Signal processing is usually done to amplify or filter out embedded information
ABSTRACT
Signal processing is usually done to amplify or filter out embedded information, detect patterns, prepareth signal to survive a transition channel, prevent interference with other signals sharing a medium, undo distortion contributed by a distortion channel, 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 review of complex numbers and complex arithmetic in Section 2.1. We
provide some examples of useful words in Section 2.2. We then discuss LTI systems and convolution in Section 2.3. This is followed by the Fourier series (Section 2.4) and Fourier transform (Section
2.5). These sections (Sections 2.1 through Section 2.5) correspond to a review of material that
is part of the assumed background of this textbook’s core content. However, even readers
familiar with the material are encouraged to skim through it quickly to gain familiarity
with the notation. Thus gets us to the point where we can classify signals and systems based
on the frequency band they occupy. Specifically, we discuss baseband and passband signals and
systems in Sections 2.7 and 2.8. Messages are typically baseband, while signals sent over channels
(especially radio channels) are usually passband. We discuss methods for going from baseband
to passband and back. We specifically emphasize that a real-valued passband signal is
an equivalent (in a mathematically convenient and physically meaningful sense) to a complex-valued
baseband signal, called the complex baseband representation, or complex envelope, of the passband signal. We note that the information carried by a passband signal resides in its complicated
pocket, so that modulation (or the process of encoding messages in waveforms that can be
sent over physical channels) consists of mapping information into a complex envelope, and then
converting this complex envelope into a passband signal. We discuss the physical significance
of the rectangular form of the sophisticated container, which corresponds to the in-phase (I) and
quadrature (Q) components of the passband signal, and that of the polar form of the complex
envelope, which corresponds to the jacket and phase of the passband signal. We conclude by
discussing the role of complex baseband in transceiver implementations, and by illustrating its
use for wireless channel modeling.
Q1 a)
i)
- b) Conversion of decimal numbers to binary equivalents can be done by dividing the decimal no by two and repeatedly dividing the quotient by 2recording down the remainders until the quotient is zero. The remainders form the binary equivalent
Encoding is the process of converting a given sequence of characters, alphabets or symbols into a specific format, for the secured transmission of data
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 voltage level, which remains constant during a bit interval. The beginning or end of a bit is not necessarily indicated and always maintains the same voltage state if the value of the previous bit and the value of the present bit is the same
NRZ-L is a variation of NRZ, and change in the polarity of the signal changes from 1 to 0 or from 0 to 1. The encoding is the same as for NRZ, however, the first bit of the input signal changes in polarity
ar time-invariant system: A linear time-invariant (LTI) system is (unsurprisingly) defined
to be a system which is both direct and time-invariant. What is surprising, however, is how
powerful the LTI property is in dictating what the input-output relationship.
. Accurately, if we know the impulse response of an LTI system (i.e., the output signal
when the input signal is the delta function), then we can compute the system response for any
input signal. Before deriving and stating this result, we illustrate the LTI property using an
example; see Figure 2.8. Suppose that the response of an LTI system to the rectangular pulse
(t) is given by the trapezoidal waveform h1(t). We can now compute the system
response to any linear combination of time shifts of the pulse p(t), as illustrated by the example
in the figure. More generally, using the LTI property, we infer that the response to an input
signal of the form x(t) = Pis y(t) = P
Can we extend the other idea to compute the system response to arbitrary input signals?
The answer is yes: if we know the system response to thinner and thinner pulses, then we
can approximate arbitrary signals better and better using linear combinations of shifts of these
pulses. Consider p∆(t) = 1
(t), where ∆ > 0 is getting smaller and smaller. No
courier series represent periodic signals in terms of sinusoids or complex exponentials. A signal
u(t) is periodic with period T if u(t + T) = u(t) for all t. Note that, if you are periodic with period
T, then it is also periodic with period nT, where n is any positive integer. The smallest time
interval for which u(t) is periodic is termed the first period. Let us denote this by T0, and
define the corresponding fundamental frequency f0 = 1/T0 (measured in Hertz if T0 is measured
in seconds). It is easy to show that if u(t) is periodic with period T, T must be an integer
multiple of T0. In the following, we often refer to the first period as a “period.”
Using mathematical knowledge of our current scope, it can be shown that any periodic signal
with period T0 (subject to mild technical conditions) can be expressed as a linear combination
of complex exponential
- ii) RZ-AMI
iii)Bi-ɸ-M (bi-phase-level)
iv)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
Data rate is calculated using the Shannon channel capacity Theorem given by;
C = B x (1+ SNR)
C = 15 kHz (1 + 5.011872)
b)s
Q3 Binary signal b(t) ={011110010101}
Q 5 a)Differential phase-shift keying (DPSK) is a modulated signal that is shifted relative to the previous signal element in which no reference signal is considered.
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 mapped into +1 for each NRZ 1. PSK can also be defined where the number of phases is rather 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
References
Arnon, S., Barry, J., Karagiannidis, G., Schober, R. and Uysal, M. eds., 2012. Advanced optical wireless communication systems. Cambridge university press.
Carlson, A.B., 2010. Communication system. Tata McGraw-Hill Education.