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Phase relationship between sine and cosine

Square Root Raised Cosine Filter in Python

November 10, 2021

Introduction

The square root raised cosine (SRRC) filter is used as a pulse shaping filter [harris2021, p.87] in many linear modulations such as BPSK, QPSK, and 16-QAM. Frustratingly neither SciPy or NumPy have a square-root raised cosine (SRRC) filter. Mathuranathan Viswanathan at GaussianWaves.com has a great post on how to build a square-root raised cosine filter. You can also find the design equations in [johnson2004, p.225, harris2021, p. 95].

I’ve written my own SRRC design script in Python which you can download from the WaveWalkerDSP GitHub page in the Blog Downloads repository.

Check out these other posts on filter design:

Example Square Root Raised Cosine Plots

Figure 1 gives the impulse response for multiple SRRC filters with different SPS (samples per symbol), span (proxy for filter length) and $\beta$ (roll-off factor) values where Figure 2 gives the corresponding frequency response. The figures show that increasing the span for consistent SPS value reduces the sidelobes at the cost of a longer filter, however increasing the SPS reduces the cut-off frequency.

Conclusion

The srrcDesign.py file can be downloaded here.

Wondering about how and why the SPS, span and $\beta$ parameters effect the frequency response of the SRRC filters? Be sure to check out the post on low-pass filter design to understand the relationships between filter length, transition bandwidth and sidelobe attenuation.

Check out these other posts on filter design:

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