Impulse Response, Transfer Function, and Constraint Length
A convolutional encoder is called so because it performs a convolution of the input stream with the encoder's impulse responses:
where is an input sequence, is a sequence from output and is an impulse response for output .
A convolutional encoder is a discrete linear time-invariant system. Every output of an encoder can be described by its own transfer function, which is closely related to the generator polynomial. An impulse response is connected with a transfer function through Z-transform.
Transfer functions for the first (non-recursive) encoder are:
Transfer functions for the second (recursive) encoder are:
Define by
where, for any rational function ,
- .
Then is the maximum of the polynomial degrees of the, and the constraint length is defined as . For instance, in the first example the constraint length is 3, and in the second the constraint length is 4.
Read more about this topic: Convolutional Code
Famous quotes containing the words impulse, transfer, constraint and/or length:
“Fatalism, whose solving word in all crises of behavior is “All striving is vain,” will never reign supreme, for the impulse to take life strivingly is indestructible in the race. Moral creeds which speak to that impulse will be widely successful in spite of inconsistency, vagueness, and shadowy determination of expectancy. Man needs a rule for his will, and will invent one if one be not given him.”
—William James (1842–1910)
“I have proceeded ... to prevent the lapse from ... the point of blending between wakefulness and sleep.... Not ... that I can render the point more than a point—but that I can startle myself ... into wakefulness—and thus transfer the point ... into the realm of Memory—convey its impressions,... to a situation where ... I can survey them with the eye of analysis.”
—Edgar Allan Poe (1809–1849)
“In America a woman loses her independence for ever in the bonds of matrimony. While there is less constraint on girls there than anywhere else, a wife submits to stricter obligations. For the former, her father’s house is a home of freedom and pleasure; for the latter, her husband’s is almost a cloister.”
—Alexis de Tocqueville (1805–1859)
“Baltimore lay very near the immense protein factory of Chesapeake Bay, and out of the bay it ate divinely. I well recall the time when prime hard crabs of the channel species, blue in color, at least eight inches in length along the shell, and with snow-white meat almost as firm as soap, were hawked in Hollins Street of Summer mornings at ten cents a dozen.”
—H.L. (Henry Lewis)