Raised Cosine FAQ
Raised-Cosine filters are commonly used in digital data modems. Here, we answer some RC filter Frequently Asked Questions (FAQs).
1. Raised Cosine Filter Basics
1.1 What are Raised-Cosine (RC) Filters?
1.2 Why are Raised-Cosine Filters used?
1.4 What are Root-Raised-Cosine (RRC) filters?
1.5 Why are both RC filters and RRC filters used?
2.1 How do I implement RC and RRC filters?
RC and RRC filters are generally implemented as FIR (Finite Impulse Response) filters. The linear-phase property of FIR filters makes them. Also, FIR filters are easy-to-implement and efficient. See our FIR Filter FAQ for more FIR information.
2.2 What are the parameters for RC and RRC filters?
The frequency responses of RC and RRC filters are fully specified by a single paramter, the "rolloff factor"; this is a number between 0.0 and 1.0. It often is symbolized as either alpha or beta. But to design a FIR filter that will actually implement an RC or RRC response, you also need two more parameters, the number of taps ("NTaps"), and the number of samples per symbol ("
2.3 How do I design RC and RRC filters?
RC and RRC filters can be designed in either the time domain (FIR impulse reponse) or the frequency domain (FIR frequency response). To design in the time domain, calculate the FIR filter coefficients directly from a formula (see below). To design in the frequency domain, use the definition of the RC or RRC response to fill an array representing the RC/RRC frequency response. Then, use the Inverse Discrete Fourier Transform (IDFT) to calculate the FIR filter's impulse response (coefficients).
2.4 What are some formulas for a Raised-Cosine and Root-Raised-CosineFilters?
See dspGuru's Raised-Cosine and Root-Raised-Cosine Formulas page.
2.4 What FIR filter design programs can design RC and RRC filters?