一、简介

数字信号是对连续变化的模拟信号进行抽样、量化和编码产生的，称为PCM（Pulse Code Modulation），即脉冲编码调制。
脉冲编码调制就是把一个时间连续，取值连续的模拟信号变换成时间离散，取值离散的数字信号后在信道中传输。脉冲编码调制就是对模拟信号先抽样，再对样值幅度量化，编码的过程。
抽样，就是对模拟信号进行周期性扫描，把时间上连续的信号变成时间上离散的信号。该模拟信号经过抽样后还应当包含原信号中所有信息，也就是说能无失真的恢复原模拟信号。它的抽样速率的下限是由抽样定理确定的。抽样速率采用8Kbit/s。
量化，就是把经过抽样得到的瞬时值将其幅度离散，即用一组规定的电平，把瞬时抽样值用最接近的电平值来表示。
一个模拟信号经过抽样量化后，得到已量化的脉冲幅度调制信号，它仅为有限个数值。
编码，就是用一组二进制码组来表示每一个有固定电平的量化值。然而，实际上量化是在编码过程中同时完成的，故编码过程也称为模/数变换，可记作A/D。
话音信号先经防混叠低通滤波器，进行脉冲抽样，变成8KHz重复频率的抽样信号（即离散的脉冲调幅PAM信号），然后将幅度连续的PCM信号用“四舍五入”办法量化为有限个幅度取值的信号，再经编码后转换成二进制码。对于电话，CCITT规定抽样率为8KHz，每抽样值编8位码，即共有2^8=256个量化值，因而每话路PCM编码后的标准数码率是64kb/s。为解决均匀量化时小信号量化误差大，音质差的问题，在实际中采用不均匀选取量化间隔的非线性量化方法，即量化特性在小信号时分层密，量化间隔小，而在大信号时分层疏，量化间隔大。

均匀量化的小信号的信噪比小。
非均匀量化: 由于一些信源信号, 如语音信号, 小幅度信号发生的概率大于大幅度信号的概率, 采用非均匀量化(即小幅度信号的量化步长小于大幅度信号的的量化步长) 效果更好好 (表现在语音信号上, 可以使信号具有足够的信噪比)。

非均匀量化特性通常是把信号通过一个非线性的设备, 小信号幅度进行放大, 大信号幅度进行压缩, 再通过均匀量化实现。

二、源代码

function varargout = PCM(varargin)
% PCM M-file for PCM.fig
%      PCM was designed in order to show how PCM works
%
%      To simplify the undesrtanding of this method, the program first takes
%      a sine wave. Then you can choose a sampling scheme, and you can see
%      the output of the sampler. You can choose one out of three sampling 
%      methods.
%      If you choose natural sampling; then you will have the chance to modify
%      the sampling window, and see the effects of this change in the output of
%      the sampler.
%
%      Once you got the sampled signal you can quantize it by a method that is 
%      known as two rules and an alorithm.
%      The option Squeezing and Stretching shows the best G(x) tha minimizes 
%      the MSE. You can better understand this using the book
%      Telecommunications Demystified written by Carl Nassar. You can find
%      information about this on Chapter four of that book. 
%      You can edit the bit's number and the number of iterations of the
%      algorithm. The bigger the number of bits, the smaller the MSE.
%      The picture shows the signal after quantization, the first iteration
%      in the quantization process and the output of the quantizer
%      
%      Then, by pressing the Bit Stream button you will see the PCM output
%      of the signal that you have selected in the input area.
%      
%      Everytime you change something, you must push the button that is
%      related with the change you have just made. For example if don't
%      want to work anymore with the sine wave and you choose the random
%      signal, then you have to push the plot button in order to see the
%      plot of the random signal, and if you change of sampling method you
%      have to push the sampling button, when you changhe the sampling 
%      window. So if you change the number of codewords or the number of 
%      the iterations you will have to press the quantize button again. 

