diff --git a/Source/FilteringFunctions/arm_biquad_cascade_df2T_f64.c b/Source/FilteringFunctions/arm_biquad_cascade_df2T_f64.c
index 09337d43..ce00cdc8 100644
--- a/Source/FilteringFunctions/arm_biquad_cascade_df2T_f64.c
+++ b/Source/FilteringFunctions/arm_biquad_cascade_df2T_f64.c
@@ -29,108 +29,103 @@
#include "dsp/filtering_functions.h"
/**
- @ingroup groupFilters
+ @ingroup groupFilters
*/
/**
- @defgroup BiquadCascadeDF2T Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure
-
- This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure.
- The filters are implemented as a cascade of second order Biquad sections.
- These functions provide a slight memory savings as compared to the direct form I Biquad filter functions.
- Only floating-point data is supported.
-
- This function operate on blocks of input and output data and each call to the function
- processes blockSize samples through the filter.
- pSrc points to the array of input data and
- pDst points to the array of output data.
- Both arrays contain blockSize values.
-
- @par Algorithm
- Each Biquad stage implements a second order filter using the difference equation:
-
- y[n] = b0 * x[n] + d1
- d1 = b1 * x[n] + a1 * y[n] + d2
- d2 = b2 * x[n] + a2 * y[n]
-
- where d1 and d2 represent the two state values.
- @par
- A Biquad filter using a transposed Direct Form II structure is shown below.
- \image html BiquadDF2Transposed.gif "Single transposed Direct Form II Biquad"
- Coefficients b0, b1, and b2 multiply the input signal x[n] and are referred to as the feedforward coefficients.
- Coefficients a1 and a2 multiply the output signal y[n] and are referred to as the feedback coefficients.
- Pay careful attention to the sign of the feedback coefficients.
- Some design tools flip the sign of the feedback coefficients:
-
- y[n] = b0 * x[n] + d1;
- d1 = b1 * x[n] - a1 * y[n] + d2;
- d2 = b2 * x[n] - a2 * y[n];
-
- In this case the feedback coefficients a1 and a2 must be negated when used with the CMSIS DSP Library.
- @par
- Higher order filters are realized as a cascade of second order sections.
- numStages refers to the number of second order stages used.
- For example, an 8th order filter would be realized with numStages=4 second order stages.
- A 9th order filter would be realized with numStages=5 second order stages with the
- coefficients for one of the stages configured as a first order filter (b2=0 and a2=0).
- @par
- pState points to the state variable array.
- Each Biquad stage has 2 state variables d1 and d2.
- The state variables are arranged in the pState array as:
-
- {d11, d12, d21, d22, ...}
-
- where d1x refers to the state variables for the first Biquad and
- d2x refers to the state variables for the second Biquad.
- The state array has a total length of 2*numStages values.
- The state variables are updated after each block of data is processed; the coefficients are untouched.
- @par
- The CMSIS library contains Biquad filters in both Direct Form I and transposed Direct Form II.
- The advantage of the Direct Form I structure is that it is numerically more robust for fixed-point data types.
- That is why the Direct Form I structure supports Q15 and Q31 data types.
- The transposed Direct Form II structure, on the other hand, requires a wide dynamic range for the state variables d1 and d2.
- Because of this, the CMSIS library only has a floating-point version of the Direct Form II Biquad.
- The advantage of the Direct Form II Biquad is that it requires half the number of state variables, 2 rather than 4, per Biquad stage.
-
- @par Instance Structure
- The coefficients and state variables for a filter are stored together in an instance data structure.
- A separate instance structure must be defined for each filter.
- Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.
-
- @par Init Functions
- There is also an associated initialization function.
- The initialization function performs following operations:
- - Sets the values of the internal structure fields.
- - Zeros out the values in the state buffer.
- To do this manually without calling the init function, assign the follow subfields of the instance structure:
- numStages, pCoeffs, pState. Also set all of the values in pState to zero.
- @par
- Use of the initialization function is optional.
- However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
- To place an instance structure into a const data section, the instance structure must be manually initialized.
- Set the values in the state buffer to zeros before static initialization.
- For example, to statically initialize the instance structure use
-
- arm_biquad_cascade_df2T_instance_f64 S1 = {numStages, pState, pCoeffs};
- arm_biquad_cascade_df2T_instance_f32 S1 = {numStages, pState, pCoeffs};
-
- where numStages is the number of Biquad stages in the filter;
- pState is the address of the state buffer.
- pCoeffs is the address of the coefficient buffer;
- */
+ @defgroup BiquadCascadeDF2T Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure
+ This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure.
+ The filters are implemented as a cascade of second order Biquad sections.
