Information AboutUpsampling |
| CATEGORIES ABOUT UPSAMPLING | |
| digital signal processing | |
| signal processing | |
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The upsampling factor (commonly denoted by ''L'') is usually an integer or a rational fraction greater than unity. This factor multiplies the sampling rate or, equivalently, divides the sampling period. For example, if Compact Disc audio is upsampled by a factor of 5/4 then the resulting sampling rate goes from 44,100 Hz to 55,125 Hz, which increases the Bit Rate from 1,411,200 bit/s to 1,764,000 bit/s. The range of valid frequencies (i.e., those that satisfy the Nyquist-Shannon Sampling Theorem ) has gone from 22,050 Hz to 27,562.5 (an increase in 5,512.5 Hz). SAMPLING THEOREM SATISFACTION The upsampled signal satisfies the Nyquist-Shannon sampling theorem if the original signal does. Unlike in Downsampling which uses a Low-pass Filter as an Anti-aliasing Filter , upsampling uses an interpolation filter, which also is a low-pass filter. UPSAMPLING PROCESS Consider a Discrete Signal on a radian frequency Digital Frequency range. Upsampling by integer factor Let ''L'' denote the upsampling factor. #Add ''L-1'' zeros between each sample in . Or, equivalently define #Filter with a low-pass filter which, theoretically, should be the Sinc Filter with frequency cut off at The second step calls for the use of a perfect low-pass filter, which is not implementable. When choosing a realizable low-pass filter this will have to be considered and it will have Aliasing effects. Upsampling by rational fraction Let ''L/M'' denote the upsampling factor. #Upsample by a factor of ''L'' # Downsample by a factor of ''M'' Note that upsampling requires an interpolation filter after increasing the data rate and that downsampling requires a filter before decimation. These two filters can be combined into a single filter. Since both interpolation and anti-aliasing filters are low-pass filters, the filter with the smallest bandwidth is more restrictive and, thus, can be used in place of both filters. Since the rational fraction ''L/M'' is greater than unity then and the single low-pass filter should have cutoff at . SEE ALSO |
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