FIR ফিল্টার ইমপ্লিমেন্টেশন — ডাইরেক্ট ফর্ম

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
M = 31
center = (M - 1)//2

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)

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)]
h = [h_ideal[n]*w[n] for n in range(M)]

# ---- পদ্ধতি ১: কনভোলিউশন ফাংশন (L31-এর প্যাটার্ন) ----
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

y_conv_full = convolve(x, h)
y_conv = y_conv_full[:len(x)]   # প্রথম len(x) নমুনা = causal আউটপুট, n=0..N-1

# ---- পদ্ধতি ২: ডাইরেক্ট ফর্ম -- স্যাম্পল-বাই-স্যাম্পল স্লাইডিং-উইন্ডো সমষ্টি ----
def fir_direct_form(x, h):
    y = []
    for n in range(len(x)):
        s = 0.0
        for k in range(len(h)):
            if n - k >= 0:
                s += h[k]*x[n-k]
        y.append(s)
    return y

y_direct = fir_direct_form(x, h)

max_diff = max(abs(y_conv[n]-y_direct[n]) for n in range(len(x)))
print(f"len(y_conv) = {len(y_conv)}   len(y_direct) = {len(y_direct)}")
print(f"সর্বোচ্চ পার্থক্য (দুই পদ্ধতির মধ্যে): {max_diff}")
print()
print(f"{'n':>3} | {'y_conv[n]':>12} | {'y_direct[n]':>12} | {'diff':>10}")
for n in [0, 1, 5, 14, 15, 16, 30, 45, 59]:
    diff = abs(y_conv[n]-y_direct[n])
    print(f"{n:>3} | {y_conv[n]:>12.8f} | {y_direct[n]:>12.8f} | {diff:>10.2e}")