《DSP using MATLAB》示例Example 9.9
阿新 • • 發佈:2017-05-26
time 產生 images length img art markers 濾波器 峰值
代碼:
%% ------------------------------------------------------------------------ %% Output Info about this m-file fprintf(‘\n***********************************************************\n‘); fprintf(‘ <DSP using MATLAB> Exameple 9.9 \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); %% ------------------------------------------------------------------------ % Given parameters: I = 5; Rp = 0.1; As = 30; wp = pi/I; ws = pi*0.32; [delta1, delta2] = db2delta(Rp, As); weights = [delta2/delta1, 1]; n = [0:50]; x = cos(0.5*pi*n); n1 = n(1:17); x1 = x(17:33); % for plotting purposes %% ----------------------------------------------------------------- %% Plot %% ----------------------------------------------------------------- % Input signal Hf1 = figure(‘units‘, ‘inches‘, ‘position‘, [1, 1, 8, 6], ... ‘paperunits‘, ‘inches‘, ‘paperposition‘, [0, 0, 6, 4], ... ‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Exameple 9.9‘); set(gcf,‘Color‘,‘white‘); TF = 10; subplot(2, 2, 1); Hs1 = stem(n1, x1, ‘filled‘); set(Hs1, ‘markersize‘, 2, ‘color‘, ‘g‘); axis([-1, 17, -1.2, 1.2]); grid on; xlabel(‘n‘, ‘vertical‘, ‘middle‘); ylabel(‘Amplitude‘); title(‘Input Signal x(n)‘, ‘fontsize‘, TF); set(gca, ‘xtick‘, [0:4:16]); set(gca, ‘ytick‘, [-1, 0, 1]); % Interpolation with Filter Design: Length M=31 M = 31; F = [0, wp, ws, pi]/pi; A = [I, I, 0, 0]; h = firpm(M-1, F, A, weights); y = upfirdn(x, h, I); delay = (M-1)/2; % Delay imparted by the filter m = delay+1:1:50*I+delay+1; y = y(m); m = 1:81; y = y(81:161); % for plotting subplot(2, 2, 2); Hs2 = stem(m, y, ‘filled‘); axis([-5, 85, -1.2, 1.2]); grid on; xlabel(‘n‘, ‘vertical‘, ‘middle‘); ylabel(‘Amplitude‘); title(‘ Output y(n): I = 5, Filter length=31‘, ‘fontsize‘, TF); set(gca, ‘xtick‘, [0:4:16]*I); set(gca, ‘ytick‘, [-1, 0, 1]); % Interpolation with Filter Design: Length M = 51 M = 51; F = [0, wp, ws, pi]/pi; A = [I, I, 0, 0]; h = firpm(M-1, F, A, weights); y = upfirdn(x, h, I); delay = (M-1)/2; % Delay imparted by the filter m = delay+1:1:50*I+delay+1; y = y(m); m = 1:81; y = y(81:161); % for plotting subplot(2, 2, 3); Hs3 = stem(m, y, ‘filled‘); axis([-5, 85, -1.2, 1.2]); grid on; set(Hs3, ‘markersize‘, 2, ‘color‘, ‘m‘); xlabel(‘n‘, ‘vertical‘, ‘middle‘); ylabel(‘Amplitude‘); title(‘Output y(n): I = 5, Filter length=51 ‘, ‘fontsize‘, TF); set(gca, ‘xtick‘, [0:4:16]*I); set(gca, ‘ytick‘, [-1, 0, 1]); % Interpolation with Filter Design : Length M = 81 M = 81; F = [0, wp, ws, pi]/pi; A = [I, I, 0, 0]; h = firpm(M-1, F, A, weights); y = upfirdn(x, h, I); delay = (M-1)/2; % Delay imparted by the filter m = delay+1:1:50*I+delay+1; y = y(m); m = 1:81; y = y(81:161); % for plotting subplot(2, 2, 4); Hs4 = stem(m, y, ‘filled‘); axis([-5, 85, -1.2, 1.2]); grid on; set(Hs4, ‘markersize‘, 2, ‘color‘, ‘m‘); xlabel(‘n‘, ‘vertical‘, ‘middle‘); ylabel(‘Amplitude‘); title(‘Output y(n): I = 5, Filter length=81 ‘, ‘fontsize‘, TF); set(gca, ‘xtick‘, [0:4:16]*I); set(gca, ‘ytick‘, [-1, 0, 1]);
運行結果:
左上圖是輸入信號x(n)的一部分,右上圖是使用長度為31的濾波器後得到的輸出y(n)。對於濾波器延遲和過渡帶響應來說,該圖是正確的。令人驚訝的是插值後的信號不是其應該的模樣。
峰值超過了1,形狀有些變形。仔細看圖9.20中的濾波器響應表現為寬的過渡帶和小的衰減,必然會導致一些譜能量的泄漏,產生變形。
對於較大的階數來說,濾波器低通特征較好。信號峰值接近1,並且其形狀接近余弦波形。因此,一個好的濾波器設計甚至對一個簡單的信號都是嚴格適用的。
《DSP using MATLAB》示例Example 9.9