2. Signals and system
Course- CSE248
Submitted To
Dr. Wasilul Haque Sadid
Submitted By
Ratul Hasan Shaon (2013-3-60-046)
Joy Das (2013-3-60-048)
Sikdar Rakin (2014-2-60-108)
Minhajul Islam Rifat (2014-3-60-020)
3. Introduction:
Any time varying physical phenomenon that can convey information is called
signal. Signals are detectable quantities or variables by means of which
messages or information can be transmitted . A wide variety of signals are of
practical importance in describing physical phenomena. A number of important
operations are often performed on signals. Most of these operation involve
transformations of the independent variable . It is important that the reader
know how to perform such operation meaning of each one. The three operation
are given below:
The Shifting Operation
The Reflection Operation
The Time Scaling Operatio
4. Shifting Operation
Time shifting is, as the name suggests, the shifting of a signal in time. This is done by
adding or subtracting the amount of the shift to the time variable in the function.
Subtracting a fixed amount from the time variable will shift the signal to the right (delay)
that amount. while adding to the time variable will shift the signal to the left (advance).
1.A time shift delay or advances the signal in time by a time interval +t0 or –t0, without
changing its shape.
y(t) = x(t-t0)
2.If t0 is positive the waveform of y(t)is obtained by shifting x(t)toward the right, relative to
the tie axis. (Delay)
3.If t0 is negative, x(t)is shifted to the left. (Advances)1
5. Reflecting operation
Reflection of signal is a very interesting operation applicable on both continuous and discrete signals.
Here in this case the vertical axis acts as the mirror, and the transformed image obtained is exactly the
mirror image of the parent signal. It can be defined as Y(t) = X( - t) Where, X(t) is the original signal. But
if the reflected signal X( - t) = X(t); then its called an even signal. Where as when X( - t) = − X(t); then its
known as an odd signal.
Let x(t) denote a continuous-time signal and y(t) is the signal obtained by
Replacing time t with –t.
y(t)=x(-t)
y(t)is the signal represents a refracted version x(t) of about t = 0.
Two special cases for continuous and discrete-time signal:
Even signal; x(-t) = x(t) an even signal is same as reflected version.
(ii) Odd signal; x(-t) = -x(t) an odd signal is the negative of its reflected
Version.
6. Scaling Operation
Time scaling compresses or details a signal by multiplying the time variable by some quantity. If that
quantity is greater than one, the signal becomes narrower and the operation is called compression . If
that quantity is less than one , the signal becomes wide and operation is called dilation.
Input Signal
Now we consider a signal
𝑥(𝑡) =
𝑡 + 1 ; −1 ≤ 𝑡 < 0
1 ; 0 ≤ 𝑡 < 2
−𝑡 + 3 ; 2 ≤ 𝑡 < 3
0 ; 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
14. Conclusion:
Signal Operations are simply modifications to the time variable of the signal to generate new signals.
These are pretty similar to the mathematical graphical transformation from our good old Calculus text.
The three kinds of signal Operation we have done Time shifting ,Time scaling and Refection. Time
Shifting is simply shifting the signal in time. When we add a constant to the time, we obtain the advanced
signal, & when we decrease the time, we get the delayed signal.
