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<span style="font-size:18.0pt; font-family:"Calibri",sans-serif">In response to the recent discussion of the classic “Psych Tone”, here I have added three items (from MEH, EN64, EN75A):
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<span class="MsoHyperlink"><span style="font-size:18.0pt; font-family:"Calibri",sans-serif"><a href="http://electronotes.netfirms.com/Noise.pdf" id="LPlnk747213" class="OWAAutoLink" previewremoved="true" tabindex="-1">http://electronotes.netfirms.com/Noise.pdf</a></span></span><span style="font-size:18.0pt; font-family:"Calibri",sans-serif"></span></p>
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<span style="font-size:18.0pt; font-family:"Calibri",sans-serif">adding to the Electronotes 76 already posted on noise generators:
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<span class="MsoHyperlink"><span style="font-size:18.0pt; font-family:"Calibri",sans-serif"><a href="http://electronotes.netfirms.com/EN76.pdf" id="LPlnk155007" class="OWAAutoLink" previewremoved="true" tabindex="-1">http://electronotes.netfirms.com/EN76.pdf</a></span></span></p>
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<span style="font-size:18.0pt; font-family:"Calibri",sans-serif">The MEH chapter 5h pages include the reference to the derivation of the feedback taps based on “primitive polynomials”.<span style="">
</span>Since EXOR feedback is anything but “linear”, I don’t understand the terminology “LFSR”, and continue to use “PRBS” (pseudo random binary sequence).
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<span style="font-size:18.0pt; font-family:"Calibri",sans-serif">PRBS generators find applications in EM for noise generators and for generators of random sequences (typically of “notes” forming a trial tune or melody). The shift register cocking interval is
the tempo. <span style=""> </span>The Psych Tone produced sequences of length 63, all notes of the same durations, (thereafter repeating) and was way too long for most composers to consider.<span style="">
</span>I modified mine for shorter sequences of say 5 to 10, and that was used at times.</span></p>
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<span style="font-size:18.0pt; font-family:"Calibri",sans-serif">When used as a noise generator we need both a much longer sequence length and much higher clocking rate (sampling frequency).<span style="">
</span>The length of the sequence is 2^N – 1.<span style=""> </span>Essentially 2^N, so (2^N)*tau, where tau is the reciprocal of the sampling frequency,
<span style=""> </span>should be at least several seconds.<span style=""> </span>
Why so long <span style=""> </span>- it <span style=""> </span>would seem we couldn’t possibly detect a repetition after hundreds of thousands!<span style="">
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<span style="font-size:18.0pt; font-family:"Calibri",sans-serif">Well we often can.<span style="">
</span>What we detect is the sub-audio repetition of a sequence of audible events “<a name="_Hlk534551500" id="LPlnk709586" class="OWAAutoLink" previewremoved="true" tabindex="-1"></a><a name="_Hlk534551156" id="LPlnk175726" class="OWAAutoLink" previewremoved="true" tabindex="-1"><span style="">clink
- - - hiss - - - clank - - - sssss - - <span style=""> </span>- buzz</span></a><span style=""> ;</span>
<span style=""> </span><span style=""> </span><span style=""> </span>clink - - - hiss - - - clank - - - sssss - -
<span style=""> </span>- buzz, . . . . . “ repeating every second or two (whatever the sequence length is). In actual circuits (and indeed, in the monolithic MN5847 this was known, and termed a “heartbeat”).<span style="">
</span>See references above.<span style=""> </span>Why? </span></p>
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<span style="font-size:18.0pt; font-family:"Calibri",sans-serif">The actual (full 2^N-1) PBRS for a proper “maximum length” case includes every possible sequence of 1’s and 0’s (except all zeros), and the feedback structure means that the generator evolves
slowly INTO special cases (like a near square wave) and once established, it evolves slowly OUT (a resulting “clink”).<span style="">
</span>It doesn’t help enough to find a set of taps with one nearly at the input end.<span style="">
</span>What does work is to have TWO (or more) PRBS generators of different lengths and multiplying (EXOR) the outputs.
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<span style="font-size:18.0pt; font-family:"Calibri",sans-serif">In the suggested case (which I may be misunderstanding) on this thread (called “127 bits” – I assume this was meant to be length N = 127), we have the curious result that the “noise” output is a
series of pitches, not white.<span style=""> </span>Why?<span style=""> </span>
Well 2^N-1 is 1.7 * 10^38, which at a digital audio rate is some 10^26 years of time. Further most PRBS generators start in the “all 1” state to avoid a stall.
<span style=""> </span>This would explain why it never (for practical purposes) even gets a start away from the initial square-wave like patterns.
<span style=""> </span><span style=""> </span>Richie apparently suspected this.</span></p>
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