DIGITAL COMMUNICATION
Introduction
In this paper, we have keenly discussed Signal processing that is usually done to amplify or filter out embedded information, detect patterns, prepared signal to survive a transition channel, prevent interference with other signals sharing a medium, undo distortion contributed by a distortion channel and also compensate for sensor deficiencies and find information record in a different domain. In this paper, we will use data from my school’s national ID in the study of communication signals. To do so, we also need methods to measure, characterize, model, and simulate transition channels. A message is a function of the time-era. Also, we are going to analyze the bit error rate of the binary phase shifting keying. On the other hand, we will be investigating the working of error probability for binary phase-shift keying modulation in widespread beamforming with phase errors.
Q1 a) i)=
But =1/
Signal frequency =4kHz
؞ =6kHz
X(f)
=3kHz
-3 3 f
- ii) = 2
but we know = 4kHz
؞ =2(4kHz) =8kHz
X(f)
=4kHz
-4 4
iii) = 5
X(f)
=5kHz
-10 10
- b) Assuming my ID no is 33822795, we shall take the last three digits of 795 and use the 8421 BCD code to convert each denary number into its 4-bit binary equivalent.
= 0111 1001 0101 (BCD)
However, encoding can be defined as the procedure that involves the conversion of characters in a sequence, symbols of alphabetical resulting in a specified format that ensures proper transfer of data. Sometimes there is the use of the medium in making the communication for instance use of emails and other communication tools (Muharemovic et al., 2016)
I)NZR-L
FOR NZR codes 0 is for low voltage level while one is for high voltage level. NRZ codes are characterised by the level of voltage, which becomes constant in the time of bit interval. The beginning or end of a bit is not necessarily indicated. It always maintains a similar state o voltage when the initial value of the bit and the present still looks the same.
NRZ-L is a variation of NRZ, in that there might be a drastic change in the polarity due to the changes experienced at the signal that moves from one to zero or vice versa at times and record the same initials. The encoding is quite similar to that of NRZ in that in the first part, the changing input signal in the polarity is a time-invariant system. This technique is primarily used for short distances between
- ii) RZ-AMI: In this encoding technique, each interval has a pulse present. The absence of pulses indicates 0s, while alternating pulses generally represent 1s. Typical types use memory elements to remember the polarity that has been transmitted last.
iii)Bi-ɸ-M (bi-phase-level); in this coding type in between two bits is when a transition is carried out. Input bit 1 gives a resultant transition from high to low amidst the interval while input 0 transits from low to high
iv)Delay modulation
1 1 1 1 0 0 1 0 1 0 1
NRZ-L
RZ- AMI
BI- Phase
Delay modulation
2(a) solution
we know the bandwidth B = 15kHz
the SNR can be numerically calculated by;
= 10 X (SNR)
SNR =
But we are told the is reduced by 65%
؞ = x20Db = 7.0dB
Hence SNR = = 5.011872
Thus, increasing rates of information become surplus leading to the rise of recorded errors in each second hence this is contradicting the expectations since it does apply the same according to the theory of Shannon.
If the in value of C is greater than the information rate R, then it becomes applicable to tackle probabilities with small error through the application of coding methods. According to Carlson (2018), to attain this probability error, we must make sure that the encoder is working on long bars of data. Also, having in mind high computational needs in conjunction with longer delays.
Data rate is calculated using the Shannon channel capacity Theorem given by;
C = B x (1+ SNR)
C = 15 kH (1 + 5.011872)
= 11.685
- b) = n . p
= 256 x 0.25= 6.635 x
=512 x 0.75=
Q3 MSK uses communication data
time
data
MSK time
signal
Binary signal b(t) = {011110010101}
b(t) = for symbol 1
for symbol 0
Therefore, Eb is place as the transmitted signal and its units are given as energy / bit. Then the phase represent the total value of phase at time t=0. This frequency and are sent in response of binary symbols 0 and 1apearaing at the input of the modulator
We can now solve for
Q 4 a) b) bandwidth = – = 3500 – 200 = 3300 Hz
m = =3500/3300 =1.2 =1.0
= 2×3500/1 = 7000 samples/sec
Natural sampling
W(t)
O t
S(t)
t
- b) switching waveform with a duty cycle
S(t) τ
c)Resulting PAM signal (natural sampling d= τ=1/3)
Q 5 a) Differential phase-shift keying (DPSK) can be defined as the process that involves modulating digital transfer of data by changing the phase related to a signal known as constant frequency reference; thus, it is not considered at times.
0 0 1 0 0 1 1 1 1 0 0 1 0 1 0 1
In Binary Phase Shift Keying (BPSK), two signals are transmitted depending on the baseband signal.0 binary baseband, -A , and for binary 1 A is sent.
Each non-return to zero data bit of value 0 is mapped into a -1 and planned into +1 for each NRZ 1. PSK can also be defined where the number of phases is slightly more than 2 in any M-ary PSK, = n bits of the binary bitstream as a signal that is transmitted as A, j=1
The probability of error (Garg and Wilkes, 1996):
- probability error = = () [ () ] =1/n {(sin ) (}
=
=W/Hz = 2T
=
References
Carlson, A.B. (2018). Communication system. Tata McGraw-Hill Education.
Muharemovic, T. and Shen, Z., Texas Instruments Inc, (2016). Methods and apparatus to allocate reference signals in wireless communication systems. U.S. Patent 9,444,650.