Chapter 7 FIR Digital Filter Design
Chapter 7 FIR Digital Filter Design
Introduce o In this chapter, we consider the FIr digita filter design problem o Unlike the iir digital filter design problem it is always possible to design FIr digital filters with exact linear-phase o In the case of fir digital filter design the stability is not a design issue as the transfer function is a polynomial in z -1
Introduce Unlike the IIR digital filter design problem, it is always possible to design FIR digital filters with exact linear-phase. In the case of FIR digital filter design, the stability is not a design issue as the transfer function is a polynomial in z-1. In this chapter, we consider the FIR digital filter design problem
Introduce o First, we describe a popular approach to the design of Fir digital filters with linear- phase. o We then consider the computer-aided design of linear-phase FIr digital filters o To this end we restrict our discussion to the use of MaTLaB in determining the transfer functions
First, we describe a popular approach to the design of FIR digital filters with linearphase. To this end, we restrict our discussion to the use of MATLAB in determining the transfer functions. We then consider the computer-aided design of linear-phase FIR digital filters. Introduce
Advantages o fir digital filter is always guaranteed stable o It is always possible to design Fir digital filters with exact linear-phase
Advantages FIR digital filter is always guaranteed stable. It is always possible to design FIR digital filters with exact linear-phase
Disadvantages o the order of the fir transfer function is usually much higher than that of an IIR transfer function meeting the same frequency response specification
Disadvantages The order of the FIR transfer function is usually much higher than that of an IIR transfer function meeting the same frequency response specification
7.1 Linear-phase FIR transfer function In the previous section, we pointed out why it is important to have a transfer function with a linear-phase property. In this section, we develop the forms of a linear-phase FIr transfer function H(z) with real impulse response h(n)
7.1 Linear-phase FIR transfer function In the previous section, we pointed out why it is important to have a transfer function with a linear-phase property. In this section, we develop the forms of a linear-phase FIR transfer function H(z) with real impulse response h(n)
7.1 Linear-phase FIR transfer function If H z is required to have a linear-phase, its frequency response must be of the form H(el)=Hg(o)e lo Where Ha(o) is called the amplitude response NOTE D Hg(o)is different from H(ejo)l a o(w) is a linear-phase function
7.1 Linear-phase FIR transfer function If H(z) is required to have a linear-phase, its frequency response must be of the form ( ) ( ) j j ( ) H e H e g = Where Hg(ω) is called the amplitude response. NOTE: Hg(ω) is different from |H(ejω)|. Θ(ω) is a linear-phase function
7.1 Linear-phase FIR transfer function Type 1 linear-phase: To T is a constant Type 2 linear-phase (o=8o-to r is a constant, 0 is a initial phase aa unify representation dElo
7.1 Linear-phase FIR transfer function Type 1 linear-phase: ( ) = − is a constant Type 2 linear-phase: A unify representation: ( ) 0 0 = − is a constant, is a initial phase d ( ) d − =
7.1 Linear-phase FIR transfer function It can be proven that the transfer function have a linear-phase, if its impulse response h(n) is either symmetric h(n)=(N-1-n),0≤n≤N-1 or is antisymmetrIC h(n)=-h(N-1-n),0≤n≤N-1
7.1 Linear-phase FIR transfer function It can be proven that the transfer function have a linear-phase, if its impulse response h(n) is either symmetric h n h N n n N ( ) = − − − ( 1 , 0 1 ) or is antisymmetric h n h N n n N ( ) = − − − − ( 1 , 0 1 )
7.1 Linear-phase FIR transfer function Center of h(n) Type 2 Center of N=9 even-svmnetrv N=8 enen-svImmetry h(n) Type 3 Center of h(n) Type 4 Center of N9 dd-svmmetrv N=8 odd-symmetry n
7.1 Linear-phase FIR transfer function