數字上變頻仿真設計

💡 我的畢業設計題目為多頻點數字上變頻器，因此先做了 DUC 的仿真，目標是將 48k 採樣率的音頻信號進 28 插值到 6.144M 的採樣率，並將其做 AM 調製後發射出去。

Matlab 仿真#

基本參數生成#

%% base data gen
fs_base=48e3;               % Sampling rate at input DUC
upsample_L=128;
fs_duc=fs_base*upsample_L;  % Sampling rate at output DUC
Fc=5e6;                     % Carrier Frequency
Fpass=20e3;                 % AM baseband width
Fstop=30e3;                 % Stopband
Ap=0.1;                     % Passband ripple
Ast=60;                     % Stopband attenuation
T = 1;                      % 持續時間
t = 0:1/fs_base:T-1/fs_base;% 時間向量
outputframe=1;
N1_cycle = 128;
N2_cycle = 64;
N3_cycle = 32;
N4_cycle = 16;

系統的整體速率為 48k×128=6.144M，通過使能信號進行採樣率的變換。信號輸出為流式輸出，幀大小為 1 。

第一级低通 FIR 插值濾波器#

%% First Lowpass Fir Interpolator

lowpassParams.FsIn=fs_base;
lowpassParams.InterpolationFactor = 2;
lowpassParams.FsOut=lowpassParams.FsIn*lowpassParams.InterpolationFactor;

lowpassSpec = fdesign.interpolator(lowpassParams.InterpolationFactor, ...
    'lowpass','Fp,Fst,Ap,Ast',Fpass,Fstop,Ap,Ast,lowpassParams.FsOut);
lowpassFilt = design(lowpassSpec,'SystemObject',true)

輸入信號採樣率為基帶速率，輸出信號採樣率為基帶速率 × 插值因子，通過 fdesign.interpolator 設計濾波器係數，濾波器的幅頻響應如下：

第二级低通半帶插值濾波器#

%%
% *Second Halfband Interpolator*
% 
% The halfband filter provides efficient interpolation by two. Halfband 
% filters are efficient for hardware because approximately half of their 
% coefficients are equal to zero, and those multipliers are excluded from
% the hardware implementation.   

 hbParams.FsIn = lowpassParams.FsOut;
 hbParams.InterpolationFactor = 2;
 hbParams.FsOut = lowpassParams.FsOut*hbParams.InterpolationFactor;
 hbParams.TransitionWidth = hbParams.FsIn - 2*Fstop; % 通帶，由於插值後頻譜會根據輸入信號的採樣率做周期延拓
                                                     % 減去 2 倍的 Fstop 是為了確保插值後保留的信號帶寬不會引入混疊，同時保證足夠的衰減
 hbParams.StopbandAttenuation = Ast;
 
 hbSpec = fdesign.interpolator(hbParams.InterpolationFactor,'halfband', ...
          'TW,Ast', ...
          hbParams.TransitionWidth, ...
          hbParams.StopbandAttenuation, ...
          hbParams.FsOut);

hbFilt = design(hbSpec,'SystemObject',true)

半帶濾波器的通帶為輸入信號採樣率減去兩倍的截止頻率，確保插值後產生的頻譜延拓的頻帶都能被濾除，不會引入混疊，同時保證了足夠的衰減。

半帶濾波器的幅頻響應及兩級濾波器級聯的響應如下：

第三級 CIC 補償濾波器#

由於 CIC 插值濾波器通帶內不平坦，因此要加入補償濾波器。

% *CIC Compensation Interpolator*
% 
% Because the magnitude response of the last CIC filter has a significant 
% _droop_ within the passband region, the example uses an FIR-based droop 
% compensation filter to flatten the passband response. The droop 
% compensator has the same properties as the CIC interpolator. This filter
% implements interpolation by a factor of two, 
% so you must also specify bandlimiting characteristics for the filter.
% Also, specify the CIC interpolator properties that are used for this
% compensation filter as well as the later CIC interpolator. 
% 
% Use the |design| function to return a filter System object with the 
% specified characteristics. 

compParams.FsIn = hbParams.FsOut;
compParams.InterpolationFactor = 2;                                 % CIC compensation interpolation factor
compParams.FsOut = compParams.FsIn*compParams.InterpolationFactor;  % New sampling rate
compParams.Fpass = 1/2*compParams.FsIn + Fpass;                     % CIC compensation passband frequency
compParams.Fstop = 1/2*compParams.FsIn + 1/4*compParams.FsIn;       % CIC compensation stopband frequency
compParams.Ap = Ap;                                                 % Same passband ripple as overall filter
compParams.Ast = Ast;                                               % Same stopband attenuation as overall filter
N = 31;                                                             % 32 tap filter to take advantage of 16 cycles between input 

cicParams.InterpolationFactor = 16;  % CIC interpolation factor
cicParams.DifferentialDelay = 1;    % CIC interpolator differential delayb   
cicParams.NumSections = 4;          % CIC interpolator number of integrator and comb sections

compSpec = fdesign.interpolator(compParams.InterpolationFactor,'ciccomp', ...
           cicParams.DifferentialDelay, ...
           cicParams.NumSections, ...
           cicParams.InterpolationFactor, ...
           'N,Fp,Ap,Ast', ...
           N,compParams.Fpass,compParams.Ap,compParams.Ast, ...
           compParams.FsOut);
compFilt = design(compSpec,'SystemObject',true)

補償濾波器的通帶和阻帶頻率的設定原因如下：

compParams.Fpass = 1/2 * compParams.FsIn + Fpass:
這裡的通帶頻率 Fpass 的設定是基於輸入採樣率 compParams.FsIn。CIC 濾波器通常對頻率響應的衰減從 FsIn/2 開始變得明顯，所以補償濾波器的通帶設定為 FsIn/2 + Fpass，這樣可以確保補償濾波器修正 CIC 濾波器在通帶內的增益，特別是在高頻部分。
compParams.Fstop = 1/2 * compParams.FsIn + 1/4 * compParams.FsIn:
阻帶頻率的設定為 FsIn/2 + 1/4 * FsIn，其目的是進一步保證在插值之後，信號頻譜的帶外部分能夠被足夠衰減，防止混疊現象的發生。由於插值過程會把輸入信號的頻譜周期性延拓，濾波器的阻帶需要覆蓋到這些延拓部分，以保證無用信號被濾除。

補償濾波器的幅頻響應圖如下：

第四級 CIC 插值濾波器#

%%
% *CIC Interpolator*
% 
% The last filter stage is implemented as a CIC interpolator because of this
% type of filter's ability to efficiently implement a large decimation factor.
% The response of a CIC filter is similar to a cascade of moving average 
% filters, but a CIC filter uses no multiplication or division. As a result,
% the CIC filter has a large DC gain.
cicParams.InterpolationFactor = 16;  % CIC interpolation factor
cicParams.DifferentialDelay = 1;    % CIC interpolator differential delayb   
cicParams.NumSections = 4;          % CIC interpolator number of integrator and comb sections

cicParams.FsIn = compParams.FsOut;
cicParams.FsOut = cicParams.FsIn*cicParams.InterpolationFactor;

cicFilt = dsp.CICInterpolator(cicParams.InterpolationFactor, ...
          cicParams.DifferentialDelay,cicParams.NumSections)