It took me a while to figure out what the problem was, and it turns out to be that the passband frequencies must be normalised by the Nyquist frequency, while the posted code normalises them by the sampling frequency. The result is that the frequencies in the uncorrected code are half of what they should be.
%% testing
Fs = 1e7; % sampling frequency
L = 126204866; % length of signal
% Parameters for the implementation of a BandPass filter
f3 = 300e3; % low cut-off frequency for Bandpass: 700e3, 300e3
f4 = 750e3; % high cut-off frequency for Bandpass: 1450e3, 750e3
fpass = [f3 f4];
hc = fir1(200,fpass/(Fs/2),"bandpass");
% Break the frequency axis into "L" bins/buckets
f = (-0.5:1/L:0.5-1/L)*Fs; % create the frequency vector (frequency X-axis)
Y = 20*log10(abs(fftshift(fft(hc,L))));
[h,w] = freqz(hc, 1, 2^16, Fs);
idx = find(w >= mean(fpass), 1, 'first');
idxv = [1 idx; idx+1 numel(w)];
format short eng
absh = abs(h);
for k = 1:2
idxr = idxv(k,1) : idxv(k,2);
hpf(k) = interp1(mag2db(absh(idxr)), w(idxr), -6);
% figure
% plot(w(idxr),mag2db(absh(idxr)))
% grid
end
fprintf('Half-Power (-6 dB) Frequencies = [%8.3E, %8.3E]',hpf)
figure;
freqz(hc, 1, 2^16, Fs)
set(subplot(2,1,1), 'XLim',[0 1]*1E+6)
yline(subplot(2,1,1), -3)
xline(subplot(2,1,1),hpf,'-r')
set(subplot(2,1,2), 'XLim',[0 1]*1E+6)
title('Filter Frequency Response')
grid on
Also, the bulit-in freqz function is the correct way to depict discrete filter Bode plots in MATLAB.
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