In this section, we implement a Python FIR (Finite Impulse Response) filter design class using the window method. We use a design table based on the DSP textbook to construct this class.

We consider the following window functions:

• Rectangular
• Hanning
• Hamming
• Blackman
• Kaiser

We consider the following filter types:

• Lowpass (LPF)
• Highpass (HPF)
• Bandpass (BPF)
• Bandreject (BRJF)

Formula 1:

$$ 2fc \cdot \frac{\sin(nwc)}{nwc} $$

Formula 2:

$$ -2fc \cdot \frac{\sin(nwc)}{nwc} $$

Formula 3:

$$ 2f_{2} \cdot \frac{\sin(nwc_{2})}{nwc2}-2f_{1} \cdot \frac{\sin(nwc_{1})}{nwc_{1}} $$

Formula 4:

$$ 2f_{1} \cdot \frac{\sin(nwc_{1})}{nwc_{1}}-2f2 \cdot \frac{\sin(nwc2)}{nwc2} $$

$$ y[n] = \sum_{k=0}^{N} h[k] \cdot x[n-k] $$