chap5-sampling rate conversion.pptx
TRANSCRIPT
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Chapter 5• Sampling Rate Conversion
• Content
Introduction Decimation by a factor D Interpolation by a factor I Sampling rate conversion by a rational
factor I/D
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In many practical applications of DSP, one is faced with the problem of changing the sampling rate of a signal.
The process of converting a signal from a given rate to a different rate is called sampling rate conversion.
Systems that employ multiple sampling rates in the processing of digital signals are called multirate digital signal processing systems.
• Introduction
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There are two general methods to accomplish the sampling rate conversion of a digital signal. To pass the digital signal through a D/A converter, filter
it if necessary, and then to resample the resulting analog signal at the desired rate;
To perform the sampling rate conversion entirely in the digital domain.
The process of reducing the sampling rate by an integer factor D (downsampling by D) is called decimation.
The process of increasing the sampling rate by an integer factor I (upsampling by I) is called interpolation.
• Introduction
• return
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• In downsampling by an integer factor D>1, every D-th samples of the input sequence are kept and others are removed:
• D
•Decimation by a factor D
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Relationship in time domain
Input sequence
• Periodic train of impulses
• Output sequence
• demo
•Decimation by a factor D
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Relationship in frequency domain
•Decimation by a factor D
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• demo
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• h(n) • D
Using a digital low-pass filter to prevent aliasing
•Decimation by a factor D
• return
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• 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.
• I • h(n)
• demo
• Interpolation by a factor I
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Relationship in frequency domain
Input sequence
• demo
• Interpolation by a factor I
• return
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If is a rational number
• h1(n)
• h2(n)
• I
• D
• interpolation • decimation
• Sampling rate conversion by a rational factor I/D
• Sampling period
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• h (n)
• I
• D
• example1
• Sampling Rate Conversion
• example2
• return
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-15 -10 -5 0 5 10 150
2
n
-15 -10 -5 0 5 10 150
0.5
1
n
-15 -10 -5 0 5 10 150
2
n
-15 -10 -5 0 5 10 150
2
n
• return
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• return
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0 4 8 12 16 20 24 28 32 36 40 44 480
2
4
n
0 4 8 12 16 20 24 28 32 36 40 44 480
2
4
n
0 4 8 12 16 20 24 28 32 36 40 44 480
2
4
n
• return
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• return
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• return
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P137, No.26 in textbook
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• return