#!/usr/bin/awk -f

### fir_window_hamming.awk
# generate a Hamming raised cosine 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.
# note: the forms provided from wikipedia do not give expected results and
# appear to show inconsistency between raised cosine variations. need to
# cross-check these forms against DSP/signaling texts.


# 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)
}


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
        }
    }
}