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barcode generator for ssrs Sample Rate Increase by an Integer Factor in Software
3.5.2 Sample Rate Increase by an Integer Factor Scanning Code 128 In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. ANSI/AIM Code 128 Generation In None Using Barcode encoder for Software Control to generate, create Code 128C image in Software applications. Suppose that we would like to increase the sampling rate by an integer factor L. If x a ( t ) is sampled with a sampling frequency f s = I / T,, then Code 128C Recognizer In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Code 128C Generator In Visual C#.NET Using Barcode encoder for .NET framework Control to generate, create Code 128A image in .NET applications. x ( n ) = xa(nTs) Printing Code 128A In .NET Using Barcode creation for ASP.NET Control to generate, create Code 128C image in ASP.NET applications. Encoding Code 128C In .NET Using Barcode maker for .NET framework Control to generate, create Code 128A image in .NET applications. To increase the sampling rate by an integer factor L, it is necessary to extract the samples
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Scanning Code39 In Java Using Barcode reader for Java Control to read, scan read, scan image in Java applications. Generating Code128 In Visual C#.NET Using Barcode generation for Visual Studio .NET Control to generate, create Code 128 Code Set A image in .NET applications. Shown in Fig. 312(a) is an upsampler that produces the sequence Zi(n) = x(n/L) n = O , f L , f 2 L , ... otherwise EAN / UCC  14 Creator In Visual C#.NET Using Barcode printer for VS .NET Control to generate, create GTIN  128 image in .NET applications. Barcode Recognizer In .NET Using Barcode Control SDK for ASP.NET Control to generate, create, read, scan barcode image in ASP.NET applications. In other words, the upsampler expands the time scale by a factor of L by inserting L  1 zeros between each sample of x(n). In the frequency domain, the upsampler is described by Recognizing Data Matrix ECC200 In .NET Framework Using Barcode scanner for VS .NET Control to read, scan read, scan image in .NET applications. Create Bar Code In VS .NET Using Barcode drawer for .NET framework Control to generate, create bar code image in VS .NET applications. Therefore, X(eJW) simply scaled in frequency. After upsampling, it is necessary to remove the frequency is scaled images of X,(jQ), except those that are at integer multiples of 2 x . This is accomplished by filtering Z;(n) Fig. 312. (a) Upsampling by an integer factor L . (b)Interpolation by a factor of L .
with a lowpass filter that has a cutoff frequency of n / L and a gain of L. In the time domain, the lowpass filter interpolates between the samples at integer multiples of L as shown in Fig. 313. The cascade of an upsampler with a lowpass filter shown in Fig. 312(b) is called an interpolator. The interpolation process in the frequency domain is illustrated in Fig. 314. Fig. 313. (a)The output of the upsampler. (b) The interpolation between the samples T,(n)that is performed by the lowpass filter. CHAP. 31
SAMPLING
4n L
Zn L
n L
L = 2n
Fig. 314. Frequency domain illustration of the process of interpolation. (a) The continuoustime signal. (b) The DTFT of the sampled signal x ( n ) = x,(nT,). ( c ) The DTFT of the upsampler output. (d) The ideal lowpass filter to perform the interpolation. (e) The DTFT of the interpolated signal.
3.5.3 Sample Rate Conversion by a Rational Factor
The cascade of a decimator that reduces the sampling rate by a factor of M with an interpolator that increases the sampling rate by vital factor of L results in a system that changes the sampling rate by a rational factor of L / M . This cascade is illustrated in Fig. 315(a). Because the cascade of two lowpass filters with cutoff frequencies n / M and n/L is equivalent to a single lowpass filter with a cutoff frequency the sample rate converter may be simplified as illustrated in Fig. 315(b). SAMPLING
[CHAP. 3
Fig. 315. (a) Cascade of an interpolator and a decimator for changing the sampling rate by a rational factor L I M . (b) A simplified structure that results when the two lowpass ti lters are combined. EXAMPLE 3.5.1 Suppose that a signal x,,(t) has been sampled with a sampling frequency of 8 kHz and that we would like to derive the discretetime signal that would have been obtained if x u ( ! ) had been sampled with a sampling frequency of 10 kHz. Thus, we would like to change the sampling rate by a factor of This may be accomplished by upsampling x ( n ) by a factor of 5, tiltering the upsampled signal with a lowpass filter that has a cutoff frequency w, = n / 5 and a gain of 5, and then downsampling the filtered signal by a Factor of 4. Solved Problems
AID and DIA Conversion
Consider the discretetime sequence
Find two different continuoustime signals that would produce this sequence when sampled at a frequency o f f , = 10 Hz. A continuoustime sinusoid = .%(I) = COS(QOI) cos(2n fat) that is sampled with a sampling frequency off, results in the discretetime sequence
However, note that for any integer k , cos 2rr  n Therefore, any sinusoid with a frequency
= cos 2 n fofkf'n) CHAP. 31
SAMPLING
will produce the same sequence when sampled with a sampling frequency f,. With x(n) = cos(nn/8), we want fo = i!g fs = 625 Hz
Therefore, two signals that produce the given sequence are x,(t) = cos(1250nf) .r2(t) = cos(21250nt) If the Nyquist rate for x a ( t ) is a , , what is the Nyquist rate for each of the following signals that are derived from xa (r ) dxa(t) 7 (b) xa ( 2 t ) (c) ~ , 2 ( t ) (4 x a 0 ) cos(Qot)

