The Fourier transform of the triangular pulsex(t) in Fig. P7.3-4 is expressed as1X(a)(e Jjwe Jo-1)Use this information, and the time-shifting andtime-scaling properties, to find the Fourier trans-forms of the signals x;(t)(i= 1,2,3,4,5) shownin Fig. P7.3-4 - 1012-1/3-1.5-0.50.51.5Figure P7.3-4

Question
Asked Nov 13, 2019
46 views

Determine a matrix representation if possible for each mapping in the problem. 

The Fourier transform of the triangular pulse
x(t) in Fig. P7.3-4 is expressed as
1
X(a)
(e Jjwe Jo-1)
Use this information, and the time-shifting and
time-scaling properties, to find the Fourier trans-
forms of the signals x;(t)(i= 1,2,3,4,5) shown
in Fig. P7.3-4
help_outline

Image Transcriptionclose

The Fourier transform of the triangular pulse x(t) in Fig. P7.3-4 is expressed as 1 X(a) (e Jjwe Jo-1) Use this information, and the time-shifting and time-scaling properties, to find the Fourier trans- forms of the signals x;(t)(i= 1,2,3,4,5) shown in Fig. P7.3-4

fullscreen
- 1
0
1
2
-1/3
-1.5
-0.5
0.5
1.5
Figure P7.3-4
help_outline

Image Transcriptionclose

- 1 0 1 2 -1/3 -1.5 -0.5 0.5 1.5 Figure P7.3-4

fullscreen
check_circle

Expert Answer

Step 1

As per our norms, we will be answering only first 3 sub-parts. If you would like to get the answers of other sub-parts, then kindly re-post the same specifying the required sub-parts.

Step 2

We are given the Fourier transform of the triangular pulse x(t) of the figure below is expressed as

1
X(w)
(ejojej1)
-ja
w2
0
1 -
help_outline

Image Transcriptionclose

1 X(w) (ejojej1) -ja w2 0 1 -

fullscreen
Step 3

Here,

...
We will be using the information in step-1, the time scaling and time shifting
properties, to find the Fourier transforms of the signals x(t) (i 1,2,3,4,5) shown in
the figure(in the Q.)
Formulas to be used:
1. Let F{x(t) = X(w)
2. F is linear i.e.; F{a x(t) b y(t)} aF{x(t)} + bF{y(t)}.
3. Shifting Property:
e-jwax (w)
F{x(t - a)
4. Change of scale property:
1
F(x(at))
X
а
аn
(t(-jw)"X(w), where n is a positive integer
5.
F
dtn
6. F(1)2 8(w), where 8(@) is the Dirac delta function
help_outline

Image Transcriptionclose

We will be using the information in step-1, the time scaling and time shifting properties, to find the Fourier transforms of the signals x(t) (i 1,2,3,4,5) shown in the figure(in the Q.) Formulas to be used: 1. Let F{x(t) = X(w) 2. F is linear i.e.; F{a x(t) b y(t)} aF{x(t)} + bF{y(t)}. 3. Shifting Property: e-jwax (w) F{x(t - a) 4. Change of scale property: 1 F(x(at)) X а аn (t(-jw)"X(w), where n is a positive integer 5. F dtn 6. F(1)2 8(w), where 8(@) is the Dirac delta function

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Advanced Math