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