Operation on signals - Dependent variables

15EE55C – DIGITAL SIGNAL PROCESSING AND
ITS APPLICATIONS
BASIC OPERATIONS ON SIGNALS – DEPENDENT
VARIABLES
Dr. M. Bakrutheen AP(SG)/EEE
Mr. K. Karthik Kumar AP/EEE
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
NATIONAL ENGINEERING COLLEGE, K.R. NAGAR, KOVILPATTI – 628 503
(An Autonomous Institution, Affiliated to Anna University – Chennai)

BASIC OPERATIONS ON SIGNALS
 Basic signal operations categorized into two types depending on
whether they operated on dependent or independent variable(s)
representing the signals.
 Addition, subtraction, multiplication fall under the category of basic
signal operations acting on the dependent variable.
 Time shifting, time scaling and time reversal, which manipulate the
signal characteristics by acting on the independent variable(s) fall under
the category basic operation depends on the independent variable.

ADDITION
 The first and foremost operation which we will consider will be
addition.
 The addition of signals is very similar to traditional mathematics. That
is, if x1(t) and x2(t) are the two continuous time signals, then the addition
of these two signals is expressed as x1(t) + x2(t).
 The resultant signal can be represented as y(t) from which we can write.
y(t) = x1(t) + x2(t)
 Similarly for discrete time signals, x1[n] and x2[n], we can write
y[n] = x1[n] + x2[n]

ADDITION – PRACTICAL SCENARIO
 A practical aspect in which signal addition plays its role is in the case of
transmission of a signal through a communication channel.
 This is because, here, we see that the undesired noise gets added up with
the desired signal.
 Another example which can be quoted is of dithering where the noise is
added to the signal intentionally.
 This is because, when done so, one can effectively reduce undesired
artifacts created as an aftermath of quantization errors.

SUBTRACTION
 Similar to the case of addition, subtraction deals with the subtraction of
two or more signals in order to obtain a new signal. Mathematically it
can be represented as
 y(t) = x1(t) - x2(t) … for continuous time signals, x1(t) and x2(t)
 y[n] = x1[n] - x2[n] … for discrete time signals, x1[n] and x2[n]

SUBTRACTION – PRACTICAL SCENARIO
 One practical aspect which connects with that of subtracting the signals is that of a
Moving Target Indicator (MTI) used in radar communications.
 Here the most recent signal is subtracted from its previous version so as to obtain the
signal which indicates just the moving targets by eliminating the stationary ones.
 This is very much necessary so as to facilitate PPI (Plan Position Indicator) display
of radar systems.
 Yet another example which extensively makes use of signal subtraction is the design
of closed-loop control systems.
 Such systems employ negative feedback in order to accurately control an output
variable, and this negative-feedback structure relies upon subtraction (the feedback
signal is subtracted from the setpoint signal).

MULTIPLICATION
 The next basic signal operation performed over the dependent variable
is multiplication.
 In this case, as you might have already guessed, two or more signals will
be multiplied so as to obtain the new signal.
 Mathematically, this can be given as:
 y(t) = x1(t) × x2(t) … for continuous-time signals x1(t) and x2(t)
 y[n] = x1[n] × x2[n] … for discrete-time signals x1[n] and x2[n]

MULTIPLICATION – PRACTICAL SCENARIO
 Multiplication of signals is exploited in the field of analog
communication when performing amplitude modulation (AM).
 In AM, the message signal is multiplied with the carrier signal so as to
obtain a modulated signal.
 Another example in which signal multiplication plays an important role
is frequency shifting in RF (radio frequency) systems.
 Frequency shifting is a fundamental aspect of RF communication, and it
is accomplished using a mixer, which is similar to an analog multiplier

Operation on signals - Dependent variables

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Operation on signals - Dependent variables