reducing order of fir filter design

[lakshmikalyani]

clc;
clear all;
close all;

a= mfilt.firdecim(2,firls(32,[0 .32 .48 1],[1 1 0 0]));
b= mfilt.firdecim(2,firls(32,[0 .32 .48 1],[0 0 1 1]));
ch1=cascade(a,a,b);
ch2=cascade(a,a);
fvtool(ch2);
fvtool(ch1);
fvtool(b);
fvtool(a);

i came to know that cascading means generating new filter with new cutoff frequencies but i want to know how it is deciding the new cutoff frequency
i observed that it is multiplying the frequencies but not exactly
please help me to know the mathematical calculations

 

[FvM]

You're cascading decimators (multi-rate filters) rather than basic FIR filters. The decimation factor are respectively multiplied. The effect hasn't to do with cascading filters as discussed in this thread before.