1. MULTI-RATE DIGITAL SIGNAL PROCESSING
Unit-V
MULTI-RATE DIGITAL SIGNAL PROCESSING

5. Multi-rate Digital Signal Processing
Basic Sampling Rate Alteration Devices
Up-sampler - Used to increase the sampling rate by an integer factor
Down-sampler - Used to decrease the sampling rate by an integer factor

7. DECIMATION

8. DECIMATION

9. Down-Sampler Time-Domain Characterization
An down-sampler with a down-sampling factor M, where M is a positive integer, develops an output sequence y[n] with a sampling rate that is (1/M)-th of that of the input sequence x[n]
Block-diagram representation M
x[n]
y[n]

10. Down-Sampler
Down-sampling operation is implemented by keeping every M-th sample of x[n] and removing in-between samples to generate y[n]
Input-output relation
y[n] = x[nM]

11. Decimation by a factor D
In downsampling by an integer factor D>1, every D-th samples of the input sequence are kept and others are removed:
取样率按整数因子减小时用抽取方法 D 11

12. Decimation by a factor D
Relationship in time domain
Input sequence
Periodic train of impulses
Output sequence

13. Decimation by a factor D
Relationship in frequency domain
p(n)是周期为D的周期性序列，因此可展成级数。 C 13

14. 当n不为D的整数倍时，xp(n)=0 C 14

15. Decimation by a factor D
Using a digital low-pass filter to prevent aliasing
h(n) D

16. INTERPOLATION

17. INTERPOLATION

18. Up-Sampler Time-Domain Characterization
An up-sampler with an up-sampling factor L, where L is a positive integer, develops an output sequence with a sampling rate that is L times larger than that of the input sequence x[n]
Block-diagram representation L
x[n]

19. Up-Sampler
Up-sampling operation is implemented by inserting equidistant zero-valued samples between two consecutive samples of x[n]
Input-output relation

20. Up-Sampler
In practice, the zero-valued samples inserted by the up-sampler are replaced with appropriate nonzero values using some type of filtering process
Process is called interpolation and will be discussed later

21. Interpolation by a factor I
In up-sampling by an integer factor I >1, I -1 equidistant zeros-valued samples are inserted between each two consecutive samples of the input sequence. Then a digital low-pass filter is applied.
取样率按整数因子扩大时用内插方法 I
h(n) 21

22. Interpolation by a factor I
Relationship in frequency domain
Input sequence

23. Sampling rate conversion by a rational factor I/D
If is a rational number
h1(n)
h2(n) I D
interpolation
decimation
取样率按非整数因子(但为有理数)时可先内插,然后再抽取.
如果先抽取，则会产生信息的丢失，还可能造成频率响应的混叠失真。所以，先插值，再抽取。比较合理
Sampling period 23

24. Sampling Rate Conversion
h (n) I D
Example1是教材P132上的例3－3 24

25. E:\MATLAB6p1\work\digital signal processing\chap3\example9.m25

27. E:\MATLAB6p1\work\digital signal processing\chap3\example10.m27