diff --git a/frft_codegen/bizinter.m b/frft_codegen/bizinter.m new file mode 100644 index 0000000..a2ca9ad --- /dev/null +++ b/frft_codegen/bizinter.m @@ -0,0 +1,37 @@ +function xint=bizinter(x) + +N=length(x); +im = 0; +if sum(abs(imag(x)))>0 + im = 1; + imx = imag(x); + x = real(x); +end + +x2=x(:); +x2=[x2.'; zeros(1,N)]; +x2=x2(:); +xf=fft(x2); +if rem(N,2)==1 %N = odd + N1=fix(N/2+1); N2=2*N-fix(N/2)+1; + xint=2*real(ifft([xf(1:N1); zeros(N,1) ;xf(N2:2*N)].')); +else + xint=2*real(ifft([xf(1:N/2); zeros(N,1) ;xf(2*N-N/2+1:2*N)].')); +end +if ( im == 1) + x2=imx(:); + x2=[x2.'; zeros(1,N)]; + x2=x2(:); + xf=fft(x2); + if rem(N,2)==1 %N = odd + N1=fix(N/2+1); N2=2*N-fix(N/2)+1; + xmint=2*real(ifft([xf(1:N1); zeros(N,1) ;xf(N2:2*N)].')); + else + xmint=2*real(ifft([xf(1:N/2); zeros(N,1) ;xf(2*N-N/2+1:2*N)].')); + end + xint = xint + 1j*xmint; +end + +xint = xint(:); + +end \ No newline at end of file diff --git a/frft_codegen/fracF_cg.m b/frft_codegen/fracF_cg.m new file mode 100644 index 0000000..95e7337 --- /dev/null +++ b/frft_codegen/fracF_cg.m @@ -0,0 +1,80 @@ +function F = fracF_cg(f, a) +%#codegen +%% fracF_cg Fractional Fourier Transform (FrFT) - codegen-ready version +% +% Author: Canisio Barth +% +% F = fracF_cg(f, a) computes the Fractional Fourier Transform (FrFT) +% of the input signal 'f' for a single transform order 'a'. +% +% This version is adapted for MATLAB Coder and hardware-oriented workflows. +% +% Key characteristics: +% - Fixed input size: [1024 x 1] complex(single) +% - Output size: [512 x 1] complex(single) +% - Assumes input 'f' is already interpolated externally +% - No input validation (assumes valid scalar 'a' in core region) +% - Deterministic execution (no branching, no dynamic allocation) +% +% INPUTS: +% f - [1024 x 1] complex(single) +% a - scalar single +% +% OUTPUTS: +% F - [512 x 1] complex(single) +% +% Notes: +% - Internal FFT size = 2048 +% - Designed for code generation and future FPGA mapping + +% Fixed sizes +N = 1024; +%N2 = 512; +Nfft = 2048; + +% Ensure types +pi_s = single(pi); + +% Transform parameter +phi = a * (pi_s / 2); + +% Precompute trig terms +tan_half_phi = tan(phi / 2); +sin_phi = sin(phi); +cos_phi = cos(phi); + +csc_phi = 1 / sin_phi; +cot_phi = cos_phi / sin_phi; + +twoDelta = 2 * sqrt(single(N) / 2); + +%% === Chirp A === +n = single((-N/2:N/2-1).') / twoDelta; + +Achirp = exp(-1j * pi_s * (n .* n) * tan_half_phi); + +%% Chirp multiplication #1 +g = Achirp .* f; + +%% === Chirp B === +m = single((-N:N-1).') / twoDelta; + +Bchirp = exp(1j * pi_s * csc_phi .* (m .* m)); + +%% === Zero-padded buffer === +g_pad = complex(zeros(Nfft,1,'single')); +g_pad(1:N) = g; + +%% === FFT convolution === +G = ifft( fft(g_pad) .* fft(Bchirp) ); + +%% Extract valid part and decimate +G_valid = G(N+1:2:end); % [512 x 1] + +%% Complex phase constant +Aphi = sqrt(1 - 1j * cot_phi); + +%% === Chirp multiplication #2 === +F = (Aphi / twoDelta) .* G_valid .