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Complex FFT Functions

Content

 Complex FFT Tables
 

Functions

void arm_cfft_f32 (const arm_cfft_instance_f32 *S, float32_t *p1, uint8_t ifftFlag, uint8_t bitReverseFlag)
 Processing function for the floating-point complex FFT. More...
 
void arm_cfft_f64 (const arm_cfft_instance_f64 *S, float64_t *p1, uint8_t ifftFlag, uint8_t bitReverseFlag)
 Processing function for the Double Precision floating-point complex FFT. More...
 
arm_status arm_cfft_init_f32 (arm_cfft_instance_f32 *S, uint16_t fftLen)
 Initialization function for the cfft f32 function. More...
 
arm_status arm_cfft_init_f64 (arm_cfft_instance_f64 *S, uint16_t fftLen)
 Initialization function for the cfft f64 function. More...
 
arm_status arm_cfft_init_q15 (arm_cfft_instance_q15 *S, uint16_t fftLen)
 Initialization function for the cfft q15 function. More...
 
arm_status arm_cfft_init_q31 (arm_cfft_instance_q31 *S, uint16_t fftLen)
 Initialization function for the cfft q31 function. More...
 
void arm_cfft_q15 (const arm_cfft_instance_q15 *S, q15_t *p1, uint8_t ifftFlag, uint8_t bitReverseFlag)
 Processing function for Q15 complex FFT. More...
 
void arm_cfft_q31 (const arm_cfft_instance_q31 *S, q31_t *p1, uint8_t ifftFlag, uint8_t bitReverseFlag)
 Processing function for the Q31 complex FFT. More...
 
void arm_cfft_radix2_f32 (const arm_cfft_radix2_instance_f32 *S, float32_t *pSrc)
 Radix-2 CFFT/CIFFT. More...
 
arm_status arm_cfft_radix2_init_f32 (arm_cfft_radix2_instance_f32 *S, uint16_t fftLen, uint8_t ifftFlag, uint8_t bitReverseFlag)
 Initialization function for the floating-point CFFT/CIFFT. More...
 
arm_status arm_cfft_radix2_init_q15 (arm_cfft_radix2_instance_q15 *S, uint16_t fftLen, uint8_t ifftFlag, uint8_t bitReverseFlag)
 Initialization function for the Q15 CFFT/CIFFT. More...
 
arm_status arm_cfft_radix2_init_q31 (arm_cfft_radix2_instance_q31 *S, uint16_t fftLen, uint8_t ifftFlag, uint8_t bitReverseFlag)
 Initialization function for the Q31 CFFT/CIFFT. More...
 
void arm_cfft_radix2_q15 (const arm_cfft_radix2_instance_q15 *S, q15_t *pSrc)
 Processing function for the fixed-point CFFT/CIFFT. More...
 
void arm_cfft_radix2_q31 (const arm_cfft_radix2_instance_q31 *S, q31_t *pSrc)
 Processing function for the fixed-point CFFT/CIFFT. More...
 
void arm_cfft_radix4_f32 (const arm_cfft_radix4_instance_f32 *S, float32_t *pSrc)
 Processing function for the floating-point Radix-4 CFFT/CIFFT. More...
 
arm_status arm_cfft_radix4_init_f32 (arm_cfft_radix4_instance_f32 *S, uint16_t fftLen, uint8_t ifftFlag, uint8_t bitReverseFlag)
 Initialization function for the floating-point CFFT/CIFFT. More...
 
arm_status arm_cfft_radix4_init_q15 (arm_cfft_radix4_instance_q15 *S, uint16_t fftLen, uint8_t ifftFlag, uint8_t bitReverseFlag)
 Initialization function for the Q15 CFFT/CIFFT. More...
 
arm_status arm_cfft_radix4_init_q31 (arm_cfft_radix4_instance_q31 *S, uint16_t fftLen, uint8_t ifftFlag, uint8_t bitReverseFlag)
 Initialization function for the Q31 CFFT/CIFFT. More...
 
void arm_cfft_radix4_q15 (const arm_cfft_radix4_instance_q15 *S, q15_t *pSrc)
 Processing function for the Q15 CFFT/CIFFT. More...
 
void arm_cfft_radix4_q31 (const arm_cfft_radix4_instance_q31 *S, q31_t *pSrc)
 Processing function for the Q31 CFFT/CIFFT. More...
 

