Rate signal method

Research and Implementation of Key Technologies of Satellite Signal Spectrum Monitoring System - Dong Xue

Implementation of Rate Signal Method

thought

The main idea here is to pay attention to the details of index, remember to subtract 1.

Instead of using czt to refine the spectrum, zoomfft is used to refine the spectrum. This method is easier to implement in engineering. All spectrum transformations can be done only by moving arrays, without exponential calculation. Reduce the amount of calculation. The zoomfft principle can be referred to. Here

Question: Why the refined results are not correct and deviate from the estimated results is still unclear. It is possible that approximation in some places will lead to this result.

source code

% Test Rate Signal Method
clc
clear all
close all

sr = 1000;
fs = 8e3;

N = sr;

srcData = randsrc(1, N, [0:3]);
modData = pskmod(srcData, 4);
% Pulse shaping filter
ipoint = fs / sr;
span = 21;
pointFir = span * ipoint;
upData = upsample(modData, ipoint);
sendPulser = rcosdesign(0.5, span, ipoint, 'sqrt');
sendData = conv(upData, sendPulser);
% Form the transmitting signal, here mainly subtract the time delay caused by convolution. See Digital Signal Processing for details.
sendData = sendData(pointFir/2 + 1 : end - pointFir/2);


% Computation rate signal
for i = 1:length(sendData) %Get the Rate Signal
    if(i<length(sendData))
        res(i) = (norm(sendData(i+1)-sendData(i)))*fs; %norm(x)seek x The 2 norm  
    end
end

% Find the maximum power length of 2 less than length
n=nextpow2(length(res)); %Find out 2^n >= length(res) Of n value
n=n-1;
len=2^n;
% Change in data length and resolution
df = fs / len;

res=res(1:len);
freResponse = fft(res);
ampResponse = abs(freResponse);
% Display spectrum, after removing 0 frequency, the largest frequency component is the coarse estimation of symbol rate.
plot((0:length(ampResponse)-1)*df, ampResponse);
% Removal of 0 frequency
a = ampResponse(1);
ampResponse(1) = 0;
[~, index] = max(ampResponse);
ampResponse(1) = a;
% Here's a detail. Attention matlab From 1 to index Start acquiring, and you'll miss 0.
% So our index When turning frequency, remember-1
coarseSymbolRate = (index-1) * df


% Thinning spectrum
% Set the refinement factor, which needs to be set to 2 n pow
m = 64;
n0 = len / m;

% Move the right spectrum to the right of the zero frequency
n02 = n0 / 2;
right = index + n02;
tmp = right + 1 - index;
assert(tmp == n02+1);
freResponse(1:tmp) = freResponse(index:right);
% Left spectrum to negative frequency
left = index - n02 + 1;
tmp = n02 - 1;
assert(tmp == (index - left));
freResponse((length(freResponse) - tmp+1):end) = freResponse(left:(index-1));
freResponse(right+1:end-tmp) = 0;

% ifft
timeSignal = ifft(freResponse);
% Down sampling
downTimeSignal = downsample(timeSignal, m);
downTimeSignalFreqResponse = fft(downTimeSignal, len);
leftFreq = (left-1) * df;
rightFreq = (right-1) * df;
downTimeSignalFreqResponse = circshift(downTimeSignalFreqResponse, floor(len/2));
f = linspace(leftFreq, rightFreq, len);
ampDownTimeSignalFreqResponse = abs(downTimeSignalFreqResponse);
figure()
plot(f, ampDownTimeSignalFreqResponse);
[~, index] = max(ampDownTimeSignalFreqResponse);
df = (rightFreq - leftFreq) / len;
accurateSr = (index - 1) * df + leftFreq
% The maximum point in the spectrum is the result.