Digital Signal Processing Reference
In-Depth Information
400
3
2
200
1
0
0
0
20
40
60
80
0
20
40
60
80
(a) Sample
(c) Sample
200
1
0
0
−1
−200
0
20
40
60
80
0
20
40
60
80
(b) Sample
(d) Sample
Figure 3.18:
(a) A portion of an analog 10 Hz sine wave (solid), quantized using 2 bits, Offset Method,
input biased one-half LSB, LSB = 113.33 volts (stem plot); (b) Quantization Noise; (c) Analog 10 Hz
sine wave (solid), quantized using 2 bits, Offset Method, input biased one-half LSB, in Multiples of the
LSB (stem plot); (d) Quantization Noise.
Binary0=[00] (0times 113.33 Volts)
Binary1=[01] (1times 113.33 Volts)
Binary2=[10] (2times 113.33 Volts)
Binary3=[11] (3times 113.33 Volts)
Note: For the following two examples, assume proper anti-aliasing filtering is used prior to any
sampling and that no bias is applied to the input signal.
Example 3.19.
An analog signal
x
= cos
(
2
π(
100
)t)
with
t
in seconds is sampled for one second at 200
Hz, with the first sample being taken at time 0, when the signal value is 1
.
0 volts. (a). What is the value
of the analog signal at the first four sampling times? (b). For the same signal, suppose the sampling rate
had been 400 Hz. In that case, what would have been the values of the analog signal at the first four
sampling times? (c). Assume that the sampling is done by an ADC that accepts input voltages between
0 and 1 volt. What signal adjustments need to be made prior to applying the analog signal to the ADC's
input?
(a) The call
