Questions about Representing Signals in Frequency Domain

[abdo375]

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...

 

[Maxwell]

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.

 

[berkeman]

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.

 

[Maxwell]

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.

 

[abdo375]

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

 

[Gokul43201]

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.