我需要的是可以运行的matlab代码来实现上述要求

好的，以下是一个简单的MATLAB程序，实现了巴特沃斯滤波器的模拟设计和数字转换，并以GUI的形式展示了滤波器的频率响应幅度图：

function varargout = butterworth_gui(varargin)
% BUTTERWORTH_GUI MATLAB code for butterworth_gui.fig
%      BUTTERWORTH_GUI, by itself, creates a new BUTTERWORTH_GUI or raises the existing
%      singleton*.
%
%      H = BUTTERWORTH_GUI returns the handle to a new BUTTERWORTH_GUI or the handle to
%      the existing singleton*.
%
%      BUTTERWORTH_GUI('CALLBACK',hObject,eventData,handles,...) calls the local
%      function named CALLBACK in BUTTERWORTH_GUI.M with the given input arguments.
%
%      BUTTERWORTH_GUI('Property','Value',...) creates a new BUTTERWORTH_GUI or raises the
%      existing singleton*.  Starting from the left, property value pairs are
%      applied to the GUI before butterworth_gui_OpeningFcn gets called.  An
%      unrecognized property name or invalid value makes property application
%      stop.  All inputs are passed to butterworth_gui_OpeningFcn via varargin.
%
%      *See GUI Options on GUIDE's Tools menu.  Choose "GUI allows only one
%      instance to run (singleton)".

% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...
                   'gui_Singleton',  gui_Singleton, ...
                   'gui_OpeningFcn', @butterworth_gui_OpeningFcn, ...
                   'gui_OutputFcn',  @butterworth_gui_OutputFcn, ...
                   'gui_LayoutFcn',  [] , ...
                   'gui_Callback',   []);
if nargin && ischar(varargin{1})
    gui_State.gui_Callback = str2func(varargin{1});
end

if nargout
    [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
else
    gui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT


% --- Executes just before butterworth_gui is made visible.
function butterworth_gui_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject    handle to figure
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
% varargin   command line arguments to butterworth_gui (see VARARGIN)

% Choose default command line output for butterworth_gui
handles.output = hObject;

% Update handles structure
guidata(hObject, handles);

% UIWAIT makes butterworth_gui wait for user response (see UIRESUME)
% uiwait(handles.figure1);


% --- Outputs from this function are returned to the command line.
function varargout = butterworth_gui_OutputFcn(hObject, eventdata, handles) 
% varargout  cell array for returning output args (see VARARGOUT);
% hObject    handle to figure
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

% Get default command line output from handles structure
varargout{1} = handles.output;


% --- Executes on button press in design_button.
function design_button_Callback(hObject, eventdata, handles)
% hObject    handle to design_button (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

% read input parameters from GUI
order = str2double(get(handles.order_edit, 'String'));
cutoff = str2double(get(handles.cutoff_edit, 'String'));
ripple = str2double(get(handles.ripple_edit, 'String'));
fs = str2double(get(handles.fs_edit, 'String'));

% design analog Butterworth filter
[b, a] = butter(order, 2*cutoff/fs);

% convert to digital filter using bilinear transform
[z, p, k] = butter(order, 2*cutoff/fs);
[bz, az] = bilinear(z, p, k, fs);

% plot frequency response
freq = linspace(0, fs/2, 10000);
[h, w] = freqz(bz, az, freq);
plot(handles.freq_axes, freq, 20*log10(abs(h)))
title(handles.freq_axes, 'Frequency Response')
xlabel(handles.freq_axes, 'Frequency (Hz)')
ylabel(handles.freq_axes, 'Magnitude (dB)')

% save filter coefficients
handles.b = bz;
handles.a = az;
guidata(hObject, handles);


% --- Executes on button press in clear_button.
function clear_button_Callback(hObject, eventdata, handles)
% hObject    handle to clear_button (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

% clear input fields
set(handles.order_edit, 'String', '');
set(handles.cutoff_edit, 'String', '');
set(handles.ripple_edit, 'String', '');
set(handles.fs_edit, 'String', '');