Description

The Fast Fourier Transform (FFT) is an efficient algorithm for computing the Discrete Fourier Transform (DFT). The FFT can be orders of magnitude faster than the DFT, especially for long lengths. The algorithms described in this section operate on complex data. A separate set of functions is devoted to handling of real sequences.
There are separate algorithms for handling floating-point, Q15, and Q31 data types. The algorithms available for each data type are described next.
The FFT functions operate in-place. That is, the array holding the input data will also be used to hold the corresponding result. The input data is complex and contains 2*fftLen interleaved values as shown below.
{real[0], imag[0], real[1], imag[1], ...} 
The FFT result will be contained in the same array and the frequency domain values will have the same interleaving.
Floating-point
The floating-point complex FFT uses a mixed-radix algorithm. Multiple radix-8 stages are performed along with a single radix-2 or radix-4 stage, as needed. The algorithm supports lengths of [16, 32, 64, ..., 4096] and each length uses a different twiddle factor table.
The function uses the standard FFT definition and output values may grow by a factor of fftLen when computing the forward transform. The inverse transform includes a scale of 1/fftLen as part of the calculation and this matches the textbook definition of the inverse FFT.
For the MVE version, the new arm_cfft_init_f32 initialization function is mandatory. Compilation flags are available to include only the required tables for the needed FFTs. Other FFT versions can continue to be initialized as explained below.
For not MVE versions, pre-initialized data structures containing twiddle factors and bit reversal tables are provided and defined in arm_const_structs.h. Include this header in your function and then pass one of the constant structures as an argument to arm_cfft_f32. For example:
arm_cfft_f32(arm_cfft_sR_f32_len64, pSrc, 1, 1)
computes a 64-point inverse complex FFT including bit reversal. The data structures are treated as constant data and not modified during the calculation. The same data structure can be reused for multiple transforms including mixing forward and inverse transforms.
Earlier releases of the library provided separate radix-2 and radix-4 algorithms that operated on floating-point data. These functions are still provided but are deprecated. The older functions are slower and less general than the new functions.
An example of initialization of the constants for the arm_cfft_f32 function follows:
const static arm_cfft_instance_f32 *S;
...
switch (length) {
case 16:
break;
case 32:
break;
case 64:
break;
case 128:
break;
case 256:
break;
case 512:
break;
case 1024:
break;
case 2048:
break;
case 4096:
break;
}
The new arm_cfft_init_f32 can also be used.
Q15 and Q31
The floating-point complex FFT uses a mixed-radix algorithm. Multiple radix-4 stages are performed along with a single radix-2 stage, as needed. The algorithm supports lengths of [16, 32, 64, ..., 4096] and each length uses a different twiddle factor table.
The function uses the standard FFT definition and output values may grow by a factor of fftLen when computing the forward transform. The inverse transform includes a scale of 1/fftLen as part of the calculation and this matches the textbook definition of the inverse FFT.
Pre-initialized data structures containing twiddle factors and bit reversal tables are provided and defined in arm_const_structs.h. Include this header in your function and then pass one of the constant structures as an argument to arm_cfft_q31. For example:
arm_cfft_q31(arm_cfft_sR_q31_len64, pSrc, 1, 1)
computes a 64-point inverse complex FFT including bit reversal. The data structures are treated as constant data and not modified during the calculation. The same data structure can be reused for multiple transforms including mixing forward and inverse transforms.
Earlier releases of the library provided separate radix-2 and radix-4 algorithms that operated on floating-point data. These functions are still provided but are deprecated. The older functions are slower and less general than the new functions.
An example of initialization of the constants for the arm_cfft_q31 function follows:
const static arm_cfft_instance_q31 *S;
...
switch (length) {
case 16:
break;
case 32:
break;
case 64:
break;
case 128:
break;
case 256:
break;
case 512:
break;
case 1024:
break;
case 2048:
break;
case 4096:
break;
}

