This document discusses various operations that can be performed on continuous time signals, including shifting, scaling, reflection, and even/odd symmetry. It uses an example signal x(t) to demonstrate how each operation mathematically and graphically transforms the signal. Shifting moves the signal in time, scaling stretches or compresses it, reflection flips it across an axis, and even/odd symmetry relates the signal value at t to its value at -t. The document concludes that understanding these operations helps convey information contained within signals.

1. OPERATIONS ON
CONTINUOUS TIME
SIGNALS
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2. Presented By
1. Md. Jayedul Islam
2015-2-65-017
2. Al-Amin Islam Hridoy
2016-1-60-023
3. Nawan Islam
2016-1-60-027
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3. Overview
 Introduction
 Operations
 Conclusion
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4. Introduction
What is signal?
 Signals are detectable physical quantities or variables by means of
which messages or information can be transmitted. Example include
human voice, television pictures, teletype data, atmospheric
temperature etc.
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5. Types of Operations
 Shifting operation
 Reflection operation
 Scaling operation
 Symmetric
Even Symmetric
Odd Symmetric
 Even And Odd Part
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6. Let’s Consider a signal:
𝒙(𝒕) =
𝒕 + 𝟏 ; 𝟎 ≤ 𝒕 < 𝟏
−𝒕 + 𝟏 ; 𝟏 ≤ 𝒕 < 𝟐
𝟏 ; 𝟐 ≤ 𝒕 < 𝟑
𝟎 ; 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆
The Graphical Expression of the signal:
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7. Shifting Operation
 It represents time-shifted version of x(t).
That is x(t – t0)
 If t0 > 0, the signal is delayed by t0 seconds
 If t0 < 0, the signal represents an advanced replica
of x(t)
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8. Applying shifting Operation
𝒙(𝒕 + 𝟑) =
𝒕 + 𝟒 ; −𝟑 ≤ 𝒕 < −𝟐
−𝒕 + 𝟐 ; −𝟐 ≤ 𝒕 < −𝟏
𝟏 ; −𝟏 ≤ 𝒕 < 𝟎
𝟎 ; 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆
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9. Applying shifting Operation
Similarly:
𝒙(𝒕 − 𝟑) =
𝒕 − 𝟐 ; 𝟑 ≤ 𝒕 < 𝟒
−𝒕 − 𝟒 ; 𝟒 ≤ 𝒕 < 𝟓
𝟏 ; 𝟓 ≤ 𝒕 < 𝟔
𝟎 ; 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆
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10. Scaling Operation
 Scaled version of x(t) is x(ƞ t).
 If |ƞ|>1 the signal is compressed
 if |ƞ|<1 the signal is expanded.
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11. Applying Scaling Operation
Compressed version:
𝒙(𝟑𝒕) =
𝟑𝒕 + 𝟏 ; 𝟎 ≤ 𝒕 <
𝟏
𝟑
−𝟑𝒕 + 𝟏 ;
𝟏
𝟑
≤ 𝒕 <
𝟐
𝟑
𝟏 ;
𝟐
𝟑
≤ 𝒕 < 𝟏
𝟎 ; 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆
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12. Applying Scaling Operation
Expand version:
𝒙(
𝒕
𝟑
) =
𝒕
𝟑
+ 𝟏 ; 𝟎 ≤ 𝒕 < 𝟑
−
𝒕
𝟑
+ 𝟏 ; 𝟑 ≤ 𝒕 < 𝟔
𝟏 ; 𝟔 ≤ 𝒕 < 𝟗
𝟎 ; 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆
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13. Reflection Operation
 Reflection version is x(-t), which is the reversion of
x(t).
 It flips the signal horizontally
 horizontal axis acts as the mirror
 transformed image is exactly the mirror image of the parent signal
 Also -x(t), which is the upside down reversion of
x(t).
 It flips the signal vertically
 vertical axis acts as the mirror
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14. Applying Reflection Operation
𝒙(−𝒕) =
−𝒕 + 𝟏 ; −𝟏 ≤ 𝒕 < 𝟎
𝒕 + 𝟏 ; −𝟐 ≤ 𝒕 < −𝟏
𝟏 ; −𝟑 ≤ 𝒕 < −𝟐
𝟎 ; 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆
−𝒙(𝒕) =
−𝒕 − 𝟏 ; 𝟎 ≤ 𝒕 < 𝟏
𝒕 − 𝟏 ; 𝟏 ≤ 𝒕 < 𝟐
−𝟏 ; 𝟐 ≤ 𝒕 < 𝟑
𝟎 ; 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆
−𝒙(−𝒕) =
𝒕 − 𝟏 ; −𝟏 ≤ 𝒕 < 𝟎
−𝒕 − 𝟏 ; −𝟐 ≤ 𝒕 < −𝟏
−𝟏 ; −𝟑 ≤ 𝒕 < −𝟐
𝟎 ; 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆
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Reflection with
X Axis
Reflection with
Y Axis
Reflection with
both X & Y Axis

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16. Even or Odd symmetric
 If x(t) = x(-t), then the signal is Even symmetric
 If x(t) = -x(-t), then the signal is Odd symmetric
→ Here x(-t) is the reflected version with X Axis
→ Here –x(-t) is the reflected version with both X & Y Axis
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17. Even Symmetric:
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Here, the signal is not even symmetric.
Comparing
x(t) and x(-t)

18. Odd Symmetric:
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Here, the signal is not odd symmetric.
Comparing
x(t) and -x(-t)

19. Even Part and Odd Part
The Even part of a signal is defined by, 𝒙’(𝒕) =
𝒙 𝒕 +𝒙 −𝒕
𝟐
The Odd part of a signal is defined by, 𝒙’(𝒕) =
𝒙 𝒕 −𝒙 −𝒕
𝟐
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20. Conclusion
In our project, we have showed how to
implement signal transformation
mathematically and graphically applying
the operations like shifting, scaling,
reflection, symmetric, even and odd part
in order to convey the signal information.
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