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I have the following signal for which amplitude and phase spectrums have to be computed:

enter image description here

This exercise also has a solution which begins by deriving the signal twice.

Next, they say the spectral density function for the given signal is:

$$X(j\omega)=\dfrac{X''(j\omega)}{(j\omega)^2} $$

In my attempt to figure out how did they get to that, I found the derivative property of the Fourier transform in the few pages of notes I have(there should be an F above the equivalency sign):

$$x''(t) \Leftrightarrow (j\omega)^2X(j\omega) $$

It looks quite a lot to what they have, but I do not know what do from here in order to reach their equation(formula). Also, can this property be applied to this signal or it only applies to irregularnon-periodic signals?

Please understand that this is an adjacent course that was very poorly presented to us. I did consult the few notes I have and also searched google before posting it. But I found nothing except what I already wrote. Also, there are so many notation used in the courses found on google that make it quite hard for a person who had little to do with this to understand or make connections with other courses found. I firstly very wrongfully misinterpreted the fourier derivation property and gave the first commenter and the two downvoters the impression of an undocumented question, based on the mistakes found in my other posts. (I wouldn't have guessed that the integration formula I am using is wrong if I hadn't posted it here). I wasn't looking for a full solution to the presented question, but a suggestion, which, by looking now at the answer given I don't see how could I had found it by myself.

I have the following signal for which amplitude and phase spectrums have to be computed:

enter image description here

This exercise also has a solution which begins by deriving the signal twice.

Next, they say the spectral density function for the given signal is:

$$X(j\omega)=\dfrac{X''(j\omega)}{(j\omega)^2} $$

In my attempt to figure out how did they get to that, I found the derivative property of the Fourier transform in the few pages of notes I have(there should be an F above the equivalency sign):

$$x''(t) \Leftrightarrow (j\omega)^2X(j\omega) $$

It looks quite a lot to what they have, but I do not know what do from here. Also, can this property be applied to this signal or it only applies to irregular signals?

Please understand that this is an adjacent course that was very poorly presented to us. I did consult the few notes I have and also searched google before posting it. But I found nothing except what I already wrote. Also, there are so many notation used in the courses found on google that make it quite hard for a person who had little to do with this to understand or make connections with other courses found. I firstly very wrongfully misinterpreted the fourier derivation property and gave the first commenter and the two downvoters the impression of an undocumented question, based on the mistakes found in my other posts. (I wouldn't have guessed that the integration formula I am using is wrong if I hadn't posted it here). I wasn't looking for a full solution to the presented question, but a suggestion, which, by looking now at the answer given I don't see how could I had found it by myself.

I have the following signal for which amplitude and phase spectrums have to be computed:

enter image description here

This exercise also has a solution which begins by deriving the signal twice.

Next, they say the spectral density function for the given signal is:

$$X(j\omega)=\dfrac{X''(j\omega)}{(j\omega)^2} $$

In my attempt to figure out how did they get to that, I found the derivative property of the Fourier transform in the few pages of notes I have(there should be an F above the equivalency sign):

$$x''(t) \Leftrightarrow (j\omega)^2X(j\omega) $$

It looks quite a lot to what they have, but I do not know what do from here in order to reach their equation(formula). Also, can this property be applied to this signal or it only applies to non-periodic signals?

    Post Closed as "unclear what you're asking" by Dilip Sarwate, jojek, Deve, Paul R, PAK-9
5 added 907 characters in body
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I have the following signal for which amplitude and phase spectrums have to be computed:

enter image description here

This exercise also has a solution which begins by deriving the signal twice.

Next, they say the spectral density function for the given signal is:

$$X(j\omega)=\dfrac{X''(j\omega)}{(j\omega)^2} $$

I do not understand where this comes from.In my attempt to figure out how did they get to that, I thought of usingfound the derivative property of the Fourier transform in the few pages of notes I have(there should be an F above the equivalency sign):

$$x''(t) \Leftrightarrow (j\omega)^2X(j\omega) $$

ButIt looks quite a lot to what they have, but I do not know what do from here I'm lost. Also, can this property be applied to this signal or it only applies to irregular signals?

