Part C:The Transfer Function Chapter 6C Part C ◆Definition ●●● ●●● Transfer Function Expression ●●● Frequency Response from Transfer Function z-Transform The Transfer Function Geometric Interpretation of Frequency Response Computation Stability Condition in Terms of Poles Locations 1.Definition 1.Definition 1.Definition Example 1 .The concept of transfer function is a Y(z)=- generalization of the frequency response H(e) - Consider the M-point moving average FIR The z-transform H(z)of the impulse 三国之刘必] filter with an impulse response response h(n)of the filter is called the 1/M,0<n<M-1 transfer function or the system function h(m)= 0.otherwise The transfer function is derived through the Its transfer function is then given by method similar to that of the frequency 1 1-2w z”-1 response FM0-2可Mz-(e-) =H(z)X(2) H()MChapter 6C z-Transform Part C The Transfer Function 3 Part C: The Transfer Function Definition Transfer Function Expression Frequency Response from Transfer Function Geometric Interpretation of Frequency Geometric Interpretation of Frequency Response Computation Stability Condition in Terms of Poles Locations Stability Condition in Terms of Poles Locations 4 1. Definition The concept of transfer function is a generalization of the frequency response The z-transform H(z) of the impulse response h(n) of the filter is called the transfer function or the system function The transfer function is derived through the method similar to that of the frequency response ( ) j H e 5 1. Definition ( ) () ()( ) () ( ) ( ) () ( ) () () () n n k n k n lnk l k k l l k k l Y z hkxn k z hk xn kz hk xlz hk xlz z HzXz                                        6 1. Definition Example 1 Consider the M-point moving average FIR filter with an impulse response Its transfer function is then given by 1/ 0 1 ( ) 0 otherwise M nM h n      ˈˈ 1 1 1 0 11 1 ( ) (1 ) ( 1) M M M n M n z z Hz z M M z Mz z