fir_window.awk


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#!/usr/bin/awk -f

### fir_window.awk
# generate a FIR 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 window
function gaussian(n) {
    # sigma <= 0.5
    sigma = 0.4
    en[n] = (n - M)/(sigma*M)
    return exp(-0.5*e[n]*e[n])
}


# Hamming window (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 = 4.0*atan2(1.0, 1.0)

    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
        }
    }
}