Signals and Systems - Electrical Engineering

644 C H A P T E R 11: Introduction to the Design of Discrete Filters For practical reasons, these filters are causal (i.e., h[n] ...

11.2 Frequency-Selective Discrete Filters 645 |H ( 2 e jω )| <H ( 2 e jω ) 0 1 2 3 0.5 1 1.5 2 ω |H ( 1 je ω) | <H ( 1 je ...

646 C H A P T E R 11: Introduction to the Design of Discrete Filters That is, the outputy[n] is a combination of the inputx[n] a ...

11.2 Frequency-Selective Discrete Filters 647 0 10 20 30 40 50 60 70 80 90 100 − 10 0 10 x[ n] 0 102030405060708090100 0 1020304 ...

648 C H A P T E R 11: Introduction to the Design of Discrete Filters 11.3 FILTER SPECIFICATIONS There are two ways to specify a ...

11.3 Filter Specifications 649 FIGURE 11.7 Lossα(dB) for normalized gain|G|. 10 −^5 10 −^4 10 −^3 10 −^2 10 −^1 100 Loss α (dB) ...

650 C H A P T E R 11: Introduction to the Design of Discrete Filters Solution The loss specifications are then 0 ≤α(ejω)≤0.92 0 ...

11.3 Filter Specifications 651 FIGURE 11.8 Not-normalized loss specifications for a low-pass filter. ω α(ejω)(dB) α 3 α 2 α (^1) ...

652 C H A P T E R 11: Introduction to the Design of Discrete Filters Then the dc loss is 10 dB andαmax=1 andαmin=40 dB. Suppose ...

11.4 IIR Filter Design 653 frequency response in 0≤ω≤πis Hd(ejω)= { 1 e−jωN 0 ≤ω≤ωc 0 ωc< ω≤π The desired impulse response fo ...

654 C H A P T E R 11: Introduction to the Design of Discrete Filters The optimal approach designs the filter directly, setting t ...

11.4 IIR Filter Design 655 with basesx((n− 1 )Ts)andx(nTs)and heightTs(this is called the trapezoidal rule approximation of an i ...

656 C H A P T E R 11: Introduction to the Design of Discrete Filters FIGURE 11.10 Bilinear transformation mapping ofs-plane into ...

11.4 IIR Filter Design 657 FIGURE 11.11 Relation betweenandω forK= 1. −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 − 10 − 8 − 6 − 4 − ...

658 C H A P T E R 11: Introduction to the Design of Discrete Filters 11.4.2 Design of Butterworth Low-Pass Discrete Filters Our ...

11.4 IIR Filter Design 659 why this is an efficient approach consider the following issues that derive from the application of t ...

660 C H A P T E R 11: Introduction to the Design of Discrete Filters is sampled using the Nyquist frequency and processed with a ...

11.4 IIR Filter Design 661 − 1 0 1 2 Real part Imaginary part − 5 05 − 2 − 1 0 1 2 t x( t) − 1 −0.5 0 0.5 1 t y( t) 0 0.^020. 04 ...

662 C H A P T E R 11: Introduction to the Design of Discrete Filters n Applying the bilinear transformation by hand to filters o ...

11.4 IIR Filter Design 663 %%%%%%%%%%%%%%%% % Example 11.7 %%%%%%%%%%%%%%%% % LP Butterworth alphamax = 2; alphamin = 9; % loss ...