jasonkee111
Junior Member level 3
Ouput of LFSR Properties that confuse me:
1. "Ones and zeroes occur in 'runs'. The output stream 0110100, for example consists of five runs of lengths 1,2,1,1,2, in order. In one period of a maximal LFSR, 2n − 1 runs occur (for example, a six bit LFSR will have 32 runs). Exactly 1/2 of these runs will be one bit long, 1/4 will be two bits long, up to a single run of zeroes n − 1 bits long, and a single run of ones n bits long. " Linear feedback shift register - Wikipedia, the free encyclopedia
2. "2. An m-sequence contains exactly 2(m-1) ones and 2(m-1)-1 zeros."
3. "6. If an m-sequence is mapped to an analog time-varying waveform, by mapping each binary zero to -1 and each binary one to +1, then the autocorrelation function for the resulting waveform will be unity for zero delay, and -1/(2m-1) for any delay greater that one bit, either positive or negative in time. The shape of the autocorrelation function between -1 bit and +1 bit will be triangular, centered around time 0. That is, the function will rise linearly from time = -(one-bit) to time 0, and then decline linearly from time 0 to time = +(one-bit)."
Properties2 and 3 Link :**broken link removed** Properties
Question on Properties 1
1. What is the use of this properties?
2. In the properties 1, "1/2 of these runs will be one bit long..." what is that means? can someone elaborate more on it? Pls give some simple example
Question on Properties 2
1. How to prove it?
FYI, i use 3bit sequence(max length). I have calculated the total number of one is 12 and number of zero is 9. Binary of 000 is not included.
Question on Properties 3
1. How is it plotted ? What is the x and y axis?
Thanks a lot
1. "Ones and zeroes occur in 'runs'. The output stream 0110100, for example consists of five runs of lengths 1,2,1,1,2, in order. In one period of a maximal LFSR, 2n − 1 runs occur (for example, a six bit LFSR will have 32 runs). Exactly 1/2 of these runs will be one bit long, 1/4 will be two bits long, up to a single run of zeroes n − 1 bits long, and a single run of ones n bits long. " Linear feedback shift register - Wikipedia, the free encyclopedia
2. "2. An m-sequence contains exactly 2(m-1) ones and 2(m-1)-1 zeros."
3. "6. If an m-sequence is mapped to an analog time-varying waveform, by mapping each binary zero to -1 and each binary one to +1, then the autocorrelation function for the resulting waveform will be unity for zero delay, and -1/(2m-1) for any delay greater that one bit, either positive or negative in time. The shape of the autocorrelation function between -1 bit and +1 bit will be triangular, centered around time 0. That is, the function will rise linearly from time = -(one-bit) to time 0, and then decline linearly from time 0 to time = +(one-bit)."
Properties2 and 3 Link :**broken link removed** Properties
Question on Properties 1
1. What is the use of this properties?
2. In the properties 1, "1/2 of these runs will be one bit long..." what is that means? can someone elaborate more on it? Pls give some simple example
Question on Properties 2
1. How to prove it?
FYI, i use 3bit sequence(max length). I have calculated the total number of one is 12 and number of zero is 9. Binary of 000 is not included.
Question on Properties 3
1. How is it plotted ? What is the x and y axis?
Thanks a lot
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