multirate digital signal processingmultirate digital signal processing prasanta kumar ghosh oct23,...
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![Page 1: Multirate digital signal processingMultirate digital signal processing Prasanta Kumar Ghosh Oct23, 2018 . Reconstruct and resample If has bandwidth less than , then if Note the infinite](https://reader030.vdocument.in/reader030/viewer/2022040105/5e8196af5247bb7b3451297d/html5/thumbnails/1.jpg)
Multirate digital signal
processing
Prasanta Kumar Ghosh
Oct23, 2018
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Reconstruct and resample
If has bandwidth less than , then if
Note the infinite summation in the reconstruction (not practical)
Suppose for sampling rate conversion, we need to sample at
with a desired sampling rate of
thus obtained are accurate only if
If , components above should be filtered out before
resampling. if
If , then it is a convolution summation (LTI system)
![Page 3: Multirate digital signal processingMultirate digital signal processing Prasanta Kumar Ghosh Oct23, 2018 . Reconstruct and resample If has bandwidth less than , then if Note the infinite](https://reader030.vdocument.in/reader030/viewer/2022040105/5e8196af5247bb7b3451297d/html5/thumbnails/3.jpg)
For
Let
Integer Fraction
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Time-varying system for sampling rate conversion
**Inefficient when interpolating function is complicated
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It simplifies when where D and I are relatively prime integers
Value of mD
modulo I
Thus, can take only I distinct values
Hence, only I distinct impulse responses are possible and thus, is
periodic
A linear and periodically time-varying
discrete-time system (great simplification!)
Downsampling/Decimation
Only one impulse response for all m
Upsampling/Interpolation
Impulse response is shifted
at an increment of
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Downsampling/Decimation
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Upsampling/Interpolation
Fractional shifting results in
![Page 8: Multirate digital signal processingMultirate digital signal processing Prasanta Kumar Ghosh Oct23, 2018 . Reconstruct and resample If has bandwidth less than , then if Note the infinite](https://reader030.vdocument.in/reader030/viewer/2022040105/5e8196af5247bb7b3451297d/html5/thumbnails/8.jpg)
Other way is to create a new sequence by inserting zero samples
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Decimation by a factor D
Is decimation LTI operation?
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Decimation by a factor D
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Decimation by a factor D
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Decimation by a factor D
Evaluate the Z-transform on unit circle with frequency variable
Thus, gets stretched to by down-sampling
If is correctly designed, then aliasing is eliminated and
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Decimation by a factor D
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Interpolation by a factor I
DTFT:
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Interpolation by a factor I
As the frequency component of
are unique in the range
Images beyond that in
should be rejected by low pass
filtering
C = ?
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Interpolation by a factor I
is the desired normalization factor
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Sampling rate conversion by a rational factor I/D
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Sampling rate conversion by a rational factor I/D
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Sampling rate conversion by a rational factor I/D
Frequency response of the combined filter