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@ -198,8 +198,8 @@ for i=1:low_pass_prototype_number_of_poles |
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end |
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% Clears unneeded variables from workspace |
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clearVars = {'i', 'prototype_normalized_stop_radial_frequency', ... |
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'low_pass_prototype_half_power_radial_frequency', 'theta'}; |
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clearVars = {'i', 'prototype_normalized_stop_radial_frequency', 'theta', ... |
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'low_pass_prototype_half_power_radial_frequency', 'temp_filter_order'}; |
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clear(clearVars{:}) |
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clear clearVars |
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@ -340,12 +340,12 @@ for i=1:high_pass_number_of_poles |
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% Builds unit's transfer function |
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% Builds numerator and denominator of the transfer function using the |
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% eq. 6-68 |
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G = (units_R(1,i)+units_r2(1,i))/units_R(1,i); |
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unit_numerator = [G ... |
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temp_G = (units_R(1,i)+units_r2(1,i))/units_R(1,i); |
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unit_numerator = [temp_G ... |
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0 ... |
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0]; |
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unit_denominator = [1 ... |
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2/(units_C(1,i)*units_R(1,i))+(1-G)/(units_C(1,i)*units_R(1,i)) ... |
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2/(units_C(1,i)*units_R(1,i))+(1-temp_G)/(units_C(1,i)*units_R(1,i)) ... |
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1/(units_C(1,i)^2*units_R(1,i)^2)]; |
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units_transfer_functions(1,i) = ... |
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@ -375,52 +375,112 @@ for i=1:high_pass_number_of_poles |
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end |
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% Clears unneeded variables from workspace |
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clearVars = {'i'}; |
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clearVars = {'i', 'temp_G', 'unit_numerator', 'unit_denominator'}; |
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clear(clearVars{:}) |
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clear clearVars |
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clear -regexp _transfer_function$ |
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% ========== UNITS IMPLEMENTATION END ========== |
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%% ========== GAIN ADJUSTMENT START ========== |
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% |
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total_gain_high = units_k(1,1)*units_k(1,2); |
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unit_adjustment_gain = 1/total_gain_high; |
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% We arbitrarily choose to use a 10KOhm series resistor in the adjustment |
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% unit |
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unit_adjustment_feedback_resistor = 10*10^3*unit_adjustment_gain; |
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% |
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% ========== GAIN ADJUSTMENT END ========== |
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%% ========== TRANSFER FUNCTIONS STUDY START ========== |
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total_transfer_function = series(units_transfer_functions(1,1), ... |
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units_transfer_functions(1,2)); |
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total_transfer_function = total_transfer_function*unit_adjustment_gain; |
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% Arbitrary high frequency to display the gain at high frequencies |
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high_frequency = 90000; % Hz |
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%{ |
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ltiview(units_transfer_functions(1,1), ... |
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units_transfer_functions(1,2)); |
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%} |
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% Plots each unit's frequency response |
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for i=1:high_pass_number_of_poles |
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plot_transfer_function(units_transfer_functions(1,i), ... |
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(high_frequency)); |
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end |
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% Plots the total filter frequency response |
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plot_transfer_function(total_transfer_function, ... |
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[specification_stop_frequency ... |
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design_half_power_radial_frequency/(2*pi) ... |
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specification_pass_frequency ... |
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high_frequency]); |
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% Plots the total filter attenuation function |
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plot_transfer_function(inv(total_transfer_function), ... |
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[specification_stop_frequency ... |
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design_half_power_radial_frequency/(2*pi) ... |
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specification_pass_frequency ... |
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high_frequency]); |
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%} |
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%{ |
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ltiview(units_transfer_functions(1,1), ... |
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units_transfer_functions(1,2), ... |
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ltiview('bodemag', units_transfer_functions(1,1)); |
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ltiview('bodemag', units_transfer_functions(1,2)); |
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ltiview('bodemag', total_transfer_function); |
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ltiview('bodemag', units_transfer_functions(1,1), units_transfer_functions(1,2), ... |
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total_transfer_function); |
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%} |
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%ltiview(total_transfer_function); |
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hold off |
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sampling_time_seconds = 60; % s |
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sampling_frequency_Fs = 80000; % Hz |
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sampling_period_T = 1/sampling_frequency_Fs; % s |
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sampling_time_vector = 0:sampling_period_T: ... |
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sampling_time_seconds-sampling_period_T; |
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sampling_length_L = length(sampling_time_vector); |
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frequency_vector = sampling_frequency_Fs/sampling_length_L* ... |
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(0:(sampling_length_L/2)); |
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input_cos_signal_frequency_1 = 0.2*specification_stop_radial_frequency; |
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input_cos_signal_frequency_2 = 0.7*specification_stop_radial_frequency; |
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input_cos_signal_frequency_3 = 1.6*specification_pass_radial_frequency; |
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input_cos_signal_frequency_4 = 2.4*specification_pass_radial_frequency; |
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input_cos_signal_frequency_5 = 3.5*specification_pass_radial_frequency; |
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input_signal = cos(input_cos_signal_frequency_1*sampling_time_vector)+ ... |
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0.6*cos(input_cos_signal_frequency_2*sampling_time_vector)+ ... |
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1.5*cos(input_cos_signal_frequency_3*sampling_time_vector)+ ... |
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0.7*cos(input_cos_signal_frequency_4*sampling_time_vector)+ ... |
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0.4*cos(input_cos_signal_frequency_5*sampling_time_vector); |
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system_output = lsim(total_transfer_function, input_signal, ... |
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sampling_time_vector); |
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% Plots only the first 500 samples |
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figure(1) |
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plot(sampling_time_vector(1:500), input_signal(1:500), ... |
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sampling_time_vector(1:500), system_output(1:500)); |
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grid on |
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% Plots the power spectrum of the input signal |
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input_signal_fft = fft(input_signal); |
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Pyy = input_signal_fft.*conj(input_signal_fft)/sampling_length_L; |
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figure(2) |
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semilogx(frequency_vector,Pyy(1:sampling_length_L/2+1)) |
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grid on |
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% Plots the power spectrum of the output signal |
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system_output_fft = fft(system_output, length(sampling_time_vector)); |
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Pyy = system_output_fft.*conj(system_output_fft)/sampling_length_L; |
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figure(3) |
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semilogx(frequency_vector,Pyy(1:sampling_length_L/2+1)) |
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grid on |
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%{ |
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plot_transfer_function(total_transfer_function, ... |
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[design_half_power_radial_frequency/(2*pi) ... |
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specification_stop_frequency ... |
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specification_pass_frequency ... |
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15000]); |
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%} |
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% Clears unneeded variable from workspace |
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clearVars = {'total_transfer_function'}; |
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clearVars = {'high_frequency', 'total_transfer_function', 'Pyy', ... |
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'frequency_vector', 'system_output', 'system_output_fft'}; |
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clear(clearVars{:}) |
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clear clearVars |
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clear -regexp _transfer_functions$ |
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clear -regexp ^sampling_ |
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clear -regexp ^input_ |
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% ========== GAIN ADJUSTMENT END ========== |
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% ========== TRANSFER FUNCTIONS STUDY END ========== |
