Generating 7-bit and 13-bit Barker Codes with Spectral Analysis

To generate 7-bit or 13-bit Barker codes in MATLAB, employ the following implementation approach. Begin by creating a Barker code generator object using the `comm.BarkerCode` function from the Communications System Toolbox, specifying the desired code length through the 'Length' property parameter. The algorithm generates pseudorandom sequences with optimal autocorrelation properties using predefined Barker code polynomials stored in MATLAB's signal processing library. For code generation, utilize the object's default method (equivalent to the legacy `step` function) to output the bipolar (±1) Barker sequence. The implementation handles the mapping between polynomial coefficients and the actual sequence generation automatically. To analyze spectral characteristics, compute the power spectral density using the `pwelch` function with appropriate windowing parameters (e.g., Hamming window) and FFT length for accurate frequency resolution. Alternatively, you can apply `fft` directly to the code sequence followed by `abs().^2` operation for power spectrum calculation. Visualization is achieved through MATLAB's plotting functions like `plot` or `stem` for time-domain representation, and `semilogy` for logarithmic frequency-domain displays. This methodology provides valuable insights into Barker codes' spectral properties, including their main lobe width and sidelobe suppression characteristics, which are critical for performance evaluation in radar pulse compression, synchronization systems, and spread-spectrum communications. The entire process demonstrates MATLAB's capabilities in digital signal processing workflow from sequence generation to analytical visualization.