FIR ফিল্টার ডিজাইন ট্রেড-অফ — অর্ডার বনাম পারফরম্যান্স

import math

fs = 200.0
f_lo = 10.0
f_hi = 60.0
N = 60
x = [math.sin(2*math.pi*f_lo*n/fs) + math.sin(2*math.pi*f_hi*n/fs) for n in range(N)]

fc = 30.0
fc_norm = fc/fs

def sinc_lp(d, fc_norm):
    if d == 0:
        return 2*fc_norm
    return math.sin(2*math.pi*fc_norm*d)/(math.pi*d)

def design_filter(M):
    center = (M-1)//2
    h_ideal = [sinc_lp(n-center, fc_norm) for n in range(M)]
    w = [0.54 - 0.46*math.cos(2*math.pi*n/(M-1)) for n in range(M)]
    return [h_ideal[n]*w[n] for n in range(M)], center

def convolve(a, b):
    ny = len(a)+len(b)-1
    y = [0.0]*ny
    for n in range(ny):
        s = 0.0
        for k in range(len(b)):
            if 0 <= n-k < len(a):
                s += b[k]*a[n-k]
        y[n] = s
    return y

def dft_mag_at(sig, f, fs):
    Ns = len(sig)
    total = sum(sig[n]*complex(math.cos(-2*math.pi*f*n/fs), math.sin(-2*math.pi*f*n/fs)) for n in range(Ns))
    return abs(total)/Ns

mag_in_lo = dft_mag_at(x, f_lo, fs)
mag_in_hi = dft_mag_at(x, f_hi, fs)

results = {}
for M in [11, 41]:
    h, center = design_filter(M)
    y_full = convolve(x, h)
    y = y_full[center:center+N]
    mag_out_lo = dft_mag_at(y, f_lo, fs)
    mag_out_hi = dft_mag_at(y, f_hi, fs)
    atten_lo = 20*math.log10(mag_out_lo/mag_in_lo)
    atten_hi = 20*math.log10(mag_out_hi/mag_in_hi)
    results[M] = h
    print(f"M={M:>3} taps | প্যাসব্যান্ড (10Hz) এটেনুয়েশন: {atten_lo:>7.4f} dB | স্টপব্যান্ড (60Hz) এটেনুয়েশন: {atten_hi:>7.2f} dB")

print()
print("ট্রানজিশন শার্পনেস -- |H(f)| সরাসরি ফিল্টারের উপর মূল্যায়ন করা (কোনো ইনপুট সিগন্যাল ছাড়াই):")

def freq_response(h, f_norm):
    Nh = len(h)
    return sum(h[n]*complex(math.cos(-2*math.pi*f_norm*n), math.sin(-2*math.pi*f_norm*n)) for n in range(Nh))

print(f"{'f (Hz)':>7} | {'M=11':>10} | {'M=41':>10}")
for f_probe in [25, 30, 32, 35, 40, 45]:
    row = [abs(freq_response(results[M], f_probe/fs)) for M in [11, 41]]
    print(f"{f_probe:>7} | {row[0]:>10.6f} | {row[1]:>10.6f}")