LPC to/from Cepstral Coefficients

Convert linear prediction coefficients to cepstral coefficients or cepstral coefficients to linear prediction coefficients

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Libraries:
DSP System Toolbox / Estimation / Linear Prediction

Description

The LPC to/from Cepstral Coefficients block can convert linear prediction coefficients (LPCs) to cepstral coefficients (CCs) or cepstral coefficients to linear prediction coefficients. Set the Type of conversion parameter to LPCs to cepstral coefficients or Cepstral coefficients to LPCs to select the domain for converting your coefficients. For more information, see Algorithms.

Consider a signal x(n) as the input to an FIR analysis filter represented by LPCs. The output of this analysis filter, e(n), is known as the prediction error signal. The power of this error signal is denoted by P, the prediction error power.

Ports

Input

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A — LPC coefficients
vector | matrix

Specify the LPC coefficients as a vector or a matrix. The block treats each column of the matrix as a channel. When you specify an unoriented vector, the block treats the input as one channel.

This port is unnamed until you set Specify P to via input port.

Dependencies

To enable this port, set Type of conversion to LPCs to cepstral coefficients.

Data Types: single | double

CC — Cepstral coefficients
vector | matrix

Specify the cepstral coefficients as a vector or a matrix. The block treats each column of the matrix as a channel. When you specify an unoriented vector, the block treats the input as one channel.

Dependencies

To enable this port, set Type of conversion to Cepstral coefficients to LPCs.

Data Types: single | double

P — Prediction error power
scalar | vector

Specify the prediction error power P for each channel as a vector through this port. The length of this vector must equal the number of channels in the input.

Dependencies

To enable this port, set Specify P to via input port.

Data Types: single | double

Output

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CC — Cepstral coefficients
vector | matrix

Cepstral coefficients, returned as a vector or a matrix.

Dependencies

To enable this port, set Type of conversion to LPCs to cepstral coefficients.

Data Types: single | double

P — Prediction error power
scalar | vector

Prediction error power P for each channel, returned as a scalar or a vector through this port. The length of this vector must equal the number of channels in the input.

Dependencies

To enable this port, select Output P.

Data Types: single | double

Parameters

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Type of conversion — Type of conversion
`LPCs to cepstral coefficients` (default) | `Cepstral coefficients to LPCs`

Specify the domain for converting the coefficients as one of these:

LPCs to cepstral coefficients
Cepstral coefficients to LPCs

Specify P — Method of specifying prediction error power P
`assume P equals 1` (default) | `via input port`

Specify the prediction error power P using one of these options:

assume P equals 1 –– Specify the value of P to 1 for all channels.
via input port –– Use the P port to input the prediction error power for each channel. The length of this vector must equal the number of channels in the input.

Dependencies

To enable this parameter, set Type of conversion to LPCs to cepstral coefficients.

Output P — Output prediction error power P
`off` (default) | `on`

Select this check box to output the prediction error power for each channel from output port P.

Dependencies

To enable this parameter, set Type of conversion to Cepstral coefficients to LPCs

Output size same as input size — Output size same as input size
`off` (default) | `on`

When you select this check box, the length of the input vector of LPCs is equal to the output vector of CCs. When you do not select this check box, enter a positive scalar for the Length of output cepstral coefficients parameter.

Dependencies

To enable this parameter, set Type of conversion to LPCs to cepstral coefficients.

Length of output cepstral coefficients vector — Length of output cepstral coefficients
`10` (default) | positive integer

Specify the length of the output cepstral coefficients vector as a positive integer. This value determines the length of each channel in the output cepstral coefficients.

Dependencies

To enable this parameter, set Type of conversion to LPCs to cepstral coefficients

If first input value is not 1 — Action to take if first input value is not 1
`Replace it with 1` (default) | `Normalize` | `Normalize and warn` | `Error`

Specify the action to take if the first coefficient of the LPC coefficient vector is not 1. You can set this parameter to one of these options:

Replace it with 1 — The block changes the first value of the coefficient vector to 1. The rest of the coefficient values are unchanged.
Normalize — The block divides the entire vector of coefficients by the first coefficient so that the first coefficient of the LPC coefficient vector is 1.
Normalize and Warn — The block divides the entire vector of coefficients by the first coefficient so that the first coefficient of the LPC coefficient vector is 1. The block displays a warning message stating that the vector of coefficients has been normalized.
Error — The block displays an error stating that the first coefficient of the LPC coefficient vector is not 1.

