2
votes
0answers
41 views

Fourier Transform of inverse powers of the absolute value

I don't think this question has been asked previously, so here goes. I need to evaluate the following integrals - $$ ...
1
vote
1answer
49 views

What is the Fourier transform of an M like function

Given the function $$ f(x)= \begin{cases} \vert x \vert& \text{, for }\;\vert x\vert\le M \\ 0 & \text{, otherwise} \end{cases} $$ for some constant $M$. What would be the form for the ...
0
votes
0answers
20 views

Derivative of squared Fourier transform

I haven't found any relative to this, so I would like to get some help. I have a function $h(x) = |\mathcal{F} [P(x) e^{ic+iZ(x)a}]|^2 $ and I would like to find the derivative with respect to the ...
1
vote
1answer
369 views

how to find absolute value for complex fraction

I have a Fourier transfer equation $H(jw) = \frac{jwL}{(jw)^2LC+jw\frac{L}{R}+1}$, and I need to find frequency to make $|H(jw)|$ is max. I know I should take the derivative of $|H(jw)|$ then find ...
5
votes
2answers
556 views

Why is the absolute value needed with the scaling property of fourier tranforms?

I understand how to prove the scaling property of Fourier Transforms, except the use of the absolute value: If I transform $f(at)$ then I get $F\{f(at)\}(w) = \int f(at) e^{-jwt} dt$ where I can ...
-1
votes
1answer
128 views

The maximum absolute value of DFT of window vector

Let x=[1, ⋯ ,1, 0, ⋯ ,0] be a window vector of length N, which consists of B consecutive 1s and the remaining N-B consecutive 0s. I took the N-point DFT on x and got X=[X_0, X_1, ⋯, X_(N-1)] which is ...