Processing of Signals - Digital Signal Processing: A Practitioner's Approach - page 15

other domain is as follows:

y ð t Þ! y k ! y k c! ^ y k g

Continous Discrete Quantised Windowed
Discrete Quantised

Discrete

In reality we get only windowed, discrete and quantised signal fb y k cg ¼ f^ y k g at the

processor. Figure 1.10 depicts a 4-bit quantised, discrete and rectangular windowed
signal.

20

Signal

16

15

10

5

0

0 200 400 600 800 1000 1200

Sample

Figure 1.10 Windowed discrete quantised signal

1.5.4 Noise Power
The sample signal y k on passing through a quantiser such as an analogue-to-digital
(A/D) converter results in a signal b y k c , and this is shown in Figure 1.9 along with
the quantisation noise. The quantisation noise k ¼ y k b y k c is a random variable

2 , where n is
the length of the quantiser in bits. The noise power in decibels (dB) is given as
10 log

2 is given as ð 1

12 Þ 2 n (rv) with uniform distribution. The variance = ðÞ

2

¼ 10 log ð 12 Þ½ 20 log ð 2 Þ n. If we assume that the signal y k is equi-
probable along the range of the quantiser, it becomes a uniformly distributed signal.
We can assume without any loss of generality the range as 0 to 1. Then the signal
power is 10 log ð 12 Þ . The signal-to-noise ratio (SNR) is 20n log ð 2 Þ dB or 6 dB per
bit.
Mathematically, the given original signal got corrupted due to the process of
sampling and converting into physical world, real numbers. These are the theore-
tical modifications alone.