tailieunhanh - Biosignal and Biomedical Image Processing MATLAB-Based Applications Muya phần 4

Tham khảo tài liệu 'biosignal and biomedical image processing matlab-based applications muya phần 4', ngoại ngữ, anh văn thương mại phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 94 Chapter 4 replaced by the filter coefficients b n . Hence FIR filters can be implemented using either convolution or MATLAB s filter routine. Eq. 8 indicates that the filter coefficients or weights of an FIR filter are the same as the impulse response of the filter. Since the frequency response of a process having an impulse response h n is simply the Fourier transform of h n the frequency response of an FIR filter having coefficients b n is just the Fourier transform of b n X m X b n j mn N 9 n 0 Eq. 9 is a special case of Eq. 5 when the denominator equals one. If b n generally consists of a small number of elements this equation can sometimes be determined manually as well as by computer. The inverse operation going from a desired frequency response to the coefficient function b n is known as filter design. Since the frequency response is the Fourier transform of the filter coefficients the coefficients can be found from the inverse Fourier transform of the desired frequency response. This design strategy is illustrated below in the design of a FIR lowpass filter based on the spectrum of an ideal filter. This filter is referred to as a rectangular window filter since its spectrum is ideally a rectangular window. FIR Filter Design The ideal lowpass filter was first introduced in Chapter 1 as a rectangular window in the frequency domain Figure . The inverse Fourier transform of a rectangular window function is given in Eq. 25 in Chapter 2 and repeated here with a minor variable change bin m - 2 10 n n - L 2 where fc is the cutoff frequency Ts is the sample interval in seconds and L is the length of the filter. The argument n - L 2 is used to make the coefficient function symmetrical giving the filter linear phase characteristics. Linear phase characteristics are a desirable feature not easily attainable with IIR filters. The coefficient function b n produced by Eq. 10 is shown for two values of fc in Figure . Again this function is the same as the impulse

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