Questions about Representing Signals in Frequency Domain

In summary: No worries - I just wanted to make sure I wasn't completely misunderstanding the concept!In summary, the discussion focused on the representation of signals in the frequency domain. It was mentioned that there are separate representations for periodic and aperiodic signals using the Fourier series and Fourier Transform, respectively. The frequency domain plot shows the magnitude of different frequency components, with the x-axis representing frequency and the y-axis representing amplitude. The concept of amplitude in the frequency domain was briefly discussed, and a recommendation for a Signal & Systems book was made.
  • #1
abdo375
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I have a couple of questions regarding the representation of a signal in the frequency domain I wish someone could help me with..

1-why is it when we represent a non-periodic signal in the frequency domain it is continuous while the frequency domain of a periodic signal is discrete ?

2-what does it mean when we transfer a signal into the frequency domain
(say a rect wave what does it mean that the representation of it in the frequency domain is sinc, I know that it represents the different frequencies in the signal but why does it decay ?).

3-When plotting the signal in the freq. domain and the x-axis is the freq. in Hz what does the y-axis represent ?

thanks...
 
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  • #2
abdo375 said:
I have a couple of questions regarding the representation of a signal in the frequency domain I wish someone could help me with..
1-why is it when we represent a non-periodic signal in the frequency domain it is continuous while the frequency domain of a periodic signal is discrete ?
2-what does it mean when we transfer a signal into the frequency domain
(say a rect wave what does it mean that the representation of it in the frequency domain is sinc, I know that it represents the different frequencies in the signal but why does it decay ?).
3-When plotting the signal in the freq. domain and the x-axis is the freq. in Hz what does the y-axis represent ?
thanks...
1) That's not true. There is a separate discrete and continuous time representation for periodic signals and aperiodic signals. You can use the Fourier series for periodic signals and the Fourier Transform for aperiodic signals.

2) You answered your own question in your third question. The X axis represents frequency - the values closer to the origin are higher frequencies, as you go further out along the X axis you get lower frequencies. The frequency domain shows the magnitude of different frequency components. It does not always decay.

3) The Y axis represents amplitude.
 
  • #3
Maxwell said:
2) You answered your own question in your third question. The X axis represents frequency - the values closer to the origin are higher frequencies, as you go further out along the X axis you get lower frequencies. The frequency domain shows the magnitude of different frequency components. It does not always decay.
I may be misunderstanding Maxwell's reply on this point, but the frequency domain plots that I'm used to working with have the origin = DC (0 Hz), and the higher positive frequencies out at higher x-axis (actually f-axis) values. That's the way a SPICE plot or a spectrum analyzer displays the frequency domain data.
 
  • #4
berkeman said:
I may be misunderstanding Maxwell's reply on this point, but the frequency domain plots that I'm used to working with have the origin = DC (0 Hz), and the higher positive frequencies out at higher x-axis (actually f-axis) values. That's the way a SPICE plot or a spectrum analyzer displays the frequency domain data.
Nope, I wrote it wrong. You're right - DC at 0 and the frequency increases as you go higher up. Doesn't make sense the other way around and I'm not sure why I wrote it like that. :confused:
 
  • #5
Maxwell said:
1) That's not true. There is a separate discrete and continuous time representation for periodic signals and aperiodic signals. You can use the Fourier series for periodic signals and the Fourier Transform for aperiodic signals.
2) You answered your own question in your third question. The X axis represents frequency - the values closer to the origin are higher frequencies, as you go further out along the X axis you get lower frequencies. The frequency domain shows the magnitude of different frequency components. It does not always decay.
3) The Y axis represents amplitude.


1-I think i miss-explained my point, what i meant was if we get a periodic and non-periodic rect signal in the time domain and get the Fourier transform of it then graph it, we will get a continues sinc for the non-periodic function while we'll get a discrete sinc for the periodic one, what i was asking about was the physical interpolation of this.

3-The amplitude of what? does the frequency have amplitude?

Does anyone know a good Signal & systems book? my textbook only focuses on the math of the subject rather than the concept.

thanks
 
  • #6
abdo375 said:
3-The amplitude of what?
Recall what the original (time-domain) waveform represents : displacement from the equilibrium position vs. time.

The frequency domain (or spectral) plot represents the standard deviation (amplitude) or variance (power) from the equilibrium position vs. frequency.
 

1. What is the frequency domain?

The frequency domain is a mathematical representation of a signal or data set that shows the frequency components of the signal. It is used to analyze signals in terms of their frequency content rather than their time-domain representation.

2. How is a signal represented in the frequency domain?

A signal is represented in the frequency domain using a mathematical tool called the Fourier transform. This transform converts a signal from its time-domain representation into its frequency-domain representation, showing the different frequency components that make up the signal.

3. Why is it useful to represent signals in the frequency domain?

Representing signals in the frequency domain allows for easier analysis and manipulation of the signal. It also helps in identifying specific frequency components that may be important for a particular application or in filtering out unwanted noise from the signal.

4. What is the relationship between the time domain and the frequency domain?

The time domain and the frequency domain are two different ways of representing the same signal. The time domain shows how the signal changes over time, while the frequency domain shows the different frequencies present in the signal and their respective amplitudes. The two domains are related through the Fourier transform.

5. Can any signal be represented in the frequency domain?

Yes, any signal can be represented in the frequency domain as long as it is finite and has a well-defined Fourier transform. This includes signals from various fields such as audio, images, and scientific data.

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