Finding Fourier transform using some properties
$begingroup$
I am trying to solve a question of Fourier transform in which I am given two signals:$$X(jω)=δ(ω)+δ(ω-π)+δ(ω-5)\h(t)=u(t)-u(t-2)=begin{cases}1&0<x<2\0&text{otherwise}end{cases}$$
I am asked to find the whether the convolution of $x(t)$ and $h(t)$ is periodic or not. Now using properties I have founded the signal $x(t)$ but I am stuck at the Fourier transform of $h(t)$.
Now I need to find its Fourier Transform using the properties and the one I got is:
$$\x(t)=begin{cases}1&|t|<T _1\0&text{otherwise}end{cases} rightarrow frac{2sinomega T_1}{omega} $$
Using this property we know that the time period of the wave is 2, hence:
$$H(jomega) = frac{2sinomega2}{omega},$$
but the one mentioned in book is
$$H(jomega) = e^{-jomega} frac{2sinomega}{omega}.$$
Can somebody explain that why my expression is wrong?
fourier-transform
asked Jan 6 at 9:59
Ahmad QayyumAhmad Qayyum
677
$endgroup$
add a comment |
$begingroup$
I am trying to solve a question of Fourier transform in which I am given two signals:$$X(jω)=δ(ω)+δ(ω-π)+δ(ω-5)\h(t)=u(t)-u(t-2)=begin{cases}1&0<x<2\0&text{otherwise}end{cases}$$
I am asked to find the whether the convolution of $x(t)$ and $h(t)$ is periodic or not. Now using properties I have founded the signal $x(t)$ but I am stuck at the Fourier transform of $h(t)$.
Now I need to find its Fourier Transform using the properties and the one I got is:
$$\x(t)=begin{cases}1&|t|<T _1\0&text{otherwise}end{cases} rightarrow frac{2sinomega T_1}{omega} $$
Using this property we know that the time period of the wave is 2, hence:
$$H(jomega) = frac{2sinomega2}{omega},$$
but the one mentioned in book is
$$H(jomega) = e^{-jomega} frac{2sinomega}{omega}.$$
Can somebody explain that why my expression is wrong?
fourier-transform
asked Jan 6 at 9:59
Ahmad QayyumAhmad Qayyum
677
$endgroup$
$begingroup$
One could explain why the book's expression is right....
$endgroup$
– Lord Shark the Unknown
Jan 6 at 10:00
$begingroup$
@LordSharktheUnknown can you please point out my mistake?
$endgroup$
– Ahmad Qayyum
Jan 6 at 10:03
3
$begingroup$
I cannot point out your mistake, and nor can anyone else apart from yourself, since you have not provided details of your calculation.
$endgroup$
– Lord Shark the Unknown
Jan 6 at 10:04
$begingroup$
@LordSharktheUnknown can you point out my mistake now?
$endgroup$
– Ahmad Qayyum
Jan 6 at 11:56
1
$begingroup$
Your formula works for $x(T)$ which is $1$ on the interval $(-T_1,T_1)$ and zero outside. But your $h$ is not of this form.
$endgroup$
– Lord Shark the Unknown
Jan 6 at 14:07
add a comment |
$begingroup$
I am trying to solve a question of Fourier transform in which I am given two signals:$$X(jω)=δ(ω)+δ(ω-π)+δ(ω-5)\h(t)=u(t)-u(t-2)=begin{cases}1&0<x<2\0&text{otherwise}end{cases}$$
I am asked to find the whether the convolution of $x(t)$ and $h(t)$ is periodic or not. Now using properties I have founded the signal $x(t)$ but I am stuck at the Fourier transform of $h(t)$.
Now I need to find its Fourier Transform using the properties and the one I got is:
$$\x(t)=begin{cases}1&|t|<T _1\0&text{otherwise}end{cases} rightarrow frac{2sinomega T_1}{omega} $$
Using this property we know that the time period of the wave is 2, hence:
$$H(jomega) = frac{2sinomega2}{omega},$$
but the one mentioned in book is
$$H(jomega) = e^{-jomega} frac{2sinomega}{omega}.$$
Can somebody explain that why my expression is wrong?
fourier-transform
asked Jan 6 at 9:59
Ahmad QayyumAhmad Qayyum
677
$endgroup$
I am trying to solve a question of Fourier transform in which I am given two signals:$$X(jω)=δ(ω)+δ(ω-π)+δ(ω-5)\h(t)=u(t)-u(t-2)=begin{cases}1&0<x<2\0&text{otherwise}end{cases}$$
I am asked to find the whether the convolution of $x(t)$ and $h(t)$ is periodic or not. Now using properties I have founded the signal $x(t)$ but I am stuck at the Fourier transform of $h(t)$.
