barcodecontrol.com

Digital Signal Processing in Microsoft Office Encoding data matrix barcodes in Microsoft Office Digital Signal Processing

Digital Signal Processing using microsoft office toassign 2d data matrix barcode in asp.net web,windows application C# quantizer (see 7), DataMatrix for None and a simpler analog filter, and then have to downsample the signal. Other examples include mixing signals of different sampling rates and downsampling to reduce computation (many signal processing algorithms have a computational complexity proportional to the sampling rate or its square). A simple solution is to convert the digital signal x[n] into an analog signal x(t ) with a D/A system running at Fs and then convert it back to digital with an A/D system running at Fs .

An interesting problem is whether this could be done in the digital domain directly, and the techniques to do so belong to the general class of multi-rate processing.. Decimation If we want to reduce Microsoft Office Data Matrix barcode the sampling rate by a factor of M, i.e., T = MT , we take every M samples.

In order to avoid aliasing, we need to lowpass filter the signal to bandlimit it to frequencies 1/ T . This is shown in Figure 5.30, where the arrow pointing down indicates the decimation.

. x[n]. rT [n]. y[n]. Figure 5.30 Block diagram of the decimation process. Since the output is not desired at all instants n, but only every M samples, the computation can be reduced by a factor of M over the case where lowpass filtering is done first and decimation later. To do this we express the analog signal xl (t ) at the output of the lowpass filter as xl (t ) =. k = . x[k ]r (t kT ). (5.168). and then look at the Microsoft Office ECC200 value t = nT . The decimated signal y[n] is then given by y[n] = xl (nT ) =. k = . Mn k x[k ]r ( nT kT ) = x[k ]sinc M T k = (5.169). which can be express ed as y[n] = where h[n] = sinc(n / M ) (5.171). k = . x[k ]h [ Mn k ]. (5.170). Multirate Signal Processing In practice, the ide Microsoft Office barcode data matrix al lowpass filter h[n] is approximated by an FIR filter with a cutoff frequency of 1/(2M).. Interpolation If we want to increa Microsoft Office barcode data matrix se the sampling rate by a factor of N, so that T = T / N , we do not have any aliasing and no further filtering is necessary. In fact we already know one out of every N output samples. y[ Nn] = x[n]. (5.172). and we just need to compute the ( N 1) samples in-between. Since we know that x[n] is a bandlimited signal, we can use the sampling theorem in Eq. (5.

162) to reconstruct the analog signal as xl (t ) =. k = . x[k ]r (t kT ). (5.173). and thus the interpolated signal y[n] as y[n] = x(nT ) = Now let s define x[ Nk ] k = Nk x [k ] = otherwise 0 k = . x[k ]rT ( nT kT ) =. k = . x[k ]sinc n kN N (5.174). (5.175). which, inserted into barcode data matrix for None Eq. (5.174), gives y[n] =.

k = . x [k ]sinc ( (n Data Matrix 2d barcode for None k ) / N ). (5.176). This can be seen in ECC200 for None Figure 5.31, where the block with the arrow pointing up implements Eq. (5.

175). x[n] N rT[n] y[n]. Figure 5.31 Block diagram of the interpolation process. Equation (5.174) can Data Matrix barcode for None be expressed as y[n] =. k = . x[k ]h [ n kN ]. (5.177). Digital Signal Processing where we have define d h[n] = sinc(n / N ) (5.178). Again, in practice, Microsoft Office Data Matrix the ideal low-pass filter h[n] is approximated by an FIR filter with a cutoff frequency of 1/(2N).. Resampling To resample the sign Microsoft Office datamatrix 2d barcode al so that T = TM / N , or Fs = Fs ( N / M ) , we can first upsample the signal by N and then downsample it by M. However, there is a more efficient way. Proceeding similarly to decimation and interpolation, one can show the output is given by y[n] = where.

n h[n] = sinc max( N , M ) . k = . x[k ]h[nM kN ]. (5.179). (5.180). for the ideal case. datamatrix 2d barcode for None In practice, h[n] is an FIR filter with a cutoff frequency of 1/ ( 2 max( N , M ) ) . We can see that Eq.

(5.179) is a superset of Eqs. (5.

170) and (5.177)..

Copyright © barcodecontrol.com . All rights reserved.