tailieunhanh - Understanding digital signal processing - Chapter 6

Tài liệu tham khảo giáo trình tìm hiểu xử lý tín hiệu số bằng tiếng anh ( Understanding digital signal processing ) Chương 6. Bộ lọc đáp ứng xung vô hạn | CHAPTER SIX Infinite Impulse Response Filters Infinite impulse response HR digital filters are fundamentally different from FIR filters because practical HR filters always require feedback. Where FIR filter output samples depend only on past input samples each HR filter output sample depends on previous input samples and previous filter output samples. HR filters memory of past outputs is both a blessing and a curse. Like all feedback systems perturbations at the HR filter input could depending on the design cause the filter output to become unstable and oscillate indefinitely. This characteristic of possibly having an infinite duration of nonzero output samples even if the input becomes all zeros is the origin of the phrase infinite impulse response. It s interesting at this point to know that relative to FIR filters HR filters have more complicated structures block diagrams are harder to design and analyze and do not have linear phase responses. Why in the world then would anyone use an HR filter Because they are very efficient. HR filters require far fewer multiplications per filter output sample to achieve a given frequency magnitude response. From a hardware standpoint this means that HR filters can be very fast allowing us to build real-time IIR filters that operate over much higher sample rates than FIR filters. To illustrate the utility of HR filters Figure 6-1 contrasts the frequency magnitude responses of what s called a fourth-order low-pass HR filter and the 19-tap FIR filter of Figure 5-19 b from Chapter 5. Where the 19-tap FIR filter in Figure 6-1 requires 19 multiplications per filter output sample the fourth-order HR filter requires only 9 multiplications for each filter output sample. Not only does the IIR filter give US reduced At the end of this chapter we briefly compare the advantages and disadvantages of HR filters relative to FIR filters. 219 220 Infinite Impulse Response Filters Figure 6-1 Comparison of the frequency magnitude responses of a