These appear to be the coefficients of a linear phase (due to the even symmetry of the coefficients) 48 tap low pass filter arranged in polyphase structure and given the words interpolator in the title, for purpose of upsampling the input signal by a factor of 4.
I have detailed the approach to designing a polyphase interpolator from the FIR coefficients in this post: How to implement Polyphase filter? , with the image copied below that specifically shows how a traditional FIR structure is mapped to a polyphase structure for interpolation using to row to column mappings of the coefficients:
In the case of this specific 48 tap implementation in this post given as four 12 tap polyphase filters, the signal would first be upsampled with a zero insert just as done in the diagram I posted above (so insert 3 zero's in between each input sample resulting in a 4x increase in the sample rate). The low pass filter is designed to pass the signal of interest and reject the images that the zero-insert creates. (I have more details on that specifically but that's more detail than necessary to answer the question so will lean slightly toward brevity--- if anyone wants that added, please indicate in the comments). In this case given the completed design, a 48 tap filter was determined to be sufficient by the designer, and this was then mapped into four 12 tap poly-phase filter structures (instead of four 2 tap filters in my image above) as follows:
For FIR filter with taps h[0], h1, h[2].... h[47]
This is mapped into four poly-phase filters as:
Filter 1:
h[0] h[4] h[8] h[12] ... h[44]
Filter 2:
h[1] h[2] h[3] h[4] .... h[45]
Filter 3:
h[2] h[3] h[4] h[5] .... h[46]
Filter 4:
h[3] h[4] h[5] h[6] .... h[47]
The columns given by the OP are the taps for each of the four filters as detailed above. To view the filter response, read the coefficients back in order from each row as listed and then can use the freqz command available in Matlab, Octave or Python (SciPy) to view the response.
