MATLAB Source Code Example for Raised Cosine Roll-Off System Implementation

Implementation of Raised Cosine Roll-Off System in MATLAB The Raised Cosine Filter is a fundamental pulse shaping technique in digital communications used to minimize Inter-Symbol Interference (ISI). Its core principle involves balancing spectral efficiency and interference immunity by adjusting the roll-off factor (β). Implementation Approach: Parameter Definition: Key parameters must be defined including sampling rate, symbol period, and roll-off factor β (0≤β≤1). The roll-off factor directly controls the filter's transition bandwidth - β=0 represents an ideal low-pass filter, while β=1 yields maximum bandwidth. Time-Domain Response Generation: Generate time-domain pulses using MATLAB's built-in `rcosdesign` function or manual calculation formulas. The function accepts parameters for β value, filter length, and oversampling factor, implementing the mathematical formula: h(t) = sinc(t/T) * cos(πβt/T) / [1 - (2βt/T)²]. Frequency-Domain Analysis: Perform FFT transformation to examine spectral characteristics and verify compliance with Nyquist criterion for zero ISI. The frequency response should exhibit even symmetry about the Nyquist frequency. Application Scenario: Typically used in conjunction with matched filters - pulse shaping at the transmitter and matched filtering at the receiver to optimize signal-to-noise ratio (SNR). The implementation requires careful sampling point alignment to maintain orthogonality. Extended Considerations: Practical systems require balancing β selection: smaller β values improve bandwidth efficiency but reduce timing tolerance; larger β values enhance interference resistance at the cost of increased bandwidth consumption. In multi-carrier systems (e.g., OFDM), raised cosine filtering may be replaced by other techniques, but it remains a classical solution for single-carrier modulation schemes. This solution can be rapidly validated using MATLAB's built-in functions, making it suitable for communication system simulations and educational demonstrations. Key functions include `rcosdesign` for filter design, `fft` for frequency analysis, and `conv` for simulating filtering operations.