PAL Mathematics: Time Constants and dB Conversion

Conversions between linear smoothing factors, dB-based rates, frame durations, milliseconds, and linear gain.

PAL Mathematics: Time Constants and dB Conversion — 16 functions

KiratPalConvertFramesToMs

Signature
T_FLOAT KiratPalConvertFramesToMs(T_INT iTimeFrames, T_FLOAT fSampleRate, T_INT iFrameshift);
Description
Calculates the linear convolution of two vectors.
Mathematical operation
\(t_{ms}=N_f\,1000R/f_s\)

KiratPalConvertMsToFrames

Signature
T_INT KiratPalConvertMsToFrames(T_FLOAT fTimeMs, T_FLOAT fSampleRate, T_INT iFrameshift);
Description
Calculates the linear convolution of two vectors.
Mathematical operation
\(N_f=\operatorname{round}_{\text{KiRAT}}\!\left(t_{ms}\,10^{-3}f_s/R\right)\)

KiratPalDb10ToLinear

Signature
T_FLOAT KiratPalDb10ToLinear(T_FLOAT fDb);
Description
Converts a dB value to a linear factor.
Mathematical operation
\(g=10^{L_{dB}/10}\)

KiratPalDb20ToLinear

Signature
T_FLOAT KiratPalDb20ToLinear(T_FLOAT fDb);
Description
Converts a dB value to a linear factor.
Mathematical operation
\(g=10^{L_{dB}/20}\)

KiratPalTimeConstdBpHzToLin

Signature
T_FLOAT KiratPalTimeConstdBpHzToLin(T_FLOAT fdBpHzValue, T_FLOAT fSampleRate, T_INT iFftOrder);
Description
Converts a smoothing/time constant between linear form and dB per time/frequency unit.
Mathematical operation
\(a=10^{L_{dB/Hz}f_s/(20N_{FFT})}\)

KiratPalTimeConstdBpmsToLin

Signature
T_FLOAT KiratPalTimeConstdBpmsToLin(T_FLOAT fdBpsValue, T_FLOAT fSampleRate, T_INT iFrameshift);
Description
Converts a smoothing/time constant between linear form and dB per time/frequency unit.
Mathematical operation
\(a=10^{L_{dB/ms}\,R\,1000/(20f_s)}\)

KiratPalTimeConstdBpsToLin

Signature
T_FLOAT KiratPalTimeConstdBpsToLin(T_FLOAT fdBpsValue, T_FLOAT fSampleRate, T_INT iFrameshift);
Description
Converts a smoothing/time constant between linear form and dB per time/frequency unit.
Mathematical operation
\(a=10^{L_{dB/s}R/(20f_s)}\)

KiratPalTimeConstdBpsToLinIir

Signature
T_FLOAT KiratPalTimeConstdBpsToLinIir(T_FLOAT fdBpsValue, T_FLOAT fSampleRate, T_INT iFrameshift);
Description
Converts a smoothing/time constant between linear form and dB per time/frequency unit.
Mathematical operation
\(a=1-10^{-L_{dB/s}R/(20f_s)}\)

KiratPalTimeConstdBpsToLinIirPow

Signature
T_FLOAT KiratPalTimeConstdBpsToLinIirPow(T_FLOAT fdBpsValue, T_FLOAT fSampleRate, T_INT iFrameshift);
Description
Calculates element-wise powers.
Mathematical operation
\(a=1-10^{-L_{dB/s}R/(10f_s)}\)

KiratPalTimeConstdBpsToLinPow

Signature
T_FLOAT KiratPalTimeConstdBpsToLinPow(T_FLOAT fdBpsValue, T_FLOAT fSampleRate, T_INT iFrameshift);
Description
Calculates element-wise powers.
Mathematical operation
\(a=10^{L_{dB/s}R/(10f_s)}\)

KiratPalTimeConstLinTodBpHz

Signature
T_FLOAT KiratPalTimeConstLinTodBpHz(T_FLOAT fLinValue, T_FLOAT fSampleRate, T_INT iFftOrder);
Description
Converts a smoothing/time constant between linear form and dB per time/frequency unit.
Mathematical operation
\(L_{dB/Hz}=20\log_{10}(a)\,N_{FFT}/f_s\)

KiratPalTimeConstLinTodBpms

Signature
T_FLOAT KiratPalTimeConstLinTodBpms(T_FLOAT fLinValue, T_FLOAT fSampleRate, T_INT iFrameshift);
Description
Converts a smoothing/time constant between linear form and dB per time/frequency unit.
Mathematical operation
\(L_{dB/ms}=20\,(f_s/R)\,10^{-3}\log_{10}(a)\)

KiratPalTimeConstLinTodBps

Signature
T_FLOAT KiratPalTimeConstLinTodBps(T_FLOAT fLinValue, T_FLOAT fSampleRate, T_INT iFrameshift);
Description
Converts a smoothing/time constant between linear form and dB per time/frequency unit.
Mathematical operation
\(L_{dB/s}=20(f_s/R)\log_{10}(a)\)

KiratPalTimeConstLinTodBpsIir

Signature
T_FLOAT KiratPalTimeConstLinTodBpsIir(T_FLOAT fLinValue, T_FLOAT fSampleRate, T_INT iFrameshift);
Description
Converts a smoothing/time constant between linear form and dB per time/frequency unit.
Mathematical operation
\(L_{dB/s}=-20(f_s/R)\log_{10}(1-a)\)

KiratPalTimeConstLinTodBpsIirPow

Signature
T_FLOAT KiratPalTimeConstLinTodBpsIirPow(T_FLOAT fLinValue, T_FLOAT fSampleRate, T_INT iFrameshift);
Description
Calculates element-wise powers.
Mathematical operation
\(L_{dB/s}=-10(f_s/R)\log_{10}(1-a)\)

KiratPalTimeConstLinTodBpsPow

Signature
T_FLOAT KiratPalTimeConstLinTodBpsPow(T_FLOAT fLinValue, T_FLOAT fSampleRate, T_INT iFrameshift);
Description
Calculates element-wise powers.
Mathematical operation
\(L_{dB/s}=10(f_s/R)\log_{10}(a)\)