Taub’s Principles of Communication Systems (Herbert Taub, Donald L. Schilling, Goutam Saha) (Z-Library).pdf
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Principles of Communication Systems
Taub’s Principles of Communication Systems (Herbert Taub, Donald L. Schilling, Goutam Saha) (Z-Library).pdf
•0 likes•59 views
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Principles of Communication Systems
![noise condition any information rate is supported. For
channel with white noise or flat noise spectrum of strength
N0 the above equation can be modified to C = B log2 [1 +
S/(N0B)] bits/sec
where S is the signal strength. Note that, B in the
denominator inside log and B in the numerator outside log
give an interesting characteristics curve which we’ll discuss
later. But you are free to explore its consequence yourself if
you love number game. Before we move to next topic let’s
do some auick math.
SELF-TEST QUESTION
1. Is modulation done at transmitter end while
demodulation at receiver end?
2. Can regenerative repeater be used in analog
communication?
3. What frequencies are used in microwave
communication?
4. Is channel capacity related to SNR?
1.2 SIGNAL AND ITS PROPERTIES
In previous section we had a bird’s-eye-view of electronic
communication systems. Let us start looking into conceptual
details with basic description of a signal. We have seen in
Sec. 1.1.1 that input message has to be converted to an
electrical signal for electronic transmission. Generally
speaking, a signal is a single-valued function of one or more](https://image.slidesharecdn.com/taubsprinciplesofcommunicationsystemsherberttaubdonaldl-230528184247-f48eb49a/75/taubs-principles-of-communication-systems-herbert-taub-donald-l-schilling-goutam-saha-zlibrarypdf-45-2048.jpg?cb=1685301575)
![convolved output and v(t), h(t) are the signals being
convolved. The symbol ‘⊗’ is often used as a convolution
operator.
Note that, v(t) ⊗ h(t) = h(t) ⊗ v(t). Compare Eq. (1.10) with
Eq. (1.9) and you can see how input and output of a system
is related. You can visualize h(t) as the output generated by
the system when d(t) is input. The system that obeys this is
known as linear-time-invariant system. Linear system are
those for which principle of superposition is valid, i.e. if
inputs vx(t) and v2(t) generate output wx(t) and w2(t)
respectively then input [av(t) + bv2(t)] will generate output
[aw(t) + bw2(t)]. For a time-invariant system, if input is
shifted in time by Tunit then output too is shifted by same
amount. Please refer to Example 1.8 and its graphical
illustration (Fig. 1.11) to understand how convolution
operation works.
1.2.4 Correlation and Autocorrelation
The correlation between waveforms is a measure of the
similarity or relatedness between the waveforms. Suppose
that we have waveforms vx(t) and v2(t), not necessarily
periodic nor confined to a finite time interval. Then the
correlation between them, or more precisely the average
cross correlation between vx(t) and v2(t), is R12(t) defined as
If v1(t) and v2(t) are periodic with the same fundamental
period T0, then the average cross correlation is](https://image.slidesharecdn.com/taubsprinciplesofcommunicationsystemsherberttaubdonaldl-230528184247-f48eb49a/75/taubs-principles-of-communication-systems-herbert-taub-donald-l-schilling-goutam-saha-zlibrarypdf-62-2048.jpg?cb=1685301575)
![In the limit, as T0 ( ', Af ( 0. We then may replace Af by df
and replace n Af by a continuous variable f. Equation (1.107)
then becomes
Thus, we confirm our earlier interpretation of V(f) as an
amplitude spectral density.
Example 1.17
(a) Find the Fourier transform of S(t), an impulse of unit
strength.
(b) Given a network whose transfer function is H(f). An
impulse S(t) is applied at the input. Show that the response
vo(t) = h(t) at the output is the inverse transform of H(f), that
is, show that h(t) = F-1[H(f)].](https://image.slidesharecdn.com/taubsprinciplesofcommunicationsystemsherberttaubdonaldl-230528184247-f48eb49a/75/taubs-principles-of-communication-systems-herbert-taub-donald-l-schilling-goutam-saha-zlibrarypdf-104-2048.jpg?cb=1685301575)
![Solution
(a) The impulse 8(t) = 0 except at t = 0 and, further, has
the property that
Thus the spectral components of 8 (t) extend with uniform
amplitude and phase over the entire frequency domain.
(b) Using the result given in Eq. (1.90), we find that the
transform of the output vo(t) = h(t) is Vo(f) given by
since the transform of 8 (t), F [8 (t)] = 1. Hence the inverse
transform of Vo(f), which is the function h(t), is also the
inverse transform of H(f). Specifically, for an impulse input,
the output is We may use the result given in Eq. (1.113) to
arrive at a useful representation of d (t) itself. If H( f ) = 1,
then the response h(t) to an inpulse d (t) is the impulse itself,
Hence, setting H( f )= 1 in Eq. (1.113), we find
1.4.1 useful Fourier transform properties
Here, we present some of the useful properties of Fourier
transform. We’ll discuss convolution, correlation and
Parseval’s theorem related properties in the following
subsections.
We use notation v (t) ( V(f) as Fourier transform pairs to
describe the properties. The logic behind writing these
relations in most of the cases follows a similar procedure
adopted in deriving properties of Fourier series and hence
not repeated. The conclusions are also similar, e.g.
compressing the signal in time domain expands it in
frequency domain.](https://image.slidesharecdn.com/taubsprinciplesofcommunicationsystemsherberttaubdonaldl-230528184247-f48eb49a/75/taubs-principles-of-communication-systems-herbert-taub-donald-l-schilling-goutam-saha-zlibrarypdf-105-2048.jpg?cb=1685301575)
