3 on the design of finite impulse response filters

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Unformatted text preview: %  ¨§ ¦ % ¡£ ¢0 ¥0 ¤¢0 £¡ "  § E B' (3.35) ¡ 0 ¡ £¢ §¥ 3210¡ We will assume that the filter phase is zero. In the previous expression is the cutoff frequency. This filter can be either applied in the frequency domain or in the time domain. It is clear that if the signal to be filtered is called , then the filtered signal is given by ¥¡ 210¢ ¥ ¥ ¡ §¥ 210¡ " 20 ¢ 3210¡  (3.36) In general, it is more convenient to design short filters in the time domain and applied them via convolution2  ¥ § ¡ ) ¥ ¨§¡ 3¥ § ¡ £  § (3.37) 5 where the sequence is the Impulse Response of the filter with desired amplitude response . We can use the inverse Fourier transform to find an expression for , ¥§¡  ©¥ 0  )(& % 210¡ 3 1 ¡ B § ¥§¡  note that we are working with continuous signals. ¥ 2 ¨§¡  ¦ (  ( ¥ 2 ¡0 Evaluating the last integral leads to the following expression for the filter (3.38) ): CHAPTER 3. DISCRETE FOURIER TRANSFORM " (3.39) ¥ 210¡ ¡ §  ¡ 74 3§ 3 ) ¥ ¢ ¡...
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