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)
“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)
“At length to hospital
This man was limited,
Where screens leant on the wall
And idle headphones hung.
Since he would soon be dead
They let his wife come along
And pour out tea, each day.”
—Philip Larkin (1922–1986)