TAILIEUCHUNG - Lecture Digital signal processing: Lecture 4 - Zheng-Hua Tan

Lecture Digital signal processing - Lecture 4 present sampling and reconstruction. The main contents of this chapter include all of the following: Periodic sampling, frequency domain representation, reconstruction, changing the sampling rate using discretetime processing. | Digital Signal Processing Fall 2006 Lecture 4 Sampling and reconstruction Zheng-Hua Tan Department of Electronic Systems Aalborg University Denmark zt@ 1 Digital Signal Processing IV Zheng-Hua Tan 2006 Course at a glance MM3 MM9 MM10 MM7 MM8 ___________ 1 Mt 2 Digital Signal Processing IV Zheng-Hua Tan 2006 AALBORG UNIVERSITY 1 Part I Periodic sampling Periodic sampling Frequency domain representation Reconstruction Changing the sampling rate using discretetime processing 3 Digital Signal Processing IV Zheng-Hua Tan 2006 AALBORG UNIVERSITY Periodic sampling From continuous-time Xc ft to discrete-time x n x n xc nT -TO n x Sampling period T Sampling frequency fs 1 T Qs 2n T C D _____ jr n xcinTị Block diagram 1 representation of an ideal continuous-to-discrete-time C D converter. 4 Digital Signal Processing IV Zheng-Hua Tan 2006 AALBORG UNIVERSITY 2 Two stages In practice I inversion from impulse rain lo discrete-time c The output sequence for the two different sampling rates Mathematically Impulse train modulator Conversion of the impulse train to a sequence co s t Y t - nT n -w x t xc t s t co Xc t ZS t - nT n -w Ỹ xc nT S t - nT n -w x n xc nT - x n x w z c- J 1 xc t J xc r 8 t -T d T 5 Digital Signal Processing r Figure Sampling with a periodic impulse tram followed by conversion to a discrete-time sequence a Overall system b Xj 0 for two sampling rates Periodic sampling Tow-stage representation Strictly a mathematical representation that is convenient for gaining insight into sampling in both the time and frequency domains. Physical implementation is different. xs t a continuous-time signal an impulse train zero except at nT x n a discrete-time sequence time normalization no explicit information about sampling rate Many-to-many in general not invertible 6 Digital Signal Processing IV Zheng-Hua Tan 2006 AALBORG UNIVERSITY

• Kĩ thuật Viễn thông
• Digital signal processing
• Digital signal
• Lecture Digital signal processing
• Discrete time signals
• Periodic sampling
• „Frequency domain representation
• Xử lý tín hiệu số
• Signal processing
• DSP applications
• Digital Signal Processing Research Program
• Avanced Telecommunications and Signal Processing Program
• Signal Processing Program
• Combined Source
• Block processing methods
• Sample processing methods
• VLSI Digital signal processing systems
• DSP systems
• FIR Digital Filters
• Parallel processing
• Digital signal processing: Principles Algorithms and Applications
• Fast fourier transform algorithms
• Discrete time systems
• Design of digital filters
• Multirate digital signal processing
• Lecture Signal processing
• Xử lý tín hiệu
• Mixed signals processing
• Applications of digital signal processing
• Block diagram representation
• Signal flow graph description
• Quantization process
• Digital to analog converters
• Transfer functions
• Digital filter realization
• Discrete time signal
• Ultrasound signal processing
• Hardware software partitioning
• Digital signal processing systems
• Ultrasound devices
• Sampling theorem
• Analog reconstruction
• The z transform
• Properties of the z transform
• Discrete time fourier transform
• Discrete fourier transform
• Types of signals
• System impulse response
• Fourier transforms
• Inverse z transform
• Properties of z transform
• System analysis
• Frequency response
• Filter design
• IIR filter design
• FIR filter design
• Linear phase FIR filter
• Fourier transform
• Fast fourier transform
• Decimation in time FFT algorithms
• Loop bound
• DSP programs