Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI...
Transcript of Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI...
![Page 1: Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI operation? Decimation by a factor D. Decimation by a factor D. Decimation by a factor](https://reader034.fdocuments.net/reader034/viewer/2022042212/5eb5f44f5f14d0526f5216f0/html5/thumbnails/1.jpg)
Decimation by a factor D
Is decimation LTI operation?
![Page 2: Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI operation? Decimation by a factor D. Decimation by a factor D. Decimation by a factor](https://reader034.fdocuments.net/reader034/viewer/2022042212/5eb5f44f5f14d0526f5216f0/html5/thumbnails/2.jpg)
Decimation by a factor D
![Page 3: Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI operation? Decimation by a factor D. Decimation by a factor D. Decimation by a factor](https://reader034.fdocuments.net/reader034/viewer/2022042212/5eb5f44f5f14d0526f5216f0/html5/thumbnails/3.jpg)
Decimation by a factor D
![Page 4: Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI operation? Decimation by a factor D. Decimation by a factor D. Decimation by a factor](https://reader034.fdocuments.net/reader034/viewer/2022042212/5eb5f44f5f14d0526f5216f0/html5/thumbnails/4.jpg)
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
![Page 5: Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI operation? Decimation by a factor D. Decimation by a factor D. Decimation by a factor](https://reader034.fdocuments.net/reader034/viewer/2022042212/5eb5f44f5f14d0526f5216f0/html5/thumbnails/5.jpg)
Decimation by a factor D
![Page 6: Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI operation? Decimation by a factor D. Decimation by a factor D. Decimation by a factor](https://reader034.fdocuments.net/reader034/viewer/2022042212/5eb5f44f5f14d0526f5216f0/html5/thumbnails/6.jpg)
Interpolation by a factor I
DTFT:
![Page 7: Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI operation? Decimation by a factor D. Decimation by a factor D. Decimation by a factor](https://reader034.fdocuments.net/reader034/viewer/2022042212/5eb5f44f5f14d0526f5216f0/html5/thumbnails/7.jpg)
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 = ?
![Page 8: Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI operation? Decimation by a factor D. Decimation by a factor D. Decimation by a factor](https://reader034.fdocuments.net/reader034/viewer/2022042212/5eb5f44f5f14d0526f5216f0/html5/thumbnails/8.jpg)
Interpolation by a factor I
is the desired normalization factor
![Page 9: Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI operation? Decimation by a factor D. Decimation by a factor D. Decimation by a factor](https://reader034.fdocuments.net/reader034/viewer/2022042212/5eb5f44f5f14d0526f5216f0/html5/thumbnails/9.jpg)
Sampling rate conversion by a rational factor I/D
![Page 10: Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI operation? Decimation by a factor D. Decimation by a factor D. Decimation by a factor](https://reader034.fdocuments.net/reader034/viewer/2022042212/5eb5f44f5f14d0526f5216f0/html5/thumbnails/10.jpg)
Sampling rate conversion by a rational factor I/D
![Page 11: Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI operation? Decimation by a factor D. Decimation by a factor D. Decimation by a factor](https://reader034.fdocuments.net/reader034/viewer/2022042212/5eb5f44f5f14d0526f5216f0/html5/thumbnails/11.jpg)
Sampling rate conversion by a rational factor I/D
Frequency response of the combined filter
![Page 12: Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI operation? Decimation by a factor D. Decimation by a factor D. Decimation by a factor](https://reader034.fdocuments.net/reader034/viewer/2022042212/5eb5f44f5f14d0526f5216f0/html5/thumbnails/12.jpg)
Sampling rate conversion by a rational factor I/D
Change of variable
We know
Time-varying filter
![Page 13: Decimation by a factor D - Indian Institute of ScienceDecimation by a factor D Is decimation LTI operation? Decimation by a factor D. Decimation by a factor D. Decimation by a factor](https://reader034.fdocuments.net/reader034/viewer/2022042212/5eb5f44f5f14d0526f5216f0/html5/thumbnails/13.jpg)
Sampling rate conversion by a rational factor I/D