Discrete Fourier Transform and Signal Spectrum - Digital Signal Processing: Fundamentals and Applications - page 134

4.16. Consider the following data sequence of length six:
xð 0 Þ¼ 0 ; xð 1 Þ¼ 1 ; xð 2 Þ¼ 0 ; xð 3 Þ¼ 1 ; xð 4 Þ¼ 0 ; xð 5 Þ¼ 1
Compute the windowed sequence x w ðnÞ using the
a. triangular window function;
b. Hamming window function;
c. Hanning window function.
4.17. Compute the following window functions for a size of 10:
a. Hamming window function;
b. Hanning window function.
4.18. Consider the following data sequence of length six:
xð 0 Þ¼ 0 ; xð 1 Þ¼ 0 : 2 ; xð 2 Þ¼ 0 ; xð 3 Þ¼ 0 : 2 ; xð 4 Þ¼ 0 ; xð 5 Þ¼ 0 : 2
Compute the windowed sequence x w ðnÞ using the
a. triangular window function;
b. Hamming window function;
c. Hanning window function.
4.19. Given the sequence in Figure 4.47 where f s ¼ 100 Hz and T ¼ 0 : 01 sec : , compute the
amplitude spectrum, phase spectrum, and power spectrum using the
a. triangular window;
b. Hamming window;
c. Hanning window.

x ()

4 4

4

3

2

1

2

1

1 5

n

0 2 3

4

1

1

T T
0

FIGURE 4.47

Data sequence for Problem 4.19.

4.20. Given the sinusoid

xðnÞ¼ 2 $ sin 2 ; 000 $ 2 p$ n
8 ; 000