LPC To LSF LSP — Control Systems/Signal Modeling

LPC to LSF/LSP

Control Systems / Signal Modeling

Finds the p line spectral values of the LPC vector A = [1 a₁ … a_p] by searching for them. The sum and difference polynomials P(z) = A(z) + z^−(p+1)A(1/z) and Q(z) = A(z) − z^−(p+1)A(1/z) are written as series in x = cosω, a grid of Root Finding Coarse Grid Points values running from x = 1 downwards is walked until one of them changes sign, that interval is halved Root Finding Bisection Refinement times, and a single linear interpolation finishes the value; the search then moves to the other polynomial — their roots interlace — and carries on from where it stopped.

The answer is the search's, not the exact root. At the defaults (64 points, 4 halvings) it sits about 1e−6 from the true root, and that is the number this block reproduces, because it is the number the Simulink block gives. A finer grid and more halvings move it closer.

Ports

• A – the LPC vector, an [N,1] column with N at least 2; p = N − 1 is the model order.
• LSP – the p line spectral values, [p,1], in the unit Output names, in increasing frequency.

Parameters

• Output – the unit of the result:
  • LSP in range (-1 1) (the default, as Simulink's) – the line spectral pairs, cosω itself.
  • LSF normalized in range (0 0.5) – ω/2π.
  • LSF in range (0 pi) – ω in radians.
• Root Finding Coarse Grid Points – how many grid points the search walks, at least 1; 64 by default. The step is 2 divided by this number, subtracted from 1 in turn.
• Root Finding Bisection Refinement – how many times an interval that changed sign is halved before the interpolation; 4 by default, and 0 is allowed.
• Non-Unity First Coefficient – what to do when a₀ is not 1:
  • Ignore (the default, as Simulink's) – a₀ is not used at all and a₁…a_p are taken as they are.
  • Normalize – every coefficient is divided by a₀ first.
  Simulink's two other choices (warn, error) are not offered: an exported core has nobody to warn.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. The input length, the grid, the number of halvings and the output unit are baked into the core at export time.

The three HDL targets are simulation-only: they carry the arithmetic in real and quantize only at the port boundary. The search divides by the difference of two polynomial values and the two frequency units pass through an arc cosine, neither of which the Q16.16 packages carry. The cores simulate correctly and are not offered as synthesizable.

Simulink bridge

Import and export, mapped to dsplp/LPC to LSF//LSP Conversion – the DSP System Toolbox block (a doubled // is how Simulink writes a slash INSIDE a block name, and the library breaks this block's name over two lines). "Output" to output (one to one, every option), "Root Finding Coarse Grid Points" to NSteps, "Root Finding Bisection Refinement" to NBisects, and "Non-Unity First Coefficient" to error (its first two options, one to one).

RootStatus = off, correction = off and lastLSP = off are always emitted. RootStatus adds a second output port carrying a validity flag, and the other two replace an invalid result with the previous valid one – a stored value this block does not keep. All three stay at their defaults, so the block is the plain one input, one output shape.

"Sampling Time (s)" does not cross. dsplp/LPC to LSF//LSP Conversion defines no SampleTime parameter – verified against the R2026a block dialog – and set_param on a parameter a block does not define is a hard error that aborts the whole generated script.

Notes

• Stateless and algebraic: the search runs on this sample's vector alone.
• A value the search does not find is left at the bottom of the range – −1 as an LSP, π in radians, 0.5 normalized – exactly as the Simulink block leaves it. It happens when two values of the same polynomial fall inside one grid interval, which a coarse grid or an input that is not a minimum-phase model can both cause; a finer grid finds them.
• Nothing is refused: any vector of at least two values is accepted, unstable models included, as Simulink accepts them.
• The inverse is LSF/LSP to LPC, which rebuilds A from these values.