信号与系统7-1 Chapter 7 Sampling.pptVIP

Chapter 7 Sampling The effect of sampling The sampling theorem Practical use of sampling Sampling Very important step for digital signal processing ! Widely used in signal recording, storage, compression, transmission, …… Sampling Use finite points to express a continuous curve ! Try to record a curve in discrete data ! Sampling Can we keep the information in sampling process? Can we recover the continuous curve from these sampling points ? Try to find answer in frequency domain ! Impulse-train sampling Sampling period Sampling frequency Impulse-train sampling effect In time domain, signal is discrete ; In frequency domain, signal is replicated; Impulse-train sampling effect Original spectrum and its mirrors Anti-mirror filter The sampling theorem must be a band-limited signal Sampling frequency should satisfy the Nyquist condition The Nyquist rate can be recovered by an LPF The frequency limit for signal sampling Frequency period area Over sampling The recover filter can be made easily ! Sampling data may be too much ! Critical sampling The recover filter must be ideal LPF ! Sampling data is less ! Under sampling The spectrum is overlapped with mirror ! The signal can not be recovered from sampling data ! Practical use of sampling Set an anti-aliasing filter before sampling system An analog LPF to make the signal band-limited ! Sampling with a zero-order hold Practical use of sampling Sampling with a zero-order hold If sampling condition is satisfied , the sampled signal can be recovered ! (See P.521) Practical use of sampling Sampling for narrow band signals The sampling condition: The high frequency narrow band signal can be changed to low frequency signal by sampling ! Practical use of sampling Sampling for narrow band signals