## Polar Form of the Frequency Response

When the complex-valued frequency response is expressed in*polar form*, the amplitude response and phase response explicitly appear:

Writing the basic frequency response description

*times*the filter amplitude response, and the output phase equals the input phase

*plus*the filter phase at each frequency . Equation (7.3) gives the frequency response in polar form. For completeness, recall the transformations between polar and rectangular forms (

*i.e.*, for converting real and imaginary parts to magnitude and angle, and vice versa):

#### Separating the Transfer Function Numerator and Denominator

From Eq.(6.5) we have that the transfer function of a recursive filter is a ratio of polynomials in :where

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Phase Response