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close all; clear *;
% Whether data shall be written to file or not
writeDataToFile = 0;
% Filter order
N = 7;
% Sampling frequency in <Hz>
fs = 50e6;
% Cutoff frequency in <Hz>
fc = 1e6;
% Design filter (floating-point)
h = fir1(N, fc/(fs/2));
% Plot frequency response
figure(1);
[H, f] = freqz(h, 1, 2^10, fs);
subplot(211);
plot(f/1e6, 20*log10(abs(H)), 'LineWidth', 2); grid on; hold on; box off;
xlabel('f in MHz \rightarrow'); ylabel('|H(f)| in dB \rightarrow');
subplot(212);
plot(f/1e6, unwrap(angle(H)), 'LineWidth', 2); grid on; hold on; box off;
xlabel('f in MHz \rightarrow'); ylabel('arg H(f) in rad \rightarrow');
% Plot impulse response
figure(2);
stem(0:N, h, 'LineWidth', 2); hold on;
xlabel('Coefficient index \rightarrow'); ylabel('Amplitude \rightarrow');
% Wordlength of coefficients
w_c = 12;
% Convert floating-point coefficients to fixed-point
hqi = round(h*2^(w_c-1));
hq = hqi/2^(w_c-1);
% Save integer coefficients to file for later use in VHDL model
if writeDataToFile == 1
fileID = fopen('hqi.txt','w');
fprintf(fileID, ['CONSTANT COEFFS : COEFFS_TYPE := (']);
for k = 1:N
fprintf(fileID, '%d,', hqi(k));
end
fprintf(fileID, '%d);\n', hqi(N+1));
fclose(fileID);
end
% Plot quantized frequency response
figure(1);
[Hq, f] = freqz(hq, 1, 2^10, fs);
subplot(211);
plot(f/1e6, 20*log10(abs(Hq)), 'LineWidth', 2);
title(['Transfer function, N = ' num2str(N), ', fc = ' num2str(fc/1e6) ' MHz']);
subplot(212);
plot(f/1e6, unwrap(angle(Hq)), 'LineWidth', 2);
% Plot quantized impulse response
figure(2);
stem(0:N, hq, 'x', 'LineWidth', 2); hold off;
legend('Float', ['Fixed 1.' num2str(w_c-1) 's, normalized']);
title('Impulse response');
% Create input sample stream
nofSamples = 2^12;
sigma = 0.25;
x = sigma*randn(1, nofSamples);
% Find outliers and saturate to [-1 1-LSB]
w_in = 14;
idx = (x >= 1); x(idx) = 1-2^-(w_in-1);
idx = (x < -1); x(idx) = -1;
% Display histogram
figure(3);
histogram(x, 100);
xlabel('x \rightarrow'); ylabel('Occurences \rightarrow');
title(['Distribution of input samples, \sigma = ' num2str(sigma)]);
% Quantize input sample stream to w_in bit
xqi = round(x*2^(w_in-1));
xq = xqi/2^(w_in-1);
% Save input sample stream to file
if writeDataToFile == 1
save_variable(xqi, '%d', '../../sim/fir/stimuli/fir_stimuli.dat');
end
% Filter quantized input stream with quantized impulse response
yq = filter(hq, 1, xq);
% Plot quantized input and output sample streams
figure(4);
t = (0:nofSamples-1)/fs;
plot(t*1e6, xq); hold on; box off;
plot(t*1e6, yq);
xlabel('t in microseconds \rightarrow'); ylabel('Amplitude \rightarrow');
% Estimate transfer function given specific outcome of xq
[Hxyq, f] = tfestimate(xq, yq, [], [], 2^10, fs);
% Plot estimated frequency response
figure(1);
subplot(211);
plot(f/1e6, 20*log10(abs(Hxyq)), 'LineWidth', 2);
subplot(212);
plot(f/1e6, unwrap(angle(Hxyq)), 'LineWidth', 2);
% Truncation of output result to w_out bit
w_out = 14;
% Filter quantized input with quantized impulse response
yqi = filter(hqi, 1, xqi);
% Determine dynamic wordlength of current result
w_dyn_cur = ceil(log2(max(abs(yqi)))) + 1;
disp(['Dynamic wordlength, current result: ' num2str(w_dyn_cur) ' bits']);
% Determine worst-case dynamic wordlength
w_dyn_wc = w_in + floor(log2(sum(abs(hqi)))) + 1;
disp(['Dynamic wordlength, worst-case: ' num2str(w_dyn_wc) ' bits']);
yqit = floor(yqi/2^(w_dyn_wc-w_out));
% Determine dynamic wordlength of current output
w_dyn_curs = ceil(log2(max(abs(yqit)))) + 1;
disp(['Dynamic wordlength, current output: ' num2str(w_dyn_curs) ' bits']);
% Plot truncated output sample stream
figure(4);
plot(t, yqit / 2^(w_out-1));
legend('x(t)', 'y(t)', 'y(t), truncated');
title('Quantized input and output samples');
% Estimate transfer function given specific outcome of xqint
[Hxyqints, f] = tfestimate(xqi, yqit, [], [], 2^10, fs);
% Plot the estimated frequency response
figure(1);
subplot(211);
plot(f/1e6, 20*log10(abs(Hxyqints)*2^(w_in-w_out)), 'LineWidth', 2);
legend('Float', ['Fixed 1.' num2str(w_c-1) 's'], 'Estimate', 'Estimate, truncated', 'Location','southwest');
subplot(212);
plot(f/1e6, unwrap(angle(Hxyqints)), 'LineWidth', 2);
% Save output sample stream to file
if writeDataToFile == 1
save_variable(yqit, '%d', '../../sim/fir/log/fir_result_ref.dat');
end
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