7.1 Linear-phase FIR transfer function ● Since a zero at z=±1 Is its own reciprocal,it can appear only singly e Now a type 2 Fir filter satisfies H()=z-H(2) with degree N-1 odd ● Hence,H(-1)=(-1))H(-1)=-H(-1) implying H(1=0 i.e., H(2)must have a zero at z=-1
7.1 Linear-phase FIR transfer function
7.1 Linear-phase FIR transfer function Likewise, for a Type 3 or 4 filter H(1)=-H(1) implying H(z) must have a zero at z=1 On the other hand, only the type 3 FIr filter is restricted to have a zero at z=-1 since here the degree n-1 is even and hence H(-1)=-(-1)H(-1)=-H(-1)
7.1 Linear-phase FIR transfer function
7.1 Linear-phase FIR transfer function Typical zero locations shown below Type t Type 2 N odd New Type 3 Type 4 Nodd N even
7.1 Linear-phase FIR transfer function
7.1 Linear-phase FIR transfer function Summary A Type 2 FIR filter cannot be used to design a highpass filter since it always has a zero z=-1 A Type 3 FIR filter has zeros at both z=1 and z=-1 and hence cannot be used to design either a lowpass or a highpass or a bandstop filter A Type 4 FIR filter is not appropriate to design a lowpass filter due to the presence of a zero at z=1 Type l FIR filter has no such restrictions and can be used to design almost any type of filter
7.1 Linear-phase FIR transfer function
7.2 FIR Filter Design based on Windows Function method o We now turn our attention to the design of real coefficient fir filters o These filters are described by a transfer function that is a polynomial in z-land therefore require different approaches for their design
7.2 FIR Filter Design based on Windows Function Method We now turn our attention to the design of real coefficient FIR filters. These filters are described by a transfer function that is a polynomial in z-1and therefore require different approaches for their design