In summary, the statistical results collected between 5:00 and 12:00 AM on April 2, 2025. For each injection, we calculate the frequency mean value 
(f_mean) and the peak height (P) of 194Pb ions for frames with t > 0.14 s, correct each injection’s frequency by subtracting f_mean, and only sum 
the 
spectra from injections with P > 100; moreover, by comparing the 194Pb82+ spectrum with that of 184Pt78+—whose isomer at 1.8 MeV (T1/2 = 1 ms) is 
clearly visible—the setup is demonstrated to be suitable for detecting an isomer with a lifetime of about 1 ms.
===================================================================
How to dod analysis and plot this result:
1. Add up injections and create accumulated spectrum.
(pyroot) gpuuser@appc256:/data.local/G22-00018_00203/scripts/OnlineDataAnalysisSystem/shift/20250331/data$ sh generate_data.sh /data.local/G22-
00018_00203/results/analyzers/RSA01 RSA01- 
'*.tiq_spectrogram.npz' 2025.04.02.05.00.00.000 2025.04.02.12.00.00.000 0.001 408.59e6 408.62e6 0.1 1

After run this command, you will create the accumulated spectrum under the folder with time stamp of start time and stop time.

2. Download the code "plot_fft.cxx" and plot the spectrum with following command:
...2025.04.02.05.00.00.000_2025.04.02.12.00.00.000$ root
   ------------------------------------------------------------------
  | Welcome to ROOT 6.32.10                        https://root.cern |
  | (c) 1995-2024, The ROOT Team; conception: R. Brun, F. Rademakers |
  | Built for linuxx8664gcc on Feb 12 2025, 01:50:41                 |
  | From tags/6-32-10@6-32-10                                        |
  | With                                                             |
  | Try '.help'/'.?', '.demo', '.license', '.credits', '.quit'/'.q'  |
   ------------------------------------------------------------------

root [0] .L plot_fft.cxx
root [1] plot_fft("2025.4.2 5:00~12:00",411.14e6,411.18e6,0,100)

// plot_fft.C
// This macro opens the ROOT file "combine_injection.root", retrieves the TH2D histogram
// named "FFT_accumulated", and draws it on a canvas with a logarithmic Z-axis.
// The canvas size is set to 800 x 1000, with the top margin set to 0.05 and the right margin increased.
// Additionally, the histogram title and statistics box are removed.
// You can specify the frequency (x-axis) and time (y-axis) ranges via the function parameters.

void plot_fft(const char* canvasTitle = "FFT Accumulated",double x_min = 0, double x_max = 0, double y_min = 0, double y_max = 0) {
    // Open the ROOT file
    TFile* file = TFile::Open("combine_injection.root");
    if (!file || file->IsZombie()) {
        std::cerr << "Error: Unable to open file combine_injection.root" << std::endl;
        return;
    }
    
    // Retrieve the TH2D histogram named "FFT_accumulated"
    TH2D* hist = dynamic_cast<TH2D*>(file->Get("FFT_accumulated"));
    if (!hist) {
        std::cerr << "Error: Histogram 'FFT_accumulated' not found in the file" << std::endl;
        file->Close();
        return;
    }
    
    // Remove the histogram title
    hist->SetTitle("");
    
    // Remove the statistics box
    gStyle->SetOptStat(0);
    
    // If valid ranges are provided (non-zero and x_min < x_max, etc.), apply them to the axes
    if (x_max > x_min) {
        hist->GetXaxis()->SetRangeUser(x_min, x_max);
    }
    if (y_max > y_min) {
        hist->GetYaxis()->SetRangeUser(y_min, y_max);
    }
    
    // Create a canvas with size 800 x 1000
    TCanvas* canvas = new TCanvas("canvas", canvasTitle, 800, 1000);
    
    // Adjust canvas margins: top margin 0.05, increased right margin (e.g., 0.15)
    canvas->SetTopMargin(0.05);
    canvas->SetLeftMargin(0.12);
    canvas->SetRightMargin(0.15);
    
    // Set axis titles (if desired, you can modify these)
    hist->GetXaxis()->SetTitle("Frequency [Hz]");
    hist->GetYaxis()->SetTitle("Time [s]");
    hist->GetZaxis()->SetTitle("Amplitude (arbitrary units)");
    hist->GetZaxis()->SetTitleOffset(1.2);
    
    // Set log scale for the Z-axis (color scale)
    canvas->SetLogz();
    
    // Draw the histogram using the "COLZ" option to display a color palette
    hist->Draw("COLZ");
    
    // Update the canvas to show the plot
    canvas->Update();
    // Add the canvas title at the top using TLatex
    TLatex latex;
    latex.SetNDC();             // Use normalized coordinates
    latex.SetTextAlign(22);     // Center alignment
    latex.SetTextSize(0.04);      // Adjust text size as needed
    // Draw the title at (x=0.5, y=0.95) in normalized device coordinates
    latex.DrawLatex(0.5, 0.98, canvasTitle);
    
    // Optionally, you can save the canvas as an image file (e.g., PNG)
    // canvas->SaveAs("FFT_accumulated.png");
}