Information AboutDownsampling |
| CATEGORIES ABOUT DOWNSAMPLING | |
| digital signal processing | |
| signal processing | |
|
The downsampling factor (commonly denoted by ''M'') is usually an integer or a rational fraction greater than unity. This factor multiplies the sampling time or, equivalently, divides the sampling rate. For example, if Compact Disc audio is downsampled by a factor of 5/4 then the resulting sampling rate goes from 44,100 Hz to 35,280 Hz, which reduces the Bit Rate from 1,411,200 bit/s to 1,128,960 bit/s. SAMPLING THEOREM SATISFACTION By downsampling, the sampling rate is also reduced so the Shannon-Nyquist Sampling Theorem satisfaction must be maintained. If the sampling theorem is not satisfied then the resulting signal will have Aliasing and to ensure that the sampling theorem is satisfied a Low-pass Filter is used as an Anti-aliasing Filter to reduce the bandwidth of the signal ''before'' the signal is downsampled. Note that the anti-aliasing filter must be a low-pass filter in downsampling. This unlike Sampling from a Continuous Signal , which can be either a low-pass filter or a Band-pass Filter . Remark: A bandpass signal, i.e. a band-limited signal whose minimum frequency is different from zero, can be downsampled avoiding superposition of the spectrum if we satisfy certain conditions (see e.g. {Link without Title} ). DOWNSAMPLING PROCESS Consider a Discrete Signal on a radian frequency Digital Frequency range. Downsampling by integer factor Let ''M'' denote the downsampling factor. #Filter the signal to ensure satisfaction of the sampling theorem. This filter should, theoretically, be the Sinc Filter with frequency cut off at . Let the filtered signal be denoted . #Reduce the data by picking out every sample: . Data rate reduction occurs in this step. The first 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 aliasing effects it will have. Realizable low-pass filters have a "skirt" where the response diminishes from near unity to near zero. So in practice, the cutoff frequency is placed far enough below the theoretical cutoff that the filter's skirt is contained below the theoretical cutoff. Downsampling by rational fraction Let ''M/L'' denote the downsampling 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. Also note that these two steps are generally not reversible. Downsampling results in a loss of data and, if performed first, could result in data loss if there is any data filtered out by the downsampler's low-pass 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 ''M/L'' is greater than unity then and the single low-pass filter should have cutoff at . SEE ALSO |
|
|