s 87.1 Digital Filter Specifications Here. the maximum value of the magnitude in the passband is assumed to be unity 1/v(1+82)-Maximum passband deviation, given by the minimum value of the magnitude in the passband 1/A -Maximum stopband magnitude
§7.1 Digital Filter Specifications • Here, the maximum value of the magnitude in the passband is assumed to be unity • 1/(1+ 2) - Maximum passband deviation, given by the minimum value of the magnitude in the passband • 1/A - Maximum stopband magnitude
s 87.1 Digital Filter Specifications For the normalized specification, maximum value of the gain function or the minimum value of the loss function is 0 dB Maximum passband attenuation =20l max og101+82)dB For 8<<l. it can be shown that max 20log10(1-28n)dB
§7.1 Digital Filter Specifications • For the normalized specification, maximum value of the gain function or the minimum value of the loss function is 0 dB • Maximum passband attenuation 20log (1 2 ) max 10 p dB • For p<<1, it can be shown that 2 max 10 20log 1 dB
87.1 Digital Filter Specifications In practice, passband edge frequency Fpand stopband edge frequency Fs are specified in Hz For digital filter design, normalized bandedge frequencies need to be computed from specifications in Hz using tRp=2TF T C。2hs=2兀FT T
§7.1 Digital Filter Specifications • In practice, passband edge frequency Fpand stopband edge frequency Fs are specified in Hz • For digital filter design, normalized bandedge frequencies need to be computed from specifications in Hz using F T F F F p T p T p p 2 2 F T F F F s T s T s s 2 2
87.2 Selection of Filter Type The transfer function H(z meeting the frequency response specifications should be a causal transfer function For iir digital filter design, the Ir transfer function is a real rational function of z-I H(二)= P0+n12+2+……+p 2 +d1x+dl2z2+…+dlz N H(z must be a stable transfer function and must be of lowest ordern for reduced computational complexity
§7.2 Selection of Filter Type • The transfer function H(z) meeting the frequency response specifications should be a causal transfer function • For IIR digital filter design, the IIR transfer function is a real rational function of z -1: N N M M d d z d z d z p p z p z p z H z 2 2 1 0 1 2 2 1 0 1 ( ) • H(z) must be a stable transfer function and must be of lowest order N for reduced computational complexity
87.2 Selection of Filter Type For fir digital filter design, the FIr transfer e function is a polynomial in z-I with real ● coefficients H(z)=∑[n]z n=0 For reduced computational complexity, degree N of h(z must be as small as possible If a linear phase is desired, the filter coefficients must satisfy the constraint: h[=±hN-n
§7.2 Selection of Filter Type For reduced computational complexity, degree N of H(z) must be as small as possible • If a linear phase is desired, the filter coefficients must satisfy the constraint: h[n] = h[N-n] N n n H z h n z 0 ( ) [ ] • For FIR digital filter design, the FIR transfer function is a polynomial in z -1 with real coefficients: