《DSP using MATLAB》示例Example 9.5
代码:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 | %% ------------------------------------------------------------------------ %% Output Info about this m-file fprintf ( '\n***********************************************************\n' ); fprintf ( ' <DSP using MATLAB> Exameple 9.5 \n\n' ); time_stamp = datestr ( now , 31); [wkd1, wkd2] = weekday (today, 'long' ); fprintf ( ' Now is %20s, and it is %7s \n\n' , time_stamp, wkd2); %% ------------------------------------------------------------------------ n = 0:256; x = cos ( pi *n); w = [0:100]* pi /100; %% ----------------------------------------------------------------- %% Plot %% ----------------------------------------------------------------- Hf1 = figure ( 'units' , 'inches' , 'position' , [1, 1, 8, 6], ... 'paperunits' , 'inches' , 'paperposition' , [0, 0, 6, 4], ... 'NumberTitle' , 'off' , 'Name' , 'Exameple 9.5' ); set ( gcf , 'Color' , 'white' ); TF = 10; % (a) Interpolation by I = 2, L = 4 I = 2; [y, h] = interp(x, I); H = freqz(h, 1, w); H = abs (H); subplot (2, 2, 1); plot (w/ pi , H); axis ([0, 1, 0, I+0.1]); grid on; xlabel ( '\omega in \pi units' ); ylabel ( 'Magnitude' ); title ( 'I = 2, L = 4' , 'fontsize' , TF); set ( gca , 'xtick' , [0, 0.5, 1]); set ( gca , 'ytick' , [0:1:I]); % (b) Interpolation by I = 4, L = 4 I = 4; [y, h] = interp(x, I); H = freqz(h, 1, w); H = abs (H); subplot (2, 2, 2); plot (w/ pi , H); axis ([0, 1, 0, I+0.2]); grid on; xlabel ( '\omega in \pi units' ); ylabel ( 'Magnitude' ); title ( 'I = 4, L = 4' , 'fontsize' , TF); set ( gca , 'xtick' , [0, 0.25, 1]); set ( gca , 'ytick' , [0:1:I]); % (c) Interpolation by I = 8, L = 4 I = 8; [y, h] = interp(x, I); H = freqz(h, 1, w); H = abs (H); subplot (2, 2, 3); plot (w/ pi , H); axis ([0, 1, 0, I+0.4]); grid on; xlabel ( '\omega in \pi units' ); ylabel ( 'Magnitude' ); title ( 'I = 8, L = 4' , 'fontsize' , TF); set ( gca , 'xtick' , [0, 0.125, 1]); set ( gca , 'ytick' , [0:2:I]); % (d) Interpolation by I = 8, L = 10 I = 8; [y, h] = interp(x, I, 10); H = freqz(h, 1, w); H = abs (H); subplot (2, 2, 4); plot (w/ pi , H); axis ([0, 1, 0, I+0.4]); grid on; xlabel ( '\omega in \pi units' ); ylabel ( 'Magnitude' ); title ( 'I = 8, L = 10' , 'fontsize' , TF); set ( gca , 'xtick' , [0, 0.125, 1]); set ( gca , 'ytick' , [0:2:I]); |
运行结果:
前三张图L=4,和想象的一样,滤波器是低通性质,其通带边界近似在π/I附近,并且幅度谱最大增益为I。另外注意到滤波器的过渡带和缓,
因此和理想滤波器相差较大。最后一张,L=10,和想象一样,过渡带比较陡。
任何超过L=10的情况都会导致滤波器不稳定,因此在设计过程中是必须避免的。
牢记:
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