Please understand that this is an adjacent course that was very poorly presented to us. I did consult the few notes I have and also searched google before posting it. But I found nothing except what I already wrote. Also, there are so many notation used in the courses found on google that make it quite hard for a person who had little to do with this to understand or make connections with other courses found. I firstly very wrongfully misinterpreted the fourier derivation property and gave the first commenter and the two downvoters the impression of an undocumented question, based on the mistakes found in my other posts. (I wouldn't have guessed that the integration formula I am using is wrong if I hadn't posted it here). I wasn't looking for a full solution to the presented question, but a suggestion, which, by looking now at the answer given I don't see how could I had found it by myself.

I have the following signal for which amplitude and phase spectrums have to be computed:

enter image description here

This exercise also has a solution which begins by deriving the signal twice.

Next, they say the spectral density function for the given signal is:

$$X(j\omega)=\dfrac{X''(j\omega)}{(j\omega)^2} $$

I do not understand where this comes from. I thought of using the derivative property of the Fourier transform :

$$x''(t) \Leftrightarrow (j\omega)^2X(j\omega) $$

But from here I'm lost. Also, can this property be applied to this signal or it only applies to irregular signals?

I have the following signal for which amplitude and phase spectrums have to be computed:

enter image description here

This exercise also has a solution which begins by deriving the signal twice.

Next, they say the spectral density function for the given signal is:

$$X(j\omega)=\dfrac{X''(j\omega)}{(j\omega)^2} $$

In my attempt to figure out how did they get to that, I found the derivative property of the Fourier transform in the few pages of notes I have(there should be an F above the equivalency sign):

$$x''(t) \Leftrightarrow (j\omega)^2X(j\omega) $$

It looks quite a lot to what they have, but I do not know what do from here. Also, can this property be applied to this signal or it only applies to irregular signals?

Please understand that this is an adjacent course that was very poorly presented to us. I did consult the few notes I have and also searched google before posting it. But I found nothing except what I already wrote. Also, there are so many notation used in the courses found on google that make it quite hard for a person who had little to do with this to understand or make connections with other courses found. I firstly very wrongfully misinterpreted the fourier derivation property and gave the first commenter and the two downvoters the impression of an undocumented question, based on the mistakes found in my other posts. (I wouldn't have guessed that the integration formula I am using is wrong if I hadn't posted it here). I wasn't looking for a full solution to the presented question, but a suggestion, which, by looking now at the answer given I don't see how could I had found it by myself.

4 Made it look more decent...
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I have the following signal for which amplitude and phase spectrums have to be computed:

enter image description hereenter image description here

This exercise also has a solution which begins by deriving the signal twice.

Next, they say the spectral density function for the given signal is:

enter image description here$$X(j\omega)=\dfrac{X''(j\omega)}{(j\omega)^2} $$

I do not understand where this comes from. I thought of using the differentionderivative property of the Fourier transform :

enter image description here. $$x''(t) \Leftrightarrow (j\omega)^2X(j\omega) $$

But from here I'm lost. Also, can this property be applied to this signal or it only applies onto irregular signals?

I have the following signal for which amplitude and phase spectrums have to be computed:

enter image description here

This exercise also has a solution which begins by deriving the signal twice.

Next, they say the spectral density function for the given signal is:

enter image description here

I do not understand where this comes from. I thought of using the differention property of the Fourier transform

enter image description here.

But from here I'm lost. Also, can this property be applied to this signal or it only applies on irregular signals?

I have the following signal for which amplitude and phase spectrums have to be computed:

enter image description here

This exercise also has a solution which begins by deriving the signal twice.

Next, they say the spectral density function for the given signal is:

$$X(j\omega)=\dfrac{X''(j\omega)}{(j\omega)^2} $$

I do not understand where this comes from. I thought of using the derivative property of the Fourier transform :

$$x''(t) \Leftrightarrow (j\omega)^2X(j\omega) $$

But from here I'm lost. Also, can this property be applied to this signal or it only applies to irregular signals?

3 deleted 38 characters in body
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