Now I need to find its Fourier Transform using the properties and the one I got is:
$$\x(t)=begin{cases}1&|t|<T _1\0&text{otherwise}end{cases} rightarrow frac{2sinomega T_1}{omega} $$
Using this property we know that the time period of the wave is 2, hence:
$$H(jomega) = frac{2sinomega2}{omega},$$
but the one mentioned in book is
$$H(jomega) = e^{-jomega} frac{2sinomega}{omega}.$$
Can somebody explain that why my expression is wrong?
fourier-transform
fourier-transform
asked Jan 6 at 9:59
Ahmad QayyumAhmad Qayyum
677
asked Jan 6 at 9:59
Ahmad QayyumAhmad Qayyum
677
edited Jan 6 at 11:55
Ahmad Qayyum
asked Jan 6 at 9:59
Ahmad QayyumAhmad Qayyum
677
asked Jan 6 at 9:59
Ahmad QayyumAhmad Qayyum
677
asked Jan 6 at 9:59
Ahmad QayyumAhmad Qayyum
677
677
$begingroup$
One could explain why the book's expression is right....
$endgroup$
– Lord Shark the Unknown
Jan 6 at 10:00
$begingroup$
@LordSharktheUnknown can you please point out my mistake?
$endgroup$
– Ahmad Qayyum
Jan 6 at 10:03
3
$begingroup$
I cannot point out your mistake, and nor can anyone else apart from yourself, since you have not provided details of your calculation.
$endgroup$
– Lord Shark the Unknown
Jan 6 at 10:04
$begingroup$
@LordSharktheUnknown can you point out my mistake now?
$endgroup$
– Ahmad Qayyum
Jan 6 at 11:56
1
$begingroup$
Your formula works for $x(T)$ which is $1$ on the interval $(-T_1,T_1)$ and zero outside. But your $h$ is not of this form.
$endgroup$
– Lord Shark the Unknown
Jan 6 at 14:07
add a comment |
$begingroup$
One could explain why the book's expression is right....
$endgroup$
– Lord Shark the Unknown
Jan 6 at 10:00
$begingroup$
@LordSharktheUnknown can you please point out my mistake?
$endgroup$
– Ahmad Qayyum
Jan 6 at 10:03
3
$begingroup$
I cannot point out your mistake, and nor can anyone else apart from yourself, since you have not provided details of your calculation.
$endgroup$
– Lord Shark the Unknown
Jan 6 at 10:04
$begingroup$
@LordSharktheUnknown can you point out my mistake now?
$endgroup$
– Ahmad Qayyum
Jan 6 at 11:56
1
$begingroup$
Your formula works for $x(T)$ which is $1$ on the interval $(-T_1,T_1)$ and zero outside. But your $h$ is not of this form.
$endgroup$
– Lord Shark the Unknown
Jan 6 at 14:07
$begingroup$
One could explain why the book's expression is right....
$endgroup$
– Lord Shark the Unknown
Jan 6 at 10:00
$begingroup$
One could explain why the book's expression is right....
$endgroup$
– Lord Shark the Unknown
Jan 6 at 10:00
$begingroup$
@LordSharktheUnknown can you please point out my mistake?
$endgroup$
– Ahmad Qayyum
Jan 6 at 10:03
$begingroup$
@LordSharktheUnknown can you please point out my mistake?
$endgroup$
– Ahmad Qayyum
Jan 6 at 10:03
3
3
$begingroup$
I cannot point out your mistake, and nor can anyone else apart from yourself, since you have not provided details of your calculation.
$endgroup$
– Lord Shark the Unknown
Jan 6 at 10:04
$begingroup$
I cannot point out your mistake, and nor can anyone else apart from yourself, since you have not provided details of your calculation.
$endgroup$
– Lord Shark the Unknown
Jan 6 at 10:04
$begingroup$
@LordSharktheUnknown can you point out my mistake now?
$endgroup$
– Ahmad Qayyum
Jan 6 at 11:56
$begingroup$
@LordSharktheUnknown can you point out my mistake now?
$endgroup$
– Ahmad Qayyum
Jan 6 at 11:56
1
1
$begingroup$
Your formula works for $x(T)$ which is $1$ on the interval $(-T_1,T_1)$ and zero outside. But your $h$ is not of this form.
$endgroup$
– Lord Shark the Unknown
Jan 6 at 14:07
$begingroup$
Your formula works for $x(T)$ which is $1$ on the interval $(-T_1,T_1)$ and zero outside. But your $h$ is not of this form.
$endgroup$
– Lord Shark the Unknown
Jan 6 at 14:07
add a comment |
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$begingroup$
One could explain why the book's expression is right....
$endgroup$
– Lord Shark the Unknown
Jan 6 at 10:00
$begingroup$
@LordSharktheUnknown can you please point out my mistake?
$endgroup$
– Ahmad Qayyum
Jan 6 at 10:03
3
$begingroup$
I cannot point out your mistake, and nor can anyone else apart from yourself, since you have not provided details of your calculation.
$endgroup$
– Lord Shark the Unknown
Jan 6 at 10:04
$begingroup$
@LordSharktheUnknown can you point out my mistake now?
$endgroup$
– Ahmad Qayyum
Jan 6 at 11:56
1
$begingroup$
Your formula works for $x(T)$ which is $1$ on the interval $(-T_1,T_1)$ and zero outside. But your $h$ is not of this form.
$endgroup$
– Lord Shark the Unknown
Jan 6 at 14:07