* Achirp(1:2:end); + +end \ No newline at end of file diff --git a/frft_codegen/fracF_ref.m b/frft_codegen/fracF_ref.m new file mode 100644 index 0000000..e01c0e5 --- /dev/null +++ b/frft_codegen/fracF_ref.m @@ -0,0 +1,77 @@ +function [F] = fracF_ref(f, a) +%% fracF_ref Reference Fractional Fourier Transform (FrFT) implementation +% +% Author: Canisio Barth +% +% F = fracF_ref(f, a) computes the Fractional Fourier Transform (FrFT) +% of the input signal 'f' for a single transform order 'a'. +% +% This function serves as a reference (golden model) for validation and +% comparison against future code generation and hardware-oriented +% implementations. +% +% Key characteristics: +% - Scalar transform order 'a' (no vector support). +% - Assumes input signal 'f' is already interpolated externally. +% - Maintains original algorithm structure, including internal +% decimation after convolution. +% - Uses full MATLAB flexibility (not yet restricted for codegen). +% +% INPUTS: +% f - Input signal, [N x 1] column vector. +% IMPORTANT: 'f' must already be interpolated (expanded signal). +% +% a - Scalar transform order. +% Expected to satisfy: 0.5 < |a| < 1.5 +% +% OUTPUTS: +% F - Fractional Fourier Transform, [(N/2) x 1] column vector. +% (Decimated output, consistent with original algorithm.) +% +% LIMITATIONS: +% - No internal interpolation is performed. +% - Only valid for scalar 'a'. +% - Assumes caller enforces correct parameter range and signal format. +% +% See also: fracF (Ozaktas) + +% Validate scalar 'a' +if ~isscalar(a) + error('Parameter ''a'' must be scalar.'); +end + +% Range check (core region) +if abs(a) < 0.5 || abs(a) > 1.5 + error('Parameter ''a'' must be within the interval [0.5, 1.5].'); +end + +N = length(f); % already interpolated length + +% Transform parameter +twoDelta = 2 * sqrt(N/2); +phi = a * pi / 2; + +% === Chirp A === +n = ((-N/2:N/2-1) / twoDelta).'; +Achirp = exp(-1j * pi * (n .* n) * tan(phi/2)); + +% Chirp multiplication #1 +g = Achirp .* f; + +% === Chirp B === +m = ((-N:N-1) / twoDelta).'; +Bchirp = exp(1j * pi * csc(phi) .* (m .* m)); + +% === Chirp convolution === +G = ifft(fft([g; zeros(N,1)]) .* fft(Bchirp)); + +% Extract valid part and decimate +G = G(end/2+1:2:end); + +% Complex phase constant +Aphi = sqrt(1 - 1j * cot(phi)); + +% === Chirp multiplication #2 === +F = (Aphi / twoDelta) .* G .* Achirp(1:2:end); + +end \ No newline at end of file diff --git a/frft_codegen/frft_tb_lfm.m b/frft_codegen/frft_tb_lfm.m new file mode 100644 index 0000000..62ce547 --- /dev/null +++ b/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; \ No newline at end of file diff --git a/resources/project/1PeaTwjt7iChg9Cz3Manp9LeMG4/kdEknmMqyWl3IecDM_b5vXF1cEod.xml b/resources/project/1PeaTwjt7iChg9Cz3Manp9LeMG4/kdEknmMqyWl3IecDM_b5vXF1cEod.xml new file mode 100644 index 0000000..4356a6a --- /dev/null +++ b/resources/project/1PeaTwjt7iChg9Cz3Manp9LeMG4/kdEknmMqyWl3IecDM_b5vXF1cEod.xml @@ -0,0 +1,2 @@ + + \ No newline at end of file diff --git a/resources/project/1PeaTwjt7iChg9Cz3Manp9LeMG4/kdEknmMqyWl3IecDM_b5vXF1cEop.xml 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