### FIR Filters

When you cascade two FIR filters together, the output of the first becomes the input to the second. The order does not matter. Either filter can be placed first, it makes no difference. The final result is the same even though the intermediate results are different. The figures below can help you see this idea with two cascaded filters. Note how $$v[n]$$ (in the top) differs from $$w[n]$$ (in the bottom) but see how $$y_1[n]$$ and $$y_2[n]$$ are identical. You can also click on the filters to see their respective frequency responses.
 $$x[n]$$ Click Here $$H_1(e^{j\hat\omega})$$ Click Here $$v[n]$$ Click Here $$H_2(e^{j\hat\omega})$$ Click Here $$y_1[n]$$ Click Here
 $$x[n]$$Click Here $$H_2(e^{j\hat\omega})$$Click Here $$w[n]$$Click Here $$H_1(e^{j\hat\omega})$$ Click Here $$y_2[n]$$ Click Here
 $$x[n]$$Click Here $$H_1(e^{j\hat\omega})$$Click Here Click Here $$y[n]$$Click Here $$x[n]$$Click Here $$H_2(e^{j\hat\omega})$$ Click Here Click Here