<< Chapter < Page Chapter >> Page >

Front Panel of CTFT and Its Properties: Combination of Input Signals Tab

Varying pulse width

Keep the default values of Time shift (=0) and Time scaling (=1) and vary the Pulse width of the rectangular pulse. First, set the value of the Pulse width to its minimum value (=0.01) and then increase it. Observe that increasing the Pulse width in the time domain decrements the width in the frequency domain (see [link] ). When the Pulse width is set to its maximum value (=1) in the frequency domain, only one value can be seen at the center frequency indicating the signal is of DC type (refer to Properties of CTFT section of Chapter 5).

Magnitude Spectrum for Different Pulse Widths: (a) 0.01, (b) 0.2, (c) 0.5, (d) 1

Time shift

Next, for a fixed pulse width, vary the time shift. Observe that the phase spectrum changes but the magnitude spectrum remains the same. If the signal x ( t ) size 12{x \( t \) } {} is shifted by a constant t 0 size 12{t rSub { size 8{0} } } {} , its FT magnitude does not change, but the term ωt 0 size 12{ - ωt rSub { size 8{0} } } {} gets added to its phase angle. This verifies the time-shifting property of FT as stated in Properties of CTFT section of Chapter 5 (see [link] ).

Magnitude and Phase Spectrum for Different Time Shifts: (a) 0, (b) 0.2, (c) 0.5, (d) 0.7

Time scaling

Observe that increasing the control Time scaling makes the spectrum wider. This indicates that compressing the signal in the time domain leads to expansion in the frequency domain. This verifies the time-scaling property of FT as stated in Properties of CTFT section of Chapter 5 (see [link] ).

Magnitude Spectrum for Different Time Scalings: (a) 1, (b) 2, (c) 3, (d) 4

Linearity

Here, combine two signals to examine the linearity property of FT. Select Linear Combination for the Time domain and Frequency domain combination method. This selection combines two time signals, x 1 ( t ) size 12{x rSub { size 8{1} } \( t \) } {} and x 2 ( t ) size 12{x rSub { size 8{2} } \( t \) } {} , linearly with the scaling factors, a 1 size 12{a rSub { size 8{1} } } {} and a 2 size 12{a rSub { size 8{2} } } {} , producing a new signal, a 1 x 1 ( t ) + a 2 x 2 ( t ) size 12{a rSub { size 8{1} } x rSub { size 8{1} } \( t \) +a rSub { size 8{2} } x rSub { size 8{2} } \( t \) } {} . [link] displays the FT of this linear combination. The linear combination in the frequency domain produces a new signal, a 1 X 1 ( ω ) + a 2 X 2 ( ω ) size 12{a rSub { size 8{1} } X rSub { size 8{1} } \( ω \) +a rSub { size 8{2} } X rSub { size 8{2} } \( ω \) } {} . [link] also displays the inverse FT of this combination. Observe that both combinations produce the same result in the time and frequency domains, as indicated by the linearity property stated in Properties of CTFT section of Chapter 5.

Verifying the Linearity Property of CTFT

Time convolution

In this part, convolve two signals in the time domain to examine the time-convolution property of FT. Select Convolution for Time domain and Multiplication for Frequency domain. This selection produces and displays a new signal, x 1 ( t ) x 2 ( t ) size 12{x rSub { size 8{1} } \( t \) * x rSub { size 8{2} } \( t \) } {} , by convolving the two time signals x 1 ( t ) size 12{x rSub { size 8{1} } \( t \) } {} and x 2 ( t ) size 12{x rSub { size 8{2} } \( t \) } {} . Multiplication in the frequency domain produces a new signal, X 1 ( ω ) X 2 ( ω ) size 12{X rSub { size 8{1} } \( ω \) X rSub { size 8{2} } \( ω \) } {} . The inverse FT of this multiplied signal is also displayed on the right. Note that both combinations produce the same outcome in the time and frequency domains. This verifies the time-convolution property stated in the Properties of CTFT section of Chapter 5 (see [link] ).

Verifying the Time-Convolution Property of CTFT

Frequency convolution

Convolve two signals in the frequency domain to examine the frequency-convolution property of FT. Select Convolution for Frequency domain and Multiplication for Time domain. This selection convolves the two time signals X 1 ( ω ) size 12{X rSub { size 8{1} } \( ω \) } {} and X 2 ( ω ) size 12{X rSub { size 8{2} } \( ω \) } {} to produce a new signal, X 1 ( ω ) X 2 ( ω ) size 12{X rSub { size 8{1} } \( ω \) * X rSub { size 8{2} } \( ω \) } {} . The inverse FT of the convolved signal is displayed. Multiplication in Time domain produces a new signal, x 1 ( t ) x 2 ( t ) size 12{x rSub { size 8{1} } \( t \) x rSub { size 8{2} } \( t \) } {} . The FT of this multiplied signal is also displayed. Note that both combinations produce the same outcome in the time and frequency domains. This verifies the frequency-convolution property stated in the Properties of CTFT section of Chapter 5 (see [link] ).

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, An interactive approach to signals and systems laboratory. OpenStax CNX. Sep 06, 2012 Download for free at http://cnx.org/content/col10667/1.14
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'An interactive approach to signals and systems laboratory' conversation and receive update notifications?

Ask