Circle the correct words in each of the following statements. Given that x(t) is a real function with the Fourier transform X(f): a. The real part of X(f) is an even / odd function. b. The imaginary part of X(f) is an even / odd function.

(a) even function

(b) odd function

Step-by-step explanation:

From the given information;

Any function x(t) can be said to be the sum of even and odd functions.

i.e.

where;

x(t) is a real function.

For a  real and even function, the Fourier transform is also real and even.

Also, the Fourier Transform of a real and odd function is imaginary and odd.

The behavior of X(f) largely depends on the behavior of x(t).

If x(t) is real and even, then x(f) is real and even valued function

Thus, the real part of X(f) is an even function.

If x(t) is real and odd, then x(f) is imaginary and odd valued function

Thus, the imaginary part of X(f) is an odd function.

the fist one is not equalvalent but i think th second one isand the third isnt definetly or the last one is i think. hope this !

step-by-step explanation:

so far i think you have the right thing going for you just remember soh cah toh

step-by-step explanation:

sine over hypotenuse

cosine   equals adjacent

tangent over hypotenuse