hamming.awk


1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59

#!/usr/bin/awk -f

### hamming.awk
# generate a Hamming window
# R.W. Hamming, 'Digital Filters': H = '0.23 0.54 0.23'
# https://en.wikipedia.org/wiki/Window_function provides a few values for the
# 'a0' and 'a1' parameters of the raised cosine.


### Gaussian
function gaussian(n) {
    # sigma <= 0.5
    sigma = 0.4
    e[n] = (n)/(sigma*M)
    return exp(-0.5*e[n]*e[n])
}


### Hamming, raised cosine
function hamming(n) {
    ### optimal values for equal-ripple
    #a0 = 0.53836
    #a1 = 0.46164

    a0 = (25.0/46.0)
    a1 = (21.0/46.0)
    return a0 + a1*cos((pi*n)/M)
}


### vonHann, raised cosine
function vonhann(n) {
    a0 = 0.5
    a1 = 0.5
    return a0 + a1*cos((pi*n)/M)
}


BEGIN {

    ARGV[1] ? N = ARGV[1] : N = 0
    ARGV[2] ? OFMT = "%." ARGV[2] "g" : OFMT = "%g"

    # window interval goes from -M to M
    M = 0.5*(N - 1)
    pi = 4*atan2(1,1)

    for (n=-M; n<=M; n++) {
        if (N > 1 && M > 0) {
            w[n] = hamming(n)
            print n + M, w[n]/M
        }
        else {
            print n + M, 1.0
        }
    }

}