% Edit the above text to modify the response to help PCM

% Last Modified by GUIDE v2.5 14-Mar-2021 12:32:35

% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...
                   'gui_Singleton',  gui_Singleton, ...
                   'gui_OpeningFcn', @PCM_OpeningFcn, ...
                   'gui_OutputFcn',  @PCM_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 PCM is made visible.
function PCM_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 PCM (see VARARGIN)

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

% Update handles structure
guidata(hObject, handles);

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


% --- Outputs from this function are returned to the command line.
function varargout = PCM_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 pushbutton2.
function pushbutton2_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton2 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if (get(handles.radiobutton2,'Value') == get(handles.radiobutton2,'Max')) % Verifies if Sine wave was selected
    t=linspace(0,1,60); % Creates the time variable from 0 to 1 with a length of 60 or 60 points
    y=sin(2*pi*t); % Creates a sine wave of frequency 1 with the t vector 
    axes(handles.axesanalog) % Select the proper axes  
    plot(t,y); 
    xlabel('Time');
    ylabel('Amplitude');
    grid on;
elseif (get(handles.radiobutton3,'Value') == get(handles.radiobutton3,'Max')) % Verifies if Random signal was selected
    t=linspace(0,60,60); % Creates the time variable from 0 to 60 with a length of 60 or 60 points
    y=rand([1 60]); % Creates a random signal of length 60 or with 60 points
    axes(handles.axesanalog) % Select the proper axes    
    plot(t,y);
    xlabel('Time');
    ylabel('Amplitude');
    grid on;
end
handles.amp=y; % Saves the input signal y in the amp variable at the handles structure
handles.time=t; % Saves the input signal t in the time variable at the handles structure
guidata(gcbo,handles); % Save the changes made to the handles structure

% --- Executes on button press in pushbutton3.
function pushbutton3_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton3 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
close; % Close the application

% --- Executes on button press in pushbutton4.
function pushbutton4_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton4 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if (get(handles.radiobutton4,'Value') == get(handles.radiobutton4,'Max'))
    t=handles.time; % recover the saved variable t from the handles structure
    y=handles.amp; % recover the saved variable y from the handles structure
    p=ones(1, length(t)); % creates a vector containing only ones 
    outideal=p.*y; % Multiplies the two vectors to get the output of an ideal sampler
    axes(handles.axessampled) % Select the proper axes
    stem(t,outideal,'ro');
    xlabel('Time');
    ylabel('Amplitude');
    grid on;
    handles.signal=outideal;
    guidata(gcbo,handles);
elseif (get(handles.radiobutton5,'Value') == get(handles.radiobutton5,'Max'))
    t=handles.time; % recover the saved variable t from the handles structure
    y=handles.amp; % recover the saved variable y from the handles structure
    p=ones(1, length(t)); % creates a vector containing only ones 
    outhold=p.*y; % Multiplies the two vectors to get the output of an ideal sampler
    axes(handles.axessampled) % Select the proper axes
    stairs(t,outhold,'r'); %Plot the signal in a stairs shape making it looks like a zero order hold sampler
    xlabel('Time');
    ylabel('Amplitude');
    grid on;
    handles.signal=outhold;
    guidata(gcbo,handles);
elseif (get(handles.radiobutton6,'Value') == get(handles.radiobutton6,'Max'))
    t=handles.time; % recover the saved variable t from the handles structure
    y=handles.amp; % recover the saved variable y from the handles structure
    test1=eval(get(handles.edit1,'String')); % Evals the value that is contained in the Edit 1
    if isnan(test1) % Test if it is a number or not. If not it displays an error message
        errordlg('You must enter a numeric value','Bad Input','modal')
    end
    lenp=length(t)/length(test1); %Calculates the length of the vector so it can make it a periodic signal with the 
    %right size so it can work properly
    p=ones(1, lenp); %  Creates a vector of only ones of lenght lenp 
    per=test1'*p; % Creates a matrix, containing lenp times the vector test1
    per=per(:); % Concatenates the columns of the matrix so it becomes a vector
    outnormal=per'.*y; % Multiplies the two vectors to get the output of a normal sampler
    axes(handles.axessampled) % Select the proper axes
    plot(t,outnormal,'r');
    xlabel('Time');
    ylabel('Amplitude');
    grid on;
    handles.signal=outnormal;
    guidata(gcbo,handles);
end

function edit1_Callback(hObject, eventdata, handles)
% hObject    handle to edit1 (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 edit1 as text
%        str2double(get(hObject,'String')) returns contents of edit1 as a double

% --- Executes during object creation, after setting all properties.
function edit1_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit1 (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

三、运行结果

四、备注

版本：2014a