How to use this with GaussianWaves articles
Pick symbol rate, units, and roll-off α. The shareable link stores rate, unit, and alpha so a lab partner opens the same bandwidth design.
- Why α matters: Nyquist criterion for zero ISI and raised-cosine pulse shaping.
- Matched filter: implement Tx/Rx SRRC pair in matched filter + SRRC.
- Timing: after pulse shaping, recover samples with QPSK symbol timing recovery.
Related tutorials
Rate, units, and roll-off α stay in the shareable link.
- Raised-cosine shaping: why α exists
- Matched filter + SRRC: Tx/Rx pair
FAQ
What bandwidth does this report? Two-sided occupancy about $latex R_s(1+\alpha)$ for symbol rate $latex R_s$.
Is RRC the same as RC? RRC is the square-root split of a raised-cosine — cascade Tx and Rx RRC to get RC.
Understanding Root-Raised Cosine (RRC) Pulse Shaping Filters
In digital transmission systems, Root-Raised Cosine (RRC) pulse shaping filters are deployed at both the transmitter and receiver ends to limit occupied transmission bandwidth and eliminate Inter-Symbol Interference (ISI) in accordance with the Nyquist ISI Criterion.
Nyquist Criterion & RRC Cascade
To eliminate ISI at optimum sampling instants, the combined transmitter and receiver filter cascade must yield a full Raised Cosine (RC) magnitude response:
- $$H_{\text{total}}(f) = H_{\text{RRC, Tx}}(f) \times H_{\text{RRC, Rx}}(f) = H_{\text{RC}}(f)$$
Splitting the filter equally across both ends ensures matched filtering performance, maximizing output Signal-to-Noise Ratio (SNR) in AWGN channels.
Occupied & Excess Bandwidth Formulas
The total bandwidth ($B_{\text{total}}$) occupied by an RRC-filtered signal depends on symbol rate ($R_s$) and the roll-off factor ($\alpha \in [0, 1]$):
- $B_{\text{total}} = R_s(1 + \alpha)$
- $B_{\text{excess}} = \alpha \, R_s$
Where $\alpha = 0$ represents the theoretical minimum Nyquist brick-wall filter, and $\alpha = 1$ expands the occupied bandwidth by 100%.