Dependencies

To enable this parameter, set Type of conversion to LPCs to cepstral coefficients.

Block Characteristics

Data Types	`double` \| `single`
Direct Feedthrough	`no`
Multidimensional Signals	`no`
Variable-Size Signals	`no`
Zero-Crossing Detection	`no`

Algorithms

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The cepstral coefficients are the coefficients of the Fourier transform representation of the logarithm magnitude spectrum. Consider a sequence, x(n), having a Fourier transform X(ω). The cepstrum, c_x(n), is defined by the inverse Fourier transform of C_x(ω), where C_x(ω) = log_eX (ω). See the Real Cepstrum block reference page for information on computing cepstrum coefficients from time-domain signals.

LPC to CC

In this mode, the block uses a recursion technique to convert LPCs to CCs. The LPC vector is defined by $[\begin{matrix} a_{0} & a_{1} & a_{2} & \begin{matrix} ... & a_{p} \end{matrix} \end{matrix}]$ and the CC vector is defined by $[\begin{matrix} c_{0} & c_{1} & c_{2} & ... & c_{p} & ... & c_{n - 1} \end{matrix}]$ . The recursion is defined by the following equations:

$c_{0} = \log_{e} P$

$c_{m} = - a_{m} + \frac{1}{m} \sum_{k = 1}^{m - 1} [- (m - k) \cdot a_{k} \cdot c_{(m - k)}], 1 \leq m \leq p$

$c_{m} = \sum_{k = 1}^{p} [\frac{- (m - k)}{m} \cdot a_{k} \cdot c_{(m - k)}], p < m < n$

CC to LPC

In this mode, the block uses a recursion technique to convert CCs to LPCs. The CC vector is defined by $[\begin{matrix} \begin{matrix} c_{0} & c_{1} & c_{2} & ... \end{matrix} & c_{p} & ... & c_{n} \end{matrix}]$ and the LPC vector is defined by $[\begin{matrix} a_{0} & a_{1} & a_{2} & \begin{matrix} ... & a_{p} \end{matrix} \end{matrix}]$ . The recursion is defined by the following equations

$a_{m} = - c_{m} - \frac{1}{m} \sum_{k = 1}^{m - 1} [(m - k) \cdot c_{(m - k)} \cdot a_{k}]$

$P = \exp (C_{0})$

where $m = 1, 2, ..., p$ .

References

[1] Papamichalis, Panos E. Practical Approaches to Speech Coding. Englewood Cliffs, NJ: Prentice Hall, 1987.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a

LPC to/from Cepstral Coefficients

Description

Ports

Input

A — LPC coefficients vector | matrix

Dependencies

CC — Cepstral coefficients vector | matrix

Dependencies

P — Prediction error power scalar | vector

Dependencies

Output

CC — Cepstral coefficients vector | matrix

Dependencies

P — Prediction error power scalar | vector

Dependencies

Parameters

Type of conversion — Type of conversion LPCs to cepstral coefficients (default) | Cepstral coefficients to LPCs

Specify P — Method of specifying prediction error power P assume P equals 1 (default) | via input port

Dependencies

Output P — Output prediction error power P off (default) | on

Dependencies

Output size same as input size — Output size same as input size off (default) | on

Dependencies

Length of output cepstral coefficients vector — Length of output cepstral coefficients 10 (default) | positive integer

Dependencies

If first input value is not 1 — Action to take if first input value is not 1 Replace it with 1 (default) | Normalize | Normalize and warn | Error

Dependencies

Block Characteristics

Algorithms

LPC to CC

CC to LPC

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

Version History

See Also

A — LPC coefficients
vector | matrix

CC — Cepstral coefficients
vector | matrix

P — Prediction error power
scalar | vector

CC — Cepstral coefficients
vector | matrix

P — Prediction error power
scalar | vector

Type of conversion — Type of conversion
`LPCs to cepstral coefficients` (default) | `Cepstral coefficients to LPCs`

Specify P — Method of specifying prediction error power P
`assume P equals 1` (default) | `via input port`

Output P — Output prediction error power P
`off` (default) | `on`

Output size same as input size — Output size same as input size
`off` (default) | `on`

Length of output cepstral coefficients vector — Length of output cepstral coefficients
`10` (default) | positive integer

If first input value is not 1 — Action to take if first input value is not 1
`Replace it with 1` (default) | `Normalize` | `Normalize and warn` | `Error`

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.