+ These functions provide a slight memory savings as compared to the direct form I Biquad filter functions.
+ Only floating-point data is supported.
+ This function operate on blocks of input and output data and each call to the function
+ processes blockSize samples through the filter.
+ pSrc points to the array of input data and
+ pDst points to the array of output data.
+ Both arrays contain blockSize values.
+ @par Algorithm
+ Each Biquad stage implements a second order filter using the difference equation:
+
+ y[n] = b0 * x[n] + d1
+ d1 = b1 * x[n] + a1 * y[n] + d2
+ d2 = b2 * x[n] + a2 * y[n]
+
+ where d1 and d2 represent the two state values.
+ @par
+ A Biquad filter using a transposed Direct Form II structure is shown below.
+ \image html BiquadDF2Transposed.gif "Single transposed Direct Form II Biquad"
+ Coefficients b0, b1, and b2 multiply the input signal x[n] and are referred to as the feedforward coefficients.
+ Coefficients a1 and a2 multiply the output signal y[n] and are referred to as the feedback coefficients.
+ Pay careful attention to the sign of the feedback coefficients.
+ Some design tools flip the sign of the feedback coefficients:
+
+ y[n] = b0 * x[n] + d1;
+ d1 = b1 * x[n] - a1 * y[n] + d2;
+ d2 = b2 * x[n] - a2 * y[n];
+
+ In this case the feedback coefficients a1 and a2 must be negated when used with the CMSIS DSP Library.
+ @par
+ Higher order filters are realized as a cascade of second order sections.
+ numStages refers to the number of second order stages used.
+ For example, an 8th order filter would be realized with numStages=4 second order stages.
+ A 9th order filter would be realized with numStages=5 second order stages with the
+ coefficients for one of the stages configured as a first order filter (b2=0 and a2=0).
+ @par
+ pState points to the state variable array.
+ Each Biquad stage has 2 state variables d1 and d2.
+ The state variables are arranged in the pState array as:
+
+ {d11, d12, d21, d22, ...}
+
+ where d1x refers to the state variables for the first Biquad and
+ d2x refers to the state variables for the second Biquad.
+ The state array has a total length of 2*numStages values.
+ The state variables are updated after each block of data is processed; the coefficients are untouched.
+ @par
+ The CMSIS library contains Biquad filters in both Direct Form I and transposed Direct Form II.
+ The advantage of the Direct Form I structure is that it is numerically more robust for fixed-point data types.
+ That is why the Direct Form I structure supports Q15 and Q31 data types.
+ The transposed Direct Form II structure, on the other hand, requires a wide dynamic range for the state variables d1 and d2.
+ Because of this, the CMSIS library only has a floating-point version of the Direct Form II Biquad.
+ The advantage of the Direct Form II Biquad is that it requires half the number of state variables, 2 rather than 4, per Biquad stage.
+ @par Instance Structure
+ The coefficients and state variables for a filter are stored together in an instance data structure.
+ A separate instance structure must be defined for each filter.
+ Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.
+ @par Init Functions
+ There is also an associated initialization function.
+ The initialization function performs following operations:
+ - Sets the values of the internal structure fields.
+ - Zeros out the values in the state buffer.
+ To do this manually without calling the init function, assign the follow subfields of the instance structure:
+ numStages, pCoeffs, pState. Also set all of the values in pState to zero.
+ @par
+ Use of the initialization function is optional.
+ However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
+ To place an instance structure into a const data section, the instance structure must be manually initialized.
+ Set the values in the state buffer to zeros before static initialization.
+ For example, to statically initialize the instance structure use
+
+ arm_biquad_cascade_df2T_instance_f64 S1 = {numStages, pState, pCoeffs};
+ arm_biquad_cascade_df2T_instance_f32 S1 = {numStages, pState, pCoeffs};
+
+ where numStages is the number of Biquad stages in the filter;
+ pState is the address of the state buffer.
+ pCoeffs is the address of the coefficient buffer;
+*/
/**
- @addtogroup BiquadCascadeDF2T
- @{
+ @addtogroup BiquadCascadeDF2T
+ @{
*/
/**
- @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
- @param[in] S points to an instance of the filter data structure
- @param[in] pSrc points to the block of input data
- @param[out] pDst points to the block of output data
- @param[in] blockSize number of samples to process
- @return none
+ @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
+ @param[in] S points to an instance of the filter data structure
+ @param[in] pSrc points to the block of input data
+ @param[out] pDst points to the block of output data
+ @param[in] blockSize number of samples to process
+ @return none
*/
#if defined(ARM_MATH_NEON)
void arm_biquad_cascade_df2T_f64(