Tunable digital equalizers are used to adjust gains at specific frequencies whiles maintaining the gains at all other frequencies. First order equalizers can be used to real time signal enhancement procedures to improve speech quality.
Consider a first order analog transfer function in Laplace domain:
The transfer function can be rewritten as:
where . Then, using the bi-linear transformation of , the realized digital filter becomes:
where where is the integration step of the trapezoid rule. Figure 1 below illustrates the gains at different frequencies using on the left and the gains at different frequencies using on the right.
Figure 1: Low frequency gain adjusted by varying with on the left and varying with on the right
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