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barcode generator for ssrs Find the overall frequency response of this system. in Software
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Ha(jQ) = 40001~ I 1 5 I sooh 1 n
otherwise
SAMPLING
[CHAP. 3
If we assume a sampling frequency f = 20 kHz, the frequency response of the discretetime system should be , 0 . 2 ~ 101 5 0 . 8 ~ 5 otherwise
where T, = 1/20000. Diagrammed in the figure below is a hybrid digitalanalog network.
) The discretetime system H ( e J W is a lowpass filter ~ ( e " )= I 4 5 oo
else
and the analog system Hhpf( ) is a highpass filter with a frequency response as shown below. f
t "'"' The input xa(r) is bandlimited to 4 kHz, and the sampling frequencies of the ideal C P and DIC converters are 10 kHz. Find the value for A and q that will result in perfect reconstruction of x a ( t ) , Because x a ( t ) is bandlimited to 4 kHz, the upper branch of this hybrid system acts as an ideal analog lowpass filter with a frequency response Because the analog network is a highpass filter with a cutoff frequency of 4 kHz, and
& ( t ) will be equal to x a ( t ) provided that A = 1 and
A digital sequence x ( n ) is to be transmitted across a linear timeinvariant bandlimited channel as illustrated in the figure below.
CHAP. 31
SAMPLING
Transmitter
Receiver
The transmitter is a D/C converter, and the receiver simply samples the received waveform y,(r): Assume that the channel may be modeled as an ideal lowpass filter with a cutoff frequency of 4 kHz: (a) Assuming an ideal C P and D/C, and perfect synchronization between the transmitter and receiver, what values of T, (if any) will guarantee that y(n) = x(n) (b) Suppose that the D/C is nonideal. Specifically, suppose that x(n) is first converted to an impulse train and then a zeroorder hold is used to perform the "interpolation" between the sample values. In other words, the impulse response of the interpolating filter is a pulse of duration T,: M t ) 1 = 0 051iT' otherwise
Because the received sequence y(n) will no longer be equal to x(n), in order to improve the performance of the receiver, the received samples are processed with a digital filter as shown below. Find the frequency response of the filter that should be used to filter y(n). (a) The output of the D/C converter is a bandlimited signal x a ( t ) with a Fourier transform that is equal to zero for If 1 > f s / 2 . Because x a ( t ) is passed through a bandlimited channel that rejects all frequencies greater than 4 kHz, in order for there to be no distortion at the receiver, it is necessary that Thus, the C/D and D/C converters must operate at a rate less than 8 kHz.
(b) In order to get the maximum amount of data through the channel per unit of time, we will let T, be the minimum sampling period, T = s
When the reconstruction filter in the D/C converter is a zeroorder hold, the frequency response of the discretetime system that relates the input sequence x ( n ) to the reconstructed sequence y ( n ) is SAMPLING
[CHAP. 3
where
otherwise
Therefore, and the discretetime filter for processing y(n) to remove the distortion introduced by the zeroorder hold should approximate the response Consider the following system for processing a continuoustime signal with a discretetime system: The frequency response of the discretetime filter is
Iff, = 2 kHz and x,(t) = sin(lOOO~t), the output y , ( t ) . find
Sampling n,(r) = sin(10007rr) with a sampling frequency f, = 2000 produces the discretetime sequence x(n) = x,(nT,) = sin(10007rnTs) = sin This sequence is then filtered with the discretetime filter

