Signals and Systems - Electrical Engineering

664 C H A P T E R 11: Introduction to the Design of Discrete Filters The crossings of these lines with the filter loss function ...

11.4 IIR Filter Design 665 Since the sample period is Ts= 1 /fs=( 1 / 9 )× 10 −^3 sec/sample ⇒ Kb=cot(πfhpTs)= 1 Given that the ...

666 C H A P T E R 11: Introduction to the Design of Discrete Filters − 1 −0.5 0 0.5 1 − 1 −0.5 0 0.5 1 4 Real part Imaginary par ...

11.4 IIR Filter Design 667 Replacing ′=  p =Kctan(0.5ω)= tan(0.5ω) tan(0.5ωp) (11.33) into the magnitude-squared function for ...

668 C H A P T E R 11: Introduction to the Design of Discrete Filters n Like in the discrete Butterworth, for Chebyshev filters t ...

11.4 IIR Filter Design 669 hpf = (3.01 + alpha(1))∗ones(1,M); % epsilon and half-power frequency epsi = sqrt(10ˆ(0.1∗alphamax)-1 ...

670 C H A P T E R 11: Introduction to the Design of Discrete Filters −1 0 1 −1 −0.5 0 0.5 1 2 Imaginary part 0 0.2 0.4 0.6 0.8 0 ...

11.4 IIR Filter Design 671 FIGURE 11.17 Equal-order(N= 15 )(a) Butterworth and (b) Chebyshev filters for filtering of acoustic s ...

672 C H A P T E R 11: Introduction to the Design of Discrete Filters When designing the Butterworth filter we only need to find ...

11.4 IIR Filter Design 673 n Design a prototype low-pass discrete filter and then transform it into the desired discrete filter ...

674 C H A P T E R 11: Introduction to the Design of Discrete Filters Z=ejθandz=ejωin Equation (11.44) to obtain e−jθ= e−jω−α 1 − ...

11.4 IIR Filter Design 675 support of the prototype low-pass filter, and conversely for− 1 ≤α <0 the transformation expands t ...

676 C H A P T E R 11: Introduction to the Design of Discrete Filters and to obtainαwe replaceθpbyπ−θpin Equation (11.46) to get: ...

11.4 IIR Filter Design 677 11.4.5 General IIR Filter Design with MATLAB The following functionbuttercheby1can be used to design ...

678 C H A P T E R 11: Introduction to the Design of Discrete Filters [b,a] = cheby1(lporder,R,wn,‘stop’); % stopband end [H,w] = ...

11.5 FIR Filter Design 679 %%%%%%%%%%%%%%% % band-stop Butterworth %%%%%%%%%%%%%%% figure(1) [b1,a1] = buttercheby1(15,[0.4 0.6] ...

680 C H A P T E R 11: Introduction to the Design of Discrete Filters FIGURE 11.20 (a) Elliptic band-pass filter and (b) high-pas ...

11.5 FIR Filter Design 681 The remainingM−1 poles of this filter are at the origin of thez-plane, making the filter stable. The ...

682 C H A P T E R 11: Introduction to the Design of Discrete Filters that causes the truncation ofhd[n]. The windowed impulse re ...

11.5 FIR Filter Design 683 whereα=(N− 1 )/ 2. Using a window w[n]of lengthNand centered at(N− 1 )/ 2 , the windowed impulse resp ...