Example Ripple Calculations in Matlab

Let's first consider the passband ripple spec, $\pm 0.1$ dB. Converting that to linear ripple amplitude gives, in Matlab,

    format long;
    dp=10^(0.1/20)-1
    dp =
       0.01157945425990

Let's check it:

    >> 20*log10(1+dp)
    ans =
       0.10000000000000
    >> 20*log10(1-dp)
    ans =
      -0.10116471483635

Ok, close enough. Now let's set the stopband ripple to 1/10 times the passband ripple and see where we are:

    >> ds=dp/10;
    >> 20*log10(ds)
    ans =
     -58.72623816882052

So, that's about 60 dB stop-band rejection, which is not too bad.

Setting the stopband ripple to 1/100 times the passband ripple adds another 20 dB of rejection:

    >> ds=dp/100;
    >> 20*log10(ds)
    ans =
     -78.72623816882052

which is close to the ``high fidelity'' zone of 80dB SBA

• In FIR filter-design functions such as firpm, the weighting for each band is proportional to one over the ripple amplitude in that band. (We saw previously that the ripple amplitude is $\delta/W(\omega_k)$ where $\delta$ is minimized.)

• Thus, for a unity-gain lowpass-filter, a weighting of 1 passband and 10 in the stopband yields close to 60 dB of stopband attenuation, as derived above.

• The function firpmord in Matlab finds the order needed to achieve a given set of (more user friendly) specifications.