87.2 Selection of Filter Type Advantages in using an FIR filter (1)Can be designed with exact linear phase, (2) Filter structure always stable with quantized coefficients Disadvantages in using an FIR Hilter-Order of an FIR filter, in most cases is considerably higher than the order of an equivalent IR Hilter meeting the same specifications, and FIr Hilter has thus higher computational complexity
§7.2 Selection of Filter Type • Advantages in using an FIR filter - (1) Can be designed with exact linear phase, (2) Filter structure always stable with quantized coefficients • Disadvantages in using an FIR filter - Order of an FIR filter, in most cases, is considerably higher than the order of an equivalent IIR filter meeting the same specifications, and FIR filter has thus higher computational complexity
8 7. 3 Digital Filter Design: Basic Approaches Most common approach to Iir filter design (1)Convert the digital filter specifications into an analog prototype lowpass filter specifications (2)Determine the analog lowpass filter transfer function Ha(s) 3)Transform Ha(s) into the desired digital transfer function G(z)
§7.3 Digital Filter Design: Basic Approaches • Most common approach to IIR filter design – • (1) Convert the digital filter specifications into an analog prototype lowpass filter specifications • (2) Determine the analog lowpass filter transfer function Ha(s) • (3) Transform Ha(s) into the desired digital transfer function G(z)
8 7.3 Digital Filter Design: Basic Approaches This approach has been widely used for the following reasons: (1)Analog approximation techniques are highly advanced (2) They usually yield closed-form solutions 3)Extensive tables are available for analog filter design (4) Many applications require digital simulation of analog systems
§7.3 Digital Filter Design: Basic Approaches • This approach has been widely used for the following reasons: (1) Analog approximation techniques are highly advanced (2) They usually yield closed-form solutions (3) Extensive tables are available for analog filter design (4) Many applications require digital simulation of analog systems
8 7. 3 Digital Filter Design: Basic Approaches An analog transfer function to be denoted as Ha(s)=Pa(s)/da(s) where the subscript“a” specificall indicates the analog domain a digital transfer function derived from Ha(s) shall be denoted as G(z=P(Z/D(z)
§7.3 Digital Filter Design: Basic Approaches • An analog transfer function to be denoted as Ha(s)= Pa(s) / Da(s) where the subscript “a” specifically indicates the analog domain • A digital transfer function derived from Ha(s) shall be denoted as G(z)=P(z)/D(z)
8 7.3 Digital Filter Design: Basic Approaches Basic idea behind the conversion of ha(s)into G(z is to apply a mapping from the s-domain to the z-domain so that essential properties of the analog frequency response are preserved Thus mapping function should be such that Imaginary (@2)axis in the s-plane be mapped onto the unit circle of the z-plane A stable analog transfer function be mapped into a stable digital transfer function
§7.3 Digital Filter Design: Basic Approaches • Basic idea behind the conversion of Ha(s) into G(z) is to apply a mapping from the s-domain to the z-domain so that essential properties of the analog frequency response are preserved • Thus mapping function should be such that – Imaginary (j ) axis in the s-plane be mapped onto the unit circle of the z-plane – A stable analog transfer function be mapped into a stable digital transfer function