% clear frequency response plot
cla(handles.freq_axes);

% clear filter coefficients
handles.b = [];
handles.a = [];
guidata(hObject, handles);


% --- Executes on selection change in transform_popup.
function transform_popup_Callback(hObject, eventdata, handles)
% hObject    handle to transform_popup (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)

% Hints: contents = cellstr(get(hObject,'String')) returns transform_popup contents as cell array
%        contents{get(hObject,'Value')} returns selected item from transform_popup

% read selected transform method from GUI
contents = cellstr(get(hObject,'String'));
method = contents{get(hObject,'Value')};

% convert filter coefficients using selected method
if strcmp(method, 'Impulse Invariant')
    if ~isempty(handles.b) && ~isempty(handles.a)
        [bz, az] = impinvar(handles.b, handles.a);
        handles.b = bz;
        handles.a = az;
        guidata(hObject, handles);
        % plot frequency response
        freq = linspace(0, fs/2, 10000);
        [h, w] = freqz(bz, az, freq);
        plot(handles.freq_axes, freq, 20*log10(abs(h)))
        title(handles.freq_axes, 'Frequency Response')
        xlabel(handles.freq_axes, 'Frequency (Hz)')
        ylabel(handles.freq_axes, 'Magnitude (dB)')
    end
elseif strcmp(method, 'Bilinear Transform')
    if ~isempty(handles.b) && ~isempty(handles.a)
        [bz, az] = bilinear(handles.b, handles.a, fs);
        handles.b = bz;
        handles.a = az;
        guidata(hObject, handles);
        % plot frequency response
        freq = linspace(0, fs/2, 10000);
        [h, w] = freqz(bz, az, freq);
        plot(handles.freq_axes, freq, 20*log10(abs(h)))
        title(handles.freq_axes, 'Frequency Response')
        xlabel(handles.freq_axes, 'Frequency (Hz)')
        ylabel(handles.freq_axes, 'Magnitude (dB)')
    end
end


% --- Executes during object creation, after setting all properties.
function transform_popup_CreateFcn(hObject, eventdata, handles)
% hObject    handle to transform_popup (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called

% Hint: popupmenu controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end


function order_edit_Callback(hObject, eventdata, handles)
% hObject    handle to order_edit (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)


% --- Executes during object creation, after setting all properties.
function order_edit_CreateFcn(hObject, eventdata, handles)
% hObject    handle to order_edit (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end


function cutoff_edit_Callback(hObject, eventdata, handles)
% hObject    handle to cutoff_edit (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)


% --- Executes during object creation, after setting all properties.
function cutoff_edit_CreateFcn(hObject, eventdata, handles)
% hObject    handle to cutoff_edit (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end


function ripple_edit_Callback(hObject, eventdata, handles)
% hObject    handle to ripple_edit (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)


% --- Executes during object creation, after setting all properties.
function ripple_edit_CreateFcn(hObject, eventdata, handles)
% hObject    handle to ripple_edit (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end


function fs_edit_Callback(hObject, eventdata, handles)
% hObject    handle to fs_edit (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)


% --- Executes during object creation, after setting all properties.
function fs_edit_CreateFcn(hObject, eventdata, handles)
% hObject    handle to fs_edit (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows.
%       See ISPC and COMPUTER.
if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end

需要注意的是，上述代码中的GUI设计需要在MATLAB的GUIDE中完成，这里就不再赘述了。此外，程序中使用了MATLAB内置的butter函数来进行模拟滤波器的设计，以及bilinear函数和impinvar函数来进行数字滤波器的转换。用户需要在GUI中输入滤波器的阶数、截止频率、通带最大纹波和采样频率等参数，然后选择数字滤波器的转换方法，点击设计按钮，程序会计算滤波器的系数，并绘制滤波器的频率响应幅度图。用户还可以点击清除按钮清除输入和输出，重新进行设计。