1、 Research on FIR Digital Filter Design Using an Improved Window Function TAN Jiajie , LUO Changyou, HUANG Sanwei ， DENG Xiaohui ( Department of Physics and Electronic Information Science, Hengyang Normal University, Hengyang Hunan 421008, China) Abstract : Window function has been used to design a l
2、inear phase digital filer for long times, but the use o f optimization techniques for designing digital filter has become widespread in recent year A new met ho d has been proposed to improve FIR window function in this paper ， T he window function that combines with co sine sequences in linear is d
3、ifferent from previous Hann ,Hamming and Blackman window function The paper also proposes linear programming to optimize characterization of FIR digital filter according to its magnitude condition, and gives out t he algorithm to design dig ital filter using the improved window function ,Finally , w
4、e have designed FIR filter using new window for simulation and compared w it h the filter designed by Hamming window, Blackman window function T he simulation results show that filters designed using this method to meet t he design specifications Key words: improved window function； FIR digital filt
5、er ； window function； linear programming 0 lead speech The design method of FIR digital filters are mainly: window function method, frequency sampling method and the chebyshev etc corrugated approximation method 1-4. Window function method is the most commonly used designing FIR digital filters, the
6、 simplest method of 4-5. The essence of window function method is the truncated ideal impulse response to approximate the method petitions filter index. Frequency sampling method is a design optimization method for its shortcoming is when the design that use the variable is limited to a few samples
7、values of transitional, cut-off frequency not easy control 3. Chebyshev etc corrugated approximation method is a kind of optimization design, but existing computational complexity, big disadvantage computation 1-2. Window function method is simple in design, have closed form of formula, thus very pr
8、actical. Defect is the stopband bandpass, cut-off frequency not easy control 2-3. Digital filter, window function of auto-heating window function method of selecting, the key is: design to choose the appropriate window function, choose the right order number of digital filter, improve amplitude freq
9、uency characteristics, reduce Gibbs phenomenon, solve convergence problem 1-2. 3 choose window function, through to Guass Guass window function improved, design a low-pass filter has better superiority； 4 the error information, using the known in the iteration process through the window function met
10、hod continuously revised design result in filter order number, under the condition of invariable frequency response approximation, filter ideal frequency response. 5 use integer sequence, such as where Fibonacci sequence, Golomb sequence, Conway Hofstadter Recursive sequence, Triangular series produ
11、ce window function to design the filter, its effect is better than that of classical design method. 6 choose dual window window function sequence of structure was system characteristics approximation error is the minimum； 7 will be well Saramaki Dolph - and Chebysheve window with the well designed,
12、its effect FIR digital filters than Kaiser well； 8 put good effect in Hamming ReImann well well well and Kaiser window. 9 put forward a kind of exponential window function, this window function has the width can be adjusted with the window design characteristics, the digital filters have more centra
13、lized, Lord disc energy side-lobe less features. 10 using linear programming design linear phase fir filter ascending cosine to 100 % super bandwidth. 11 linear programming method is adopted to design digital filter. This paper USES the existing window function, and carry on the weighted combination
14、, reference 10 or 11, and linear programming with long Hamming, Blackman window are compared. The advantages of this method is strong logicality, goal clear, easy to achieve, and to explore the best solutions. 1 common window function Window function select principle: window function as focus on ene
15、rgy, Lord disc transitional steep； Reduce the window function spectrum side-lobe level, increase stopband attenuation, and reduce the stopband bandpass and ripple effect. Common window function have 1-4 : Rectangle window, Hanning window, Hamming window, Blackman window, Kaiser window. Window functi
16、on method design idea of FIR filters is 1-2 : make sure the frequency response of ideal filter )( jd eH .The frequency response of practical design filter 10)()( Nnjj enheH To approximate )( jd eH .For again 10)()( Nnjj enheH Reverse transform get Finally use window function )(nw To truncate )(nhd ,
17、mean h( n) = )(nhd )(nw .To truncate )(nhd ,Will produce gibbs phenomenon, all the window function choices to reduce this phenomenon for the purpose. Judge ideal window function mainly according to the following three criteria! The Lord is high double amplitude and its width should try to narrowThe
18、amplitude side-lobe fast speed, the biggest drop side-lobe relative to the main valve should be as low as possible. # transitional requirements will try to narrow. Facts prove the two standard cannot simultaneously satisfy window function should be, so the two compromise 1-3. In order to reduce caus
19、ed due to add window truncation ripple and transitional grows wider impact in engineering design common Hamming window and Kaiser window. 2 improved window function 1-2 enumerated window function, Hanning window, Hamming window, Blackman window is cosine sequence and rectangular sequence of linear c
20、ombination. In order to restrain the amplitude, side-lobe Hanning window, Hamming window on the basis of the second, add cosine, when the harmonic component design and ideal window function and related to the frequency response of different from Blackman window, window function improved form below)(
21、14c o s12c o s)( nNRN ncN nban (1) Formula (1) of a, b, c undetermined, their size and given filter technology indexes related. For convenience, this window function length choice for odd. The next several special case discussion this type. Case 1, take a = 1, b = c = 0, for rectangular window. Cond
22、ition 2, take a = 0.5, b = - 0.5, c = 0, for Hann window. Case 3, take a = 0.53, b = - 0.46, c = 0, for Hamming window. Situation, a = 4, b = 0 0.42 j c = 0.08, 5, Blackman window for. By above knowable, the improved window function with these four window function the nature, belong to the general f
23、orm of the window function. 3 improved window function algorithm According to the given filter technology index )( jd eH ,Determine the backlog filter unit, but by sampling response formula below ask out: deeHnh jjdd )(21)( (2) Calculating the actual filter unit sampling response: h( n) = )(nhd )(nw
24、 (3) Filter the frequency response is: 10 )()( Nn jj enheH （ 4） Will formula (1) generation into the formula (4) : jnNn ndj eN ncN nbaheH 14c o s12c o s)( 10 )( (5) Reference 1-2 10 or 11, consider FIR filters satisfy the first kind of linear phase conditions, For 21N Accidentally symmetry, And N an odd number,ordering h ( n) = )(nhd 14c o s12c o s N ncN nba 。 Then the )( jeH magnitude of the next type: written 21c o s)()( 10NnnhH Nn Will continue to have the type of Jane 1-2
