The design steps for FIR filter using window techniques are

1. The specifications required for FIR filter design are-

a) Type of Filter: Low Pass, High Pass, band-pass and band-stop filters.

b) Order N (or length M) of the filter, $N=M-1$

c) Desired Frequency Response

$H_{d}\left(e^{j w}\right)=C e^{-j \alpha \omega}$ , where $\alpha=\frac{M-1}{2}$

d) Cut-off frequency: $\omega_{c}$ for $\mathrm{LPF}$ and $\mathrm{HPF}$ or $\omega_{c 1}$ and $\omega_{c 2}$ for band-pass and band-stop filters. If Cut-off frequency is $F_{c}$ . Hz and Sampling frequency is $F_{S}$ Hz then $\omega_{c}=\frac{2 \pi F_{c}}{F_{S}}$

2. Desired Impulse Response $h_{d}(n)$ is computed using above specifications by Inverse DTFT of $H_{d}\left(e^{j w}\right)$

$\therefore h_{d}(n)=\frac{1}{2 \pi} \int_{a}^{b} H_{d}(\omega) e^{j \omega n} d \omega,$

where the limits of integration are the Cut-off frequency depending on the type of filter.

3. Desired Impulse Response $h_{d}(n)$ is of infinite duration. To make if of finite duration, it is multiplied with a suitable window function

$W(n)=\left\{\begin{array}{ll}{A} & {0 \leq n \leq N-1} \\ {0} & {\text { otherwise }}\end{array}\right.$

$\therefore$ Finite Impulse Response $h(n)=h_{d}(n) \times W(n)$

Use symmetric conditions $h(n)=h(N-1-n)$

when centre of Impulse response is at $\alpha$ and $h(n)=h(-n)$ when centre of Impulse response is at origin. So only half the number of Impulse response are calculated.

4. Transfer Function of the FIR Filter is obtained by taking Z Transform of Finite Impulse Response h(n).

$\therefore$ Transfer Function of Filter $H(z)=\sum_{n=0}^{N-1} h(n) \cdot z^{-n}$

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