What does a Feedback Shift Register (FSR) do? What are the differences between Linear FSR and Filtered FSR?
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A Feedback Shift Register (FSR) is a type of shift register that incorporates feedback from certain stages or taps to generate a pseudo-random sequence of bits. It is commonly used in communication systems for various purposes such as scrambling, encryption, and error detection.
The main difference between a Linear FSR and a Filtered FSR lies in the feedback structure and the resulting characteristics of the generated sequences.
1. Linear FSR: In a Linear FSR, the feedback taps are selected such that the output sequence will have a maximum-length or nearly maximum-length property. This means that the generated sequence will have a very long periodicity, resulting in a nearly random appearance and excellent statistical properties. Linear FSRs are typically used for applications where randomness and uniform distribution of bits are essential, such as encryption algorithms or spread spectrum systems.
2. Filtered FSR: In a Filtered FSR, additional logic or components are incorporated to manipulate the output sequence and produce a desired spectral shape. The feedback taps in a Filtered FSR are chosen to achieve specific frequency response characteristics. These types of FSRs are used in applications where the spectral content of the generated sequence needs to be controlled, such as in frequency hopping communication systems or in generating sequences with specific power spectral density properties.
To summarize, a Linear FSR generates a pseudo-random sequence with excellent statistical properties and long periodicity, while a Filtered FSR modifies the output sequence to achieve specific spectral characteristics.
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