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MULTI-RATE DIGITAL SIGNAL PROCESSING

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

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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

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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

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