Fourier Transform and Modulation

In summary, the conversation is about finding the phase spectrum for a given function y(t) and checking for any mistakes in the attempted solution. The speaker is also asking for clarification on how to obtain the phase spectrum for x(t), and suggests that understanding this may lead to finding the phase spectrum for y(t). The response is positive and notes that the attempted solution looks good.
  • #1
jegues
1,097
3

Homework Statement



See figure attached.

Homework Equations





The Attempt at a Solution



See pdf attached for my attempt at the solution.

I'm a little confused as to how to draw the phase spectrum for y(t). Would it simply be a line equation of,

[tex]-\frac{\pi}{6000}f \pm \frac{\pi}{2}[/tex]

for each given triangle?(the +/- is selected accordingly of course)

Aside from that, are there any other mistakes?

Cheers!
 

Attachments

  • A1Q1.JPG
    A1Q1.JPG
    29.5 KB · Views: 385
  • Q-_0172.pdf
    1.1 MB · Views: 260
Physics news on Phys.org
  • #2
Since no one else has responded:

how did you obtain the phase spectrum of x(t)? If I knew that maybe we could figure out how to get that of y(t).

What you wrote looks very good.
 

FAQ: Fourier Transform and Modulation

1. What is the Fourier Transform and why is it important in science?

The Fourier Transform is a mathematical tool that decomposes a signal into its individual frequency components. It is important in science because it allows us to analyze and understand complex signals, such as sound waves or electrical signals, by breaking them down into simpler components.

2. How is the Fourier Transform related to modulation?

The Fourier Transform is closely related to modulation, as it is used to convert a signal from the time domain to the frequency domain. This is essential in modulation, where a carrier signal is modulated with a lower frequency signal to transmit information. The Fourier Transform helps us determine the frequency components of both the original signal and the modulated signal.

3. What is the difference between amplitude and frequency modulation?

In amplitude modulation, the amplitude of the carrier signal is varied to transmit the information, while in frequency modulation, the frequency of the carrier signal is varied. Amplitude modulation is more susceptible to noise, but can transmit a larger range of frequencies, while frequency modulation is less affected by noise but has a limited frequency range.

4. How is the Fourier Transform used in signal processing?

The Fourier Transform is used in signal processing to analyze and manipulate signals. It can be used to filter out specific frequencies, enhance certain frequency components, and extract information from signals. It is also used in compression and data storage techniques, such as MP3 audio files and JPEG images.

5. Can the Fourier Transform be applied to any type of signal?

Yes, the Fourier Transform can be applied to any type of signal, as long as it is a continuous signal. However, it is most commonly used for signals that are periodic or have a finite duration, such as sound waves and electrical signals. For signals that are not continuous, a modified version called the Discrete Fourier Transform is used.

Similar threads

Engineering Fourier transform of a shifted sine wave
Replies
3
Views
713
Question regarding Fourier Transform duality
Replies
2
Views
2K
Find Fourier transform and plot spectrum by hand & MATLAB
Replies
9
Views
4K
Fourier Transform - Solutions Error?
Replies
5
Views
903
Odd and even in complex fourier series
Replies
26
Views
3K
Evaluate Fourier series coefficients and power of a signal
Replies
4
Views
6K
Finding Fourier Series of f(x)=√(x2) -pi/2<x<pi/2
Replies
4
Views
2K
Very Basic Fourier Transform Equation
Replies
3
Views
1K
Fourier Series: Stamping Machine Positioning Function
Replies
4
Views
2K
Fourier transform (got right answer, but not matching graph)
Replies
8
Views
4K

Hot Threads

Recent Insights

Back
Top