_map_cmp) ./ ...
+              (abs(FrFT_map_ref) + eps);
+
+imagesc(a_vec, 1:N_out, rel_err_map);
+axis xy;
+xlabel('Order a');
+ylabel('Index');
+title('Absolute Difference |Ref - Cmp|');
+colorbar;
+
+
+%% ============================================================
+%% B) PEAK VS BETA (matched order)
+%% ============================================================
+
+peak_ref = zeros(size(betas));
+peak_cmp = zeros(size(betas));
+
+for i = 1:length(betas)
+    beta = betas(i);
+
+    % Generate chirp
+    x = exp(1j*pi*beta*t.^2);
+
+    % External interpolation
+    x_interp = bizinter(x);
+
+    % Matched order
+    a = -(2/pi)*atan(Fs/(beta*T));
+
+    % Compute FrFT
+    y_ref = fracF_ref(x_interp, a);
+    y_cmp = fracF_cg(x_interp, a);
+
+    % Normalized peak magnitude
+    peak_ref(i) = max(abs(y_ref)) / sqrt(N);
+    peak_cmp(i) = max(abs(y_cmp)) / sqrt(N);
+end
+
+% Plot peaks
+figure;
+plot(betas/1e12, peak_ref, 'o-', 'LineWidth', 1.5); hold on;
+plot(betas/1e12, peak_cmp, 's--', 'LineWidth', 1.5);
+xlabel('\beta (MHz/\mus)');
+ylabel('Peak Magnitude');
+title('Peak vs Chirp Rate');
+legend('Reference','Comparison');
+grid on;
+
+% Plot relative error
+figure;
+rel_err = abs(peak_ref - peak_cmp) ./ peak_ref;
+plot(betas/1e12, rel_err, 'o-', 'LineWidth', 1.5);
+xlabel('\beta (MHz/\mus)');
+ylabel('Relative Error');
+title('Relative Error between Implementations');
+grid on;