FIR . . 2 . . . .

FIR is a class of LTI filter and the transfer function of the filter is                  Now consider an FIR filter having length M can be expressed as                  =  =  We obtained the impulse response with    The impulse response of finite length   M . FIRfilter have only Zeros .FIR filter is also known as all zeros filter or feedforward or  non -recursive  or transversal.For  linear phase response  FIR digital filter satisfies the following condition  we have toknow that  Inverse Discrete time Fourier transform For highpass filter limit breakdown into two interval              since  sin(n)=0  so above equation becomeWhere        and     Impulseresponse shows non-causal behaviour  and toconvert it  into causal system by givinga  delay . Delaying term convert intolinear phase and causal .  for odd                                                                              The impulseresponse truncation is equal to multiplying the by theselecting  window. In given case the stopband attenuation is 74db which is near to the Blackman window.Blackmanwindow mathematical expression can be expressed as    for    The finalexpression for  is        Designing parameters of  high pass filter: Stopband : 0-2.

5 kHz Passband : 3kHzSamplingrate: 10 kHzStopbandattenuation:72 dBSol: Accordingto the stopband attenuation -72dB we select the Blackman window.   for    For   M=110   for    The finaloutput can be expressed as   n 0 -0.00819 -0.08 0.000652 1 . . .

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. . . 109 . . . MatlabCode:>> L=110;>> Xc=0.55;>> Qn=blackman(L+1);>> p=fir1(L,Xc,’high’ ,Qn);>> freqz(p)Outp