Time Domain: Elementary Signal Operations Flashcards
What does amplitude shifting do?
Amplitude shifting maps an input signal x to an output signal y as follows:
y(t) = x(t) + b, where b is a real number
When y(t) is plotted it shows a displacement in the vertical axis by value b.
What does amlitude scaling do?
Amplitude scaling maps an input signal x to an output signal y as follows:
y(t) = ax(t), where a is a real number
The transformation causes compression in the vertical axis if the multiplier is fraction, e.g 1/a
The transformation causes expansion in the vertical axis if a is greater than 1
The transformation causes reflection is a is negative
What is time shifting?
Time shifting is:
y(t) = x(t-b), where b is a real number
When plotted y(t) is shifted to the left/right along the time axis.
If b is positive, the graph is shifted to the right (delay in time). E.g. y(t) = x(t-1), b=1
If b is negative, the graph is shifted to the left (advance in time), e.g. y(t)=x(t+1), b = -1
The graph is shifted by the magnitude of b
What is time scaling?
y(t) = x(at), where a is a non-zero real number.
When plotted, y(t) is compressed/expanded along the time axis
- If |a| > 1 the signal is compressed along the time axis by a factor |a|
- If |a| < 0 the signal is expanded along the time axis by a factor 1/|a|
What is time reversal?
y(t) = x(-t)
when plotted, y(t) is a reflection of x(t) about the vertical axis at t = 0
How are two signals added together?
Their values ar every instant are added to produce the sum signal at that instant.
How do we sum two DT signals?
The sum can be performed only at the integer sample locations for which the signal is defined.
When is the sum of two signals periodic?
The sum of two periodic signals will onlye be periodic is T1/T2 is a rational number.
How do we find the fundamental period of two signals in which T1/T2 is a rational number?
The fundamental period of the resulting signal will be equal to the least common multiple of T1 and T2
e.g. LCM(2, 3) = 6
LCM(6, 10) = 30
