MATLAB中的傅立叶变换是一种非常常用的信号处理方法，可以用于分析信号的频率特征。而尺度变换是指对信号进行缩放以改变其时间尺度，例如将信号放大或缩小。基于MATLAB GUI的傅里叶变换分析的仿真设计可以方便地进行信号处理和分析。
下面是一个简单的MATLAB GUI程序，用于进行傅立叶变换和尺度变换的仿真设计：
```matlab
function varargout = FourierTransform(varargin)
% FOURIERTRANSFORM MATLAB code for FourierTransform.fig
%
FOURIERTRANSFORM, by itself, creates a new FOURIERTRANSFORM or raises the existing
%
singleton*.
%
%
H = FOURIERTRANSFORM returns the handle to a new FOURIERTRANSFORM or the handle to
%
the existing singleton*.
%
%
FOURIERTRANSFORM('CALLBACK',hObject,eventData,handles,...) calls the local
%
function named CALLBACK in FOURIERTRANSFORM.M with the given input arguments.
%
%
FOURIERTRANSFORM('Property','Value',...) creates a new FOURIERTRANSFORM or raises the
%
existing singleton*.
Starting from the left, property value pairs are
%
applied to the GUI before FourierTransform_OpeningFcn gets called.
An
%
unrecognized property name or invalid value makes property application
%
stop.
All inputs are passed to FourierTransform_OpeningFcn via varargin.
%
%
*See GUI Options on GUIDE's Tools menu.
Choose "GUI allows only one
%
instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES
% Edit the above text to modify the response to help FourierTransform
% Last Modified by GUIDE v2.5 19-Aug-2021 12:00:06
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',
mfilename, ...
'gui_Singleton',
gui_Singleton, ...
'gui_OpeningFcn', @FourierTransform_OpeningFcn, ...
'gui_OutputFcn',
@FourierTransform_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 FourierTransform is made visible.
function FourierTransform_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 FourierTransform (see VARARGIN)
% Choose default command line output for FourierTransform
handles.output = hObject;
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes FourierTransform wait for user response (see UIRESUME)
% uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line.
function varargout = FourierTransform_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 load_button.
function load_button_Callback(hObject, eventdata, handles)
% hObject
handle to load_button (see GCBO)
% eventdata
reserved - to be defined in a future version of MATLAB
% handles
structure with handles and user data (see GUIDATA)
[file, path] = uigetfile({'*.wav;*.mp3;*.mp4;*.avi','All Audio and Video Files';'*.wav','WAV Files (*.wav)';'*.mp3','MP3 Files (*.mp3)';'*.mp4','MP4 Files (*.mp4)';'*.avi','AVI Files (*.avi)'},'Choose an audio or video file');
if isequal(file,0)
isequal(path,0)
return;
else
[audio, fs] = audioread(fullfile(path,file));
handles.audio = audio;
handles.fs = fs;
axes(handles.original_audio);
plot(audio);
xlabel('Time (s)');
ylabel('Amplitude');
title('Original Audio');
guidata(hObject, handles);
end
% --- Executes on button press in play_button.
function play_button_Callback(hObject, eventdata, handles)
% hObject
handle to play_button (see GCBO)
% eventdata
reserved - to be defined in a future version of MATLAB
% handles
structure with handles and user data (see GUIDATA)
sound(handles.audio, handles.fs);
% --- Executes on button press in FFT_button.
function FFT_button_Callback(hObject, eventdata, handles)
% hObject
handle to FFT_button (see GCBO)
% eventdata
reserved - to be defined in a future version of MATLAB
% handles
structure with handles and user data (see GUIDATA)
audio = handles.audio;
fs = handles.fs;
L = length(audio);
NFFT = 2^nextpow2(L);
Y = fft(audio, NFFT)/L;
f = fs/2*linspace(0,1,NFFT/2+1);
axes(handles.FFT_plot);
plot(f, 2*abs(Y(1:NFFT/2+1)));
xlabel('Frequency (Hz)');
ylabel('|Y(f)|');
title('Single-Sided Amplitude Spectrum of y(t)');
% --- Executes on button press in scale_button.
function scale_button_Callback(hObject, eventdata, handles)
% hObject
handle to scale_button (see GCBO)
% eventdata
reserved - to be defined in a future version of MATLAB
% handles
structure with handles and user data (see GUIDATA)
audio = handles.audio;
fs = handles.fs;
scale_factor = str2double(get(handles.scale_factor_edit, 'String'));
scaled_audio = resample(audio, scale_factor, 1);
axes(handles.scaled_audio);
plot(scaled_audio);
xlabel('Time (s)');
ylabel('Amplitude');
title(['Scaled Audio (' num2str(scale_factor) 'x)']);
handles.scaled_audio = scaled_audio;
guidata(hObject, handles);
function scale_factor_edit_Callback(hObject, eventdata, handles)
% hObject
handle to scale_factor_edit (see GCBO)
% eventdata
reserved - to be defined in a future version of MATLAB
% handles
structure with handles and user data (see GUIDATA)
% Hints: get(hObject,'String') returns contents of scale_factor_edit as text
%
str2double(get(hObject,'String')) returns contents of scale_factor_edit as a double
% --- Executes during object creation, after setting all properties.
function scale_factor_edit_CreateFcn(hObject, eventdata, handles)
% hObject
handle to scale_factor_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
% --- Executes on button press in scaled_FFT_button.
function scaled_FFT_button_Callback(hObject, eventdata, handles)
% hObject
handle to scaled_FFT_button (see GCBO)
% eventdata
reserved - to be defined in a future version of MATLAB
% handles
structure with handles and user data (see GUIDATA)
scaled_audio = handles.scaled_audio;
fs = handles.fs;
L = length(scaled_audio);
NFFT = 2^nextpow2(L);
Y = fft(scaled_audio, NFFT)/L;
f = fs/2*linspace(0,1,NFFT/2+1);
axes(handles.scaled_FFT_plot);
plot(f, 2*abs(Y(1:NFFT/2+1)));
xlabel('Frequency (Hz)');
ylabel('|Y(f)|');
title('Single-Sided Amplitude Spectrum of y(t) (Scaled)');
```
这个GUI程序包括以下组件：
- load_button：加载音频文件
- play_button：播放音频文件
- FFT_button：将音频信号进行傅立叶变换，并绘制频谱图
- scale_factor_edit和scale_button：对音频信号进行尺度变换，并绘制缩放后的信号图
- scaled_FFT_button：对缩放后的信号进行傅立叶变换，并绘制频谱图
使用该程序，您可以通过以下步骤进行傅立叶变换和尺度变换的仿真设计：
1. 运行程序，并单击“load_button”按钮以加载音频文件。
2. 单击“play_button”按钮以播放音频文件。
3. 单击“FFT_button”按钮以进行傅立叶变换，并绘制频谱图。
4. 在“scale_factor_edit”文本框中输入缩放因子，并单击“scale_button”按钮以对音频信号进行尺度变换，并绘制缩放后的信号图。
5. 单击“scaled_FFT_button”按钮以对缩放后的信号进行傅立叶变换，并绘制频谱图。