Preparatory assignment for Speech Processing Lecture 1

Exercise 2.3.

Complete the second, third and fourth columns of table 2.1. Use a table of cosines (e.g. table 2.2), and/or a pocket calculator.

Table 2.1. Worksheet for exercise 2.1.

i i 17 cos(i 17) 32000 cos(i 17), rounded to the nearest whole number
0 0 1.0000 32000
1 17 0.9563 30603
2 34 0.8291 26534
3 51 0.6296 20148
4 68 0.3751  
5 85 0.0878  
6 102 -0.2070  
7 119 -0.4839  
8 136 -0.7185  
9 153 -0.8904  
10 170    
11      
12      
13      
14      
15      
16      
17      
18      
19      
20      
21 357    
22 374 ( = 360 + 14; 
same as 14)
   
23 391 ( = 31)    
24 408 ( = 48)    
25 425 ( = 65)    
26 442 ( = 82)    
27 476 ( = 116)    

Exercise 2.4.

Using e.g. 1 mm squared graph paper, plot 32000 cos(i 17) on the shorter dimension against i on the longer dimension. Hint: use a scale of 500 units to 1 small square on the shorter dimension, i.e. 10 small squares = 5000 units, and 10 small squares to 1 unit on the longer dimension. Put 0 in the middle, with values in the range -35000 to +35000 below and above. Another way of phrasing this exercise is: sketch a cosine wave, taking samples at 17 intervals.