I had a quick look into this topic.

Octave's fir1 () appears to be using fir2 () which looks like the filter response is derived by inverse DFT on a frequency response given on the frequency domain. But Matlabs fir1 () is based on a least squares linear phase filter design.

On the Matlab homepage we find: "fir1 uses a least-squares approximation to compute the filter coefficients and then smooths the impulse response with window"

So in the end two different concepts were compared.

I have searched the signal package for a solution and found a comparable function that was added after fir1 () was written. Octave's firls () should do the trick if the response is windowed by an appropriate window function. It follows a short "proof of concept" code. The plot shows:

i.) JWE's Matlab result as per attachment fir1-example.dat
ii.) JWE's Octave result as per attachment fir1-example.dat
iii.) firls () + hamming window for same cut off frequency

To run the code you have to download JWE's data file first. The result looks very promising. However to fix this somebody must overhaul fir1 ().

pkg load signal

data = load ("fir1-example.dat");

resp = firls (2048, [0, 100/(48000/2), 100/(48000/2), 1], [1, 1, 0, 0]).';
win = hamming (2049).';
lowpass = resp.*win;
firls = lowpass / sum (lowpass);

hold on;
## fir1 (2048, 100/(48000/2), 'low') on Matlab
plot (data(:,1), 'g');
## fir1 (2048, 100/(48000/2), 'low') on Octave PKG Signal
plot (data(:,2), 'c');
plot (firls, 'm');
grid on;
legend({"Matlab","Octave PKG signal","Octave firls () CMD"});

I received a report about differences between the results produced by Matlab and Octave's fir1 functions.  The example given was:

fir1 (2048, 100/(48000/2), 'low')

The result from Matlab is in column 1 of the attached file (fir1-example.dat) and the results I see for Octave are in column 2.  I see a maximum difference of almost 3%

In another case, the difference is larger.  I misinterpreted the original example and asked for confirmation on the maintainers mailing list for the following instead:

fir1 (2048, 100/48000/2, 'low')

The result from Matlab is in column 3 of the data file and the corresponding result from Octave is in column 4.  Here the maximum difference is about 5%

I'm using the development version of Octave and the signal package.  Octave hg id:  64461ccf3039  and signal package hg id:  2adde4d8b905.