Tham khảo tài liệu 'crc press mechatronics handbook 2002 by laxxuss episode 3 part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | FIGURE Finite-width pulse sampling signals and spectra a bandlimited signal and spectrum b finite-width train of pulses and its transform c sampled signal and its spectra d quantization process. 2002 CRC Press LLC FIGURE Finite-width pulse sampling signals and spectra a bandlimited signal and spectrum b finite-width train of pulses and its transform c sampled signal and its spectra d quantization process. 2002 CRC Press LLC The Discrete Fourier Transform Consider a finite length sequence ixjf 1 that is zero outside the interval 0 k N - 1. Evaluation of the z transform X z at N equally spaced points on the unit circle z exp ia kT exp i 2n NT kT for k 0 1 . N- 1 defines the discrete Fourier transform DFT of a signal x with a sampling period h and N measurements N-1 Xk DFT x kT y xt exp -iwklT X e 11 l 0 Notice that the discrete Fourier transform Xk N-01 is only defined at the discrete frequency points 2p Wk N-Tk for k 0 1 N- 1 In fact the discrete Fourier transform adapts the Fourier transform and the z transform to the practical requirements of finite measurements. Similar properties hold for the discrete Laplace transform with z exp sT where s is the Laplace transform variable. The Transfer Function Consider the following discrete-time linear system with input sequence uk stimulus and output sequence yk response . The dependency of the output of a linear system is characterized by the convolutiontype equation and its z transform yk y hmuk-m Vk m 0 Y z H z U z V z k y hk-mum vk k 1 0 1 2 m -tt where the sequence vk represents some external input of errors and disturbances and with Y z ị y U z u V z v as output and inputs. The weighting function h kT hk k 0 which is zero for negative k and for reasons of causality is sometimes called pulse response of the digital system compare impulse response of continuous-time systems . The pulse response and its z transform the pulse transfer function tt H z ẩ h kT y hkz-k k 0 determine the .
