Question

Given the constraints:

1) frequency response: H(e^jw) = 0 at w = 0 and w = $\pi$ .

2)

What are the impulse response coefficients h[0],h[1],h[2] that is length 3 causal and finite impulse response filter . Sketch phase and magnitude of frequency response.

Answer 1

Given constraints are Hreja) -0 at w=0 Heva) =0 at w=Tī: We Know Hireis)È hense viery H(o) = { hem As length = 3. nardo ( H) : 2 km). (*)+ 0 + bc). Similarly ut co-1) = { hensējun no @ W = 2 - E hene z hro) - how thee) =0 | 5 u celoj dw = 2 by Pausevals Energy Theodem 24 / Heig," do: a thout - hot that they = 2 _o.

Also given that it is FIR filter For FIR (near filter by symmetric I hco) = h (2). Then from 0 hostheistho)=0 2560) - chci Substituting this in 6, we get hos + (-2hces} + chest : 2 hoos tuhão =2 =) 6 = 2 2 = '3 host to h(0) 262) = 1 14 175 If we use ea , we get h(0) = I lis, ha) = It is h(1) = 1 %. So hono- f 1/3 - 2/3 , 've} (0) hoh 143, 43, 173}

H( - ). - 1 ) ( ( ( ) .. hollte et housin hole iw olet wy have the z hrozilo (2. coses) +hwe vas + zvien Cahco) cow their Hice") = zado (2000wed if hem of tara ti? Here) _ ew [-2/ Co w t%] if henv: &-%65 Ihreiny (wo <Hceive) - -- Hirectly !

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