## Design Raised Cosine Filters Using MATLAB Functions

### Section Overview

The `rcosdesign` function designs (but does not apply) filters of these types:

• Finite impulse response (FIR) raised cosine filter

• FIR square-root raised cosine filter

The function returns the FIR coefficients as output.

### Example Designing a Square-Root Raised Cosine Filter

For example, the command below designs a square-root raised cosine FIR filter with a roll-off of 0.25, a filter span of 6 symbols, and an oversampling factor of 2.

```sps = 2; num = rcosdesign(0.25, 6, sps)```
```num = Columns 1 through 7 -0.0265 0.0462 0.0375 -0.1205 -0.0454 0.4399 0.7558 Columns 8 through 13 0.4399 -0.0454 -0.1205 0.0375 0.0462 -0.0265```

Here, the vector `num` contains the coefficients of the filter, in ascending order of powers of z-1.

You can use the `upfirdn` function to filter data with a raised cosine filter generated by `rcosdesign`. The following code illustrates this usage:

```d = 2*randi([0 1], 100, 1)-1; f = upfirdn(d, num, sps); eyediagram(f(7:200),sps)``` The eye diagram shows an imperfect eye because `num` characterizes a square-root filter.