数字信号处理教学课件：2-2 Discrete-Time Signals and Systems

1、2.2.3 Convolution Sumyn = xn hn*is called the convolution sum of the sequences xn and hn and represented compactly as2 Discrete-Time Signals and SystemsExample Develop the sequence yn generated by the convolution of the sequences xn and hn : xn = hn = n + n-1 + n-2*2 Discrete-Time Signals and System

2、sxkh-kxkh1-kxkh2-kxkxkxn = hn = n + n-1 + n-2Xkh-k=1Xkh-kkkXkh1-kXkh1-k=2kXkh2-kkXkh3-kkXkh4-kh4-kh3-kXkh2-k=3Xkh3-k=2Xkh4-k=1xkhk112 Discrete-Time Signals and SystemsIn general, if the lengths of the two sequences being convolved are M and N, then the sequence generated by the convolution sum is of

3、 length M+N-1Read example 2.5 and 2.6 by yourself.yn=n+2n-1+3n-2+2n-3+n-4 2 Discrete-Time Signals and Systemsyn n11023422312.2.4 Sampling rate alterationUp-samplingDown-sampling2 Discrete-Time Signals and Systems2.2.4 Sampling rate alterationUp-samplingDown-sampling2 Discrete-Time Signals and System

4、sUp-sampling (L=3)2 Discrete-Time Signals and SystemsDown-sampling (M=3)2 Discrete-Time Signals and Systems5 Finite-Length DiscreteTransforms 2.3 Operations on Finite-length SequencesConsider length-N sequences xn defined for 0nN-1Sample values of such sequences are equal to zero for values of n 0 (right circular shift), the above equation implies5 Finite-Length DiscreteTransforms the circular shift, is defined using a modulo operation:2.3.2 Circular Shift of a SequenceIllustration of the concept of a circular shift5 Finite-Length DiscreteTransforms Read