Convert back Integral with 2 functions: x(t) = [2/(pi*t)^2] int [y(f) sin^4(pi*f*t)] df

[okto]

What will be the equation like if I want to find y(f) from equation below ?

$x(t)=\frac{2}{(\pi t)^2} \int y(f) \operatorname{Sin}^4(\pi f t) d f$

 

[Zermelo]

What will be the equation like if I want to find y(f) from equation below ?

$x(t)=\frac{2}{(\pi t)^2} \int y(f) \operatorname{Sin}^4(\pi f t) d f$

Hello, where exactly are you stuck? We can’t solve your problems for you, can only help ?
Try to solve for y(f) like you would in a regular equation. Tell us at what step are you stuck

 

[Steven G]

How can you get rid of the integral without solving the integral?????

 

[okto]

Sorry, I got stucked in the last line, since x(t) has no f variable, meaning it's constant & the diffrentiation of x(t) will be zero then?

$$\begin{aligned} & \int y(f) \operatorname{Sin}^4(\pi f t) d f=\frac{x(t)(\pi t)^2}{2} \\ & y(f) \operatorname{Sin}^4(\pi f t)=\frac{d}{d f}\left[\frac{x(t)(\pi t)}{2}\right] \\ & y(f)=\frac{1}{\operatorname{Sin}^4(\pi f t)} \frac{d}{d f}\left[\frac{x(t)(\pi t)^2}{2}\right] \end{aligned}$$

 

[Steven G]

Sorry, I got stucked in the last line, since x(t) has no f variable

It could be possible that that t is a function of f (maybe t = f+4), so x(t) might be a function of f (even if you see no f's!)