Function Documentation

void arm_cfft_f32 ( const arm_cfft_instance_f32 S,
float32_t p1,
uint8_t  ifftFlag,
uint8_t  bitReverseFlag 
)
Parameters
[in]Spoints to an instance of the floating-point CFFT structure
[in,out]p1points to the complex data buffer of size 2*fftLen. Processing occurs in-place
[in]ifftFlagflag that selects transform direction
  • value = 0: forward transform
  • value = 1: inverse transform
[in]bitReverseFlagflag that enables / disables bit reversal of output
  • value = 0: disables bit reversal of output
  • value = 1: enables bit reversal of output
Returns
none
void arm_cfft_f64 ( const arm_cfft_instance_f64 S,
float64_t p1,
uint8_t  ifftFlag,
uint8_t  bitReverseFlag 
)
Parameters
[in]Spoints to an instance of the Double Precision floating-point CFFT structure
[in,out]p1points to the complex data buffer of size 2*fftLen. Processing occurs in-place
[in]ifftFlagflag that selects transform direction
  • value = 0: forward transform
  • value = 1: inverse transform
[in]bitReverseFlagflag that enables / disables bit reversal of output
  • value = 0: disables bit reversal of output
  • value = 1: enables bit reversal of output
Returns
none
arm_status arm_cfft_init_f32 ( arm_cfft_instance_f32 S,
uint16_t  fftLen 
)
Parameters
[in,out]Spoints to an instance of the floating-point CFFT structure
[in]fftLenfft length (number of complex samples)
Returns
execution status
Use of this function is mandatory only for the MVE version of the FFT.
Other versions can still initialize directly the data structure using variables declared in arm_const_structs.h
arm_status arm_cfft_init_f64 ( arm_cfft_instance_f64 S,
uint16_t  fftLen 
)
Parameters
[in,out]Spoints to an instance of the floating-point CFFT structure
[in]fftLenfft length (number of complex samples)
Returns
execution status
Use of this function is mandatory only for the MVE version of the FFT.
Other versions can still initialize directly the data structure using variables declared in arm_const_structs.h
arm_status arm_cfft_init_q15 ( arm_cfft_instance_q15 S,
uint16_t  fftLen 
)
Parameters
[in,out]Spoints to an instance of the floating-point CFFT structure
[in]fftLenfft length (number of complex samples)
Returns
execution status
Use of this function is mandatory only for the MVE version of the FFT.
Other versions can still initialize directly the data structure using variables declared in arm_const_structs.h
arm_status arm_cfft_init_q31 ( arm_cfft_instance_q31 S,
uint16_t  fftLen 
)
Parameters
[in,out]Spoints to an instance of the floating-point CFFT structure
[in]fftLenfft length (number of complex samples)
Returns
execution status
Use of this function is mandatory only for the MVE version of the FFT.
Other versions can still initialize directly the data structure using variables declared in arm_const_structs.h
void arm_cfft_q15 ( const arm_cfft_instance_q15 S,
q15_t p1,
uint8_t  ifftFlag,
uint8_t  bitReverseFlag 
)
Parameters
[in]Spoints to an instance of Q15 CFFT structure
[in,out]p1points to the complex data buffer of size 2*fftLen. Processing occurs in-place
[in]ifftFlagflag that selects transform direction
  • value = 0: forward transform
  • value = 1: inverse transform
[in]bitReverseFlagflag that enables / disables bit reversal of output
  • value = 0: disables bit reversal of output
  • value = 1: enables bit reversal of output
Returns
none
void arm_cfft_q31 ( const arm_cfft_instance_q31 S,
q31_t p1,
uint8_t  ifftFlag,
uint8_t  bitReverseFlag 
)
Parameters
[in]Spoints to an instance of the fixed-point CFFT structure
[in,out]p1points to the complex data buffer of size 2*fftLen. Processing occurs in-place
[in]ifftFlagflag that selects transform direction
  • value = 0: forward transform
  • value = 1: inverse transform
[in]bitReverseFlagflag that enables / disables bit reversal of output
  • value = 0: disables bit reversal of output
  • value = 1: enables bit reversal of output
Returns
none
void arm_cfft_radix2_f32 ( const arm_cfft_radix2_instance_f32 S,
float32_t pSrc 
)
Deprecated:
Do not use this function. It has been superseded by arm_cfft_f32 and will be removed in the future
Parameters
[in]Spoints to an instance of the floating-point Radix-2 CFFT/CIFFT structure
[in,out]pSrcpoints to the complex data buffer of size 2*fftLen. Processing occurs in-place
Returns
none
arm_status arm_cfft_radix2_init_f32 ( arm_cfft_radix2_instance_f32 S,
uint16_t  fftLen,
uint8_