Question

5.2 Windows. Below are shown three different window functions, and the discrete-time Fourier transform of each. Match each window function with its Fourier transform. Window function A $W_1(\omega)$ 30 1 0.8 20 0.6 0.4 10 0.2 0 0 10 20 30 -1 -0.5 0 0.5 1 Window function B $W_2(\omega)$ 30 1 0.8 20 0.6 0.4 10 0.2 0 0 10 20 30 -1 -0.5 0 0.5 1 Window function C $W_3(\omega)$ 30 1 0.8 20 0.6 0.4 10 0.2 0 0 10 20 30 n -1 -0.5 0 $\omega/\pi$ 0.5 1

          5.2 Windows. Below are shown three different window functions, and the
discrete-time Fourier transform of each. Match each window function with
its Fourier transform.
Window function A
$W_1(\omega)$
30
1
0.8
20
0.6
0.4
10
0.2
0
0
10
20
30
-1
-0.5
0
0.5
1
Window function B
$W_2(\omega)$
30
1
0.8
20
0.6
0.4
10
0.2
0
0
10
20
30
-1
-0.5
0
0.5
1
Window function C
$W_3(\omega)$
30
1
0.8
20
0.6
0.4
10
0.2
0
0
10
20
30
n
-1
-0.5
0
$\omega/\pi$
0.5
1

5.2 Windows. Below are shown three different window functions, and the
discrete-time Fourier transform of each. Match each window function with
its Fourier transform.
Window function A
W1(ω)
30
1
0.8
20
0.6
0.4
10
0.2
0
0
10
20
30
-1
-0.5
0
0.5
1
Window function B
W2(ω)
30
1
0.8
20
0.6
0.4
10
0.2
0
0
10
20
30
-1
-0.5
0
0.5
1
Window function C
W3(ω)
30
1
0.8
20
0.6
0.4
10
0.2
0
0
10
20
30
n
-1
-0.5
0
ω/π
0.5
1

Added by Miguel G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert James Kiss

Step 1

For window function A, the Fourier transform is given by: W_A(k) = 0.5 * (1 + cos(2πk/30)), where k is the frequency index. For window function B, the Fourier transform is given by: W_B(k) = 0.5 * (1 + cos(2πk/21)), where k is the frequency index. For window Show more…

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Thanks for your feedback!

5.2 Windows. Below are shown three different window functions, and the discrete-time Fourier transform of each. Match each window function with its Fouriertransform Window function A W,() 30 0.8 20 0.6 0.4 10 0.2 0 10 20 30 -1 0.5 0 0.5 W() Window function B 30 0.8 20 0.6 0.4 10 0.2 0 21 10 20 30 0.5 0 0.5 Window function C W() 30 1 0.8 20 0.6 0.4 10 0.2 0 0 21 10 20 30 0.5 0 /T 0.5 1 n