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Bài giảng Xử lý tín hiệu số: Chương 6 - TS. Hà Hoàng Kha

Bài giảng "Xử lý tín hiệu số - Chapter 6: Transfer functions and di gital filter realization" gồm có những nội dung chính sau: Impulse response, difference equation, impulse response, block diagram of realization, digital filter realization. Mời các bạn cùng tham khảo. | Chapter p 6 Transfer functions g and Digital Filter Realization Ha Hoang Kha Ph.D.Click to edit Master subtitle style Ho Chi Minh City University of Technology @ Email hhkha@hcmut.edu.vn CuuDuongThanCong.com https fb.com tailieudientucntt With the aid of z-transforms we can describe the FIR and IIR filters in se several eral mathematically mathematicall equivalent eq i alent way a Ha H. Kha 2 Transfer functions and Digital Filter Realizations CuuDuongThanCong.com https fb.com tailieudientucntt Content 1 Transfer 1. T f functions f ti Impulse response Difference equation Impulse response Frequency q y response p Block diagram of realization 2 Digital filter realization 2. Direct form Canonical form Cascade form Ha H. Kha 3 Transfer functions and Digital Filter Realizations CuuDuongThanCong.com https fb.com tailieudientucntt 1. Transfer functions Given a transfer functions H z one can obtain a the th impulse i l response h n h b the difference equation satisfied the impulse response the c h I O difference diff equation i relating l i theh output y n to the h input i x n . d the block diagram realization of the filter the sample-by-sample e p y p pprocessingg algorithm g f the pole zero pattern g the frequency q y response p H w Ha H. Kha 4 Transfer functions and Digital Filter Realizations CuuDuongThanCong.com https fb.com tailieudientucntt Impulse response Taking the inverse z-transform of H z yields the impulse response h n Example p consider the transfer function To obtain the impulse response we use partial fraction expansion to write Assuming the filter is causal we find Ha H. Kha 5 Transfer functions and Digital Filter Realizations CuuDuongThanCong.com https fb.com tailieudientucntt Difference equation for impulse response The standard approach is to eliminate the denominator polynomial of H z and then transfer back to the time domain. Example p consider the transfer function Multiplying both sides by denominator we find Taking inverse z-transform z transform