IIR coefficients that simply boost the signal

Is there a way to get IIR coefficients that only amplify a signal, nothing more? I suppose some phase shifting would be ok as well as long as it's not too noticeable.

Background: I am using a MiniDSP board and I'm attempting to use the filter section as a level booster to drive the sound into a compressor downstream. The MiniDSP allows you to type in whatever filter coefficients you want in the EQ section.

• Set b0 to whatever gain you want. Set b1, b2, a1, a2 to 0.
– Ben
Apr 29 '20 at 19:43
• @Ben that should be an answer. Also please point out that scaling the coefficients of any other, already used, filter would do, too. Apr 29 '20 at 19:46

I will assume that your IIR filter is an order-2 biquad. But the reasoning remains the same if the implementation is different.

Original filter : $$H(z) = \frac{b_0+b_1\cdot z^{-1}+b\cdot z^{-2}}{1 + a_1\cdot z^{-1} + a_2\cdot z^{-2}}$$

If you want to boost your signal by G

$$H_G(z) = G\frac{b_0+b_1\cdot z^{-1}+b_2\cdot z^{-2}}{1 + a_1\cdot z^{-1} + a_2\cdot z^{-2}}$$

simply distribute G to the numerator

$$H_G(z) = \frac{G\cdot b_0+G\cdot b_1\cdot z^{-1}+G\cdot b_2\cdot z^{-2}}{1 + a_1\cdot z^{-1} + a_2\cdot z^{-2}}$$

Simply multiply your b0-b2 coefficients by G.

In the case where you simply want to boost the signal without filering it at all. Set $$b_0$$ to $$G$$, $$b_1$$, $$b_2$$ to $$0$$, as well as $$a_1$$ and $$a_2$$ to 0.

• upvoted (replaced all the $*$ with $\cdot$ to avoid confusion with convolution). Nice work! Thanks! Apr 29 '20 at 22:40

Example:

% Octave packages -------------------------------

GdB = 6.0; % gain in dB
gain = 10^(GdB/20); % convert

a = 1;
b = gain;

CB = tf(b, a, 1);

figure(1);

bode(CB,'b');
grid on;


If you need to use biquad type filter then just set those other coefficients to 0. Example: b 0 0 1 0 0 (IIRC, MiniDSP had some other ordering ...?).