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:
“The impulse to perfection cannot exist where the definition of perfection is the arbitrary decision of authority. That which is born in loneliness and from the heart cannot be defended against the judgment of a committee of sycophants. The volatile essences which make literature cannot survive the clichés of a long series of story conferences.”
—Raymond Chandler (1888–1959)
“If it had not been for storytelling, the black family would not have survived. It was the responsibility of the Uncle Remus types to transfer philosophies, attitudes, values, and advice, by way of storytelling using creatures in the woods as symbols.”
—Jackie Torrence (b. 1944)
“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)
“At length he would call to let us know where he was waiting for us with his canoe, when, on account of the windings of the stream, we did not know where the shore was, but he did not call often enough, forgetting that we were not Indians.... This was not because he was unaccommodating, but a proof of superior manners. Indians like to get along with the least possible communication and ado. He was really paying us a great compliment all the while, thinking that we preferred a hint to a kick.”
—Henry David Thoreau (1817–1862)