# 5.1 Lab 5: ctft and its applications  (Page 2/4)

 Page 2 / 4 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 $x\left(t\right)$ is shifted by a constant ${t}_{0}$ , its FT magnitude does not change, but the term $-{\mathrm{\omega t}}_{0}$ 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, ${x}_{1}\left(t\right)$ and ${x}_{2}\left(t\right)$ , linearly with the scaling factors, ${a}_{1}$ and ${a}_{2}$ , producing a new signal, ${a}_{1}{x}_{1}\left(t\right)+{a}_{2}{x}_{2}\left(t\right)$ . [link] displays the FT of this linear combination. The linear combination in the frequency domain produces a new signal, ${a}_{1}{X}_{1}\left(\omega \right)+{a}_{2}{X}_{2}\left(\omega \right)$ . [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.

## 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, ${x}_{1}\left(t\right)\ast {x}_{2}\left(t\right)$ , by convolving the two time signals ${x}_{1}\left(t\right)$ and ${x}_{2}\left(t\right)$ . Multiplication in the frequency domain produces a new signal, ${X}_{1}\left(\omega \right){X}_{2}\left(\omega \right)$ . 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] ).

## 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 ${X}_{1}\left(\omega \right)$ and ${X}_{2}\left(\omega \right)$ to produce a new signal, ${X}_{1}\left(\omega \right)\ast {X}_{2}\left(\omega \right)$ . The inverse FT of the convolved signal is displayed. Multiplication in Time domain produces a new signal, ${x}_{1}\left(t\right){x}_{2}\left(t\right)$ . 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] ).

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
hi
Loga
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers! By OpenStax By Rhodes By Madison Christian By OpenStax By Madison Christian By Tod McGrath By Christine Zeelie By OpenStax By By Madison Christian