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 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)..

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