multiratewebinar_oct2005_english.rar_english_软件无线电

%% Design of Multistage Decimators % This demo shows how to get progressively more efficient designs for % decimators given a set of design specifications. We start with a % single-section polyphase design, and then move to a multistage decimation % design. We then allow for transition-band aliasing and design a % multistage Nyquist filter. Finally, we use a CIC filter for the first % stage of a multistage design to obtain the most efficient implementation. % % Author(s): Ricardo A. Losada % Copyright 2005 The MathWorks, Inc. %% Design Specifications % These are the design specifications we will use throughout the demo Fs = 100e6; % Input sampling frequency 100 MHz Fc = 3.125e6; % Cutoff frequency 3.125 MHz Fp = 2.925e6; % Passband-edge frequency 2.925 MHz Fst = 3.325e6; % Stopband-edge frequency 3.325 MHz TW = Fst-Fp; % Transition bandwidth 0.4 MHz Ap = 1; % Passband ripple 1 dB (peak to peak) Ast = 80; % Minimum attenuation in stopband 80 dB %% Creation of an Object to Hold the Specifications % We can generate an object that groups all specifications with the % following command: Hfd = fdesign.decimator(M,'lowpass','Fp,Fst,Ap,Ast',... Fp,Fst,Ap,Ast,Fs); %% Design of the Decimation Filter % In order to design the single-stage filter, we use the 'design' command % and we specify that we want an optimal equiripple design. Hm_eq = design(Hfd,'equiripple'); info(Hm_eq) %% % The resulting filter has 642 coefficients. Since we use a polyphase % implementation, the cost of implementing this decimator is 43 % multiplications for each input sample. fvtool(Hm_eq) %% Spectrum of the Decimated Signal % Assuming that the original input signal occupies the entire Nyquist % interval in a uniform manner, the spectrum of the filtered signal % acquires the shape of the frequency response of the filter. When the % filtered signal is downsampled, the spectral replicas are positioned % adjacent to each other without superimposing themselves above the 80 dB % allowed. This way, no significant aliasing occurs. [H,f]=freqz(Hm_eq,8192,Fs,'whole'); figure plot(f-Fs/2,20*log10(abs(fftshift(H)))) hold on, plot(f-Fs/2+Fs/M,20*log10(abs(fftshift(H))),'r-') plot(f-Fs/2-Fs/M,20*log10(abs(fftshift(H))),'k-') grid on xlabel(' Frequency (Hz)') ylabel('dB') axis([-1e7 1e7 -100 5]) title('Spectrum of decimated signal') legend('Baseband spectrum','First positive replica','First negative replica') %% Creation of a Simulink Model % With a simple command, we can generate a Simulink model for the decimator % we have designed: block(Hm_eq,'Destination','new') %% Multistage Design % We will now see how to increase the computational efficiency by designing % a multistage filter for the same design specifications. Hm_multi = design(Hfd,'multistage'); fvtool(Hm_multi) %% % The result of this design are two decimation filters connected in series. % Partitioning the design in multiple stages reduces the computational % cost. For this design, the cost is 14.6 multiplications for each input % sample (on average). %% Visualizing the Multistage Filter in Simulink % To generate a Simulink model for this new design, we use the same command % that we have invoked previously: block(Hm_multi,'Destination','new') %% Design of Nyquist Filters for Decimation % Given the design specifications, it is possible to increment the % decimation factor in such a way that the spectral replicas of the % filtered signal, after downsampling, superimpose themselves only in the % transition band of the filter. This way we can increase the efficiency of % the design, using Nyquist filters, without incurring in aliasing in the % band of interest. As an example, if we had an audio signal sampled at a % very high frequency and we'd like to reduce the sampling frequency to % 44.1 kHz, we could allow superposition of spectral replicas in the % frequency band between 20 kHz and 22.05 kHz. The aliasing the occurs in % such band is not important since this band is not part of the audible % band of the human ear. M2 = 16; % Increased decimation factor Band = M2; % The band should be equal to the decimation factor Hfn = fdesign.decimator(M2,'nyquist',Band,... 'TW,Ast',TW,Ast,Fs); %% % Note that the cutoff frequency of these specifications is given by % Fs/(2*Band) which corresponds to the same cutoff frequency that we % originally had. In this manner we ensure that the design specifications % have not changed. We can also see that in this case we are not specifying % the passband ripple. It is not possible to specify the passband ripple % with Nyquist designs. However, as we will see, the resulting ripple will % be much smaller than the ripple required originally (1 dB peak to peak). %% Multistage Nyquist Design! % When we invoke the multistage command in this case, each one of the % stages of the multistage filter will be a Nyquist filter (because Hfn % specifies that we want to design a decimator using Nyquist filters). Hn_multi = design(Hfn,'multistage'); fvtool(Hn_multi) %% % The result is 4 halfband filters connected in series. Each halfband % filter is very efficient since (approximately) half of its coefficients % are equal to zero, so that it is only necessary to use half of the filter % length. In this example the computational cost of this design is 10.31 % multiplications for each input sample. %% Spectrum of the Signal Decimated with Nyquist Filters % Similarly to the previous case, we can visualize the superposition of the % spectral replicas of the decimated signal, in this case using Nyquist % filters. As we have said, in this case, the replicas superimpose % themselves more than in the previous case. However, there is no % superposition beyond the 80 dB allowed in regions other than the % transition bands. This shows that the band of interest does not incur in % significant aliasing. [H,f]=freqz(Hn_multi,8192,Fs,'whole'); figure plot(f-Fs/2,20*log10(abs(fftshift(H)))) hold on, plot(f-Fs/2+Fs/M2,20*log10(abs(fftshift(H))),'r-') plot(f-Fs/2-Fs/M2,20*log10(abs(fftshift(H))),'k-') grid on xlabel(' Frequency (Hz)') ylabel('dB') axis([-1e7 1e7 -100 5]) title('Spectrum of the signal decimated with Nyquist filters') legend('Baseband spectrum','First positive replica','First negative replica') %% Multistage Design Using CIC Filters % Finally, in order to obtain an extremely efficient decimator, we will use % a CIC filter in thefirst stage of a multistage design. First we will % design a two-stage decimator and we will see that we will obtain an % efficiency comparable to the design with Nyquist filters. We will then % move to a three-stage design and this way we will obtain the most % efficient design of all designs in this demo. %% Design of the CIC Filter % The global decimation factor is 16. We choose a decimation factor of 4 % for the CIC filter leaving a factor of 4 for the remaining stages. M1 = 4; D = 1; % Differential delay Hd1 = fdesign.decimator(M1,'cic',D,Fp,Ast,Fs); Hcic = design(Hd1,'multisection'); %% Design of the Second Stage: Compensation Filter % The compensation filter must be designed according to the design % specifications of the CIC filter to compensate. For this reason, we use % here the number of sections of the CIC filter as well as the differential % delay as design parameters. M2 = 4; Nsecs = Hcic.NumberOfSections; Hd2 = fdesign.decimator(M2,'ciccomp',D,Nsecs,Fp,Fst,Ap,Ast,Fs/M1); Hcomp = design(Hd2,'equiripple'); Hcas = cascade(Hcic,Hcomp); % series connection of the two filters %% % This design requires 10.44 multiplications for each input sample. This % is not an improvement in comparison to the multistage Nyquist design. % However, we can improve this further by using three stages instead of % two. %% Alternate Design, Second Stage: Compensation Filter % We decide to design a compensation filter with a decimation factor of % two. M3 = 2; Hd3 = fdesign.decimator(M3,'ciccomp',D,... Nsecs,Fp,Fs/(M1*M3)-Fp