# Ogg Vorbis I format specification: floor type 0 setup and decode

Last update to this document: July 19, 2002

# Overview

Vorbis floor type zero uses Line Spectral Pair [LSP, also alternately known as Line Spectral Frequency or LSF] representation to encode a smooth spectral envelope curve as the frequency response of the LSP filter. This representation is equivalent to a traditional all-pole infinite impulse response filter as would be used in linear predictive coding; LSP representation may be converted to LPC representation and vice-versa.

# Floor 0 format

Floor zero configuration consists of six integer fields and a list of VQ codebooks for use in coding/decoding the LSP filter coefficient values used by each frame.

## header decode

Configuration information for instances of floor zero decodes from the codec setup header (third packet). configuration decode proceeds as follows:

      1) [floor0_order] = read an unsigned integer of 8 bits
      2) [floor0_rate] = read an unsigned integer of 16 bits
      3) [floor0_bark_map_size] = read an unsigned integer of 16 bits
      4) [floor0_amplitude_bits] = read an unsigned integer of six bits
      5) [floor0_amplitude_offset] = read an unsigned integer of eight bits
      6) [floor0_number_of_books] = read an unsigned integer of four bits and add 1
      7) if any of [floor0_order], [floor0_rate], [floor0_bark_map_size], [floor0_amplitude_bits],
         [floor0_amplitude_offset] or [floor0_number_of_books] are less than zero, the stream is not decodable
      8) array [floor0_book_list] = read a list of [floor0_number_of_books] unsigned integers of eight bits each;

An end-of-packet condition during any of these bitstream reads renders this stream undecodable. In addition, any element of the array `[floor0_book_list]` that is greater than the maximum codebook number for this bitstream is an error condition that also renders the stream undecodable.

## packet decode

Extracting a floor0 curve from an audio packet consists of first decoding the curve amplitude and `[floor0_order]` LSP coefficient values from the bitstream, and then computing the floor curve, which is defined as the frequency response of the decoded LSP filter.

Packet decode proceeds as follows:

      1) [amplitude] = read an unsigned integer of [floor0_amplitude_bits] bits
      2) if ( [amplitude] is greater than zero ) {
           3) [coefficients] is an empty, zero length vector

           4) [booknumber] = read an unsigned integer of ilog( [floor0_number_of_books] ) bits
           5) if ( [booknumber] is greater than the highest number decode codebook ) then packet is undecodable
           6) [lastval] = zero;
           7) vector [temp_vector] = read vector from bitstream using codebook number [booknumber] in VQ context.
           8) add the scalar value [last] to each scalar in vector [temp_vector]
           9) [last] = the value of the last scalar in vector [temp_vector]
          10) concatenate [temp_vector] onto the end of the [coefficients] vector
          11) if (length of vector [coefficients] is less than [floor0_order], continue at step 6

         }

     12) done.

Take note of the following properties of decode:

- An `[amplitude]` value of zero must result in a return code that indicates this channel is unused in this frame (the output of the channel will be all-zeroes in synthesis). Several later stages of decode don't occur for an unused channel.

- An end-of-packet condition during decode should be considered a nominal occruence; if end-of-packet is reached during any read operation above, floor decode is to return 'unused' status as if the `[amplitude]` value had read zero at the beginning of decode.
- The book number used for decode can, in fact, be stored in the bitstream in ilog( `[floor0_number_of_books]` - 1 ) bits. Nevertheless, the above specification is correct and values greater than the maximum possible book value are reserved.

- The number of scalars read into the vector `[coefficients]` may be greater than `[floor0_order]`, the number actually required for curve computation. For example, if the VQ codebook used for the floor currently being decoded has a `[codebook_dimensions]` value of three and `[floor0_order]` is ten, the only way to fill all the needed scalars in `[coefficients]` is to to read a total of twelve scalars as four vectors of three scalars each. This is not an error condition, and care must be taken not to allow a buffer overflow in decode. The extra values are not used and may be ignored or discarded.

## curve computation

Given an `[amplitude]` integer and `[coefficients]` vector from packet decode as well as the [floor0_order], [floor0_rate], [floor0_bark_map_size], [floor0_amplitude_bits] and [floor0_amplitude_offset] values from floor setup, and an output vector size `[n]` specified by the decode process, we compute a floor output vector.

If the value `[amplitude]` is zero, the return value is a length `[n]` vector with all-zero scalars. Otherwise, begin by assuming the following definitions for the given vector to be synthesized:

The above is used to synthesize the LSP curve on a Bark-scale frequency axis, then map the result to a linear-scale frequency axis. Similarly, the below calculation synthesizes the output LSP curve [output] on a log (dB) amplitude scale, mapping it to linear amplitude in the last step:

      1) [i] = 0
      2) if ( [floor0_order] is odd ) {

           3) calculate [p] and [q] according to:

         } else [floor0_order] is even {

           4) calculate [p] and [q] according to:

         }

      5) calculate [linear_floor_value] according to:

      6) [iteration_condition] = map element [i]
      7) [output] element [i] = [linear_floor_value]
      8) increment [i]
      9) if ( map element [i] is equal to [iteration_condition] ) continue at step 7
     10) if ( [i] is less than [n] ) continue at step 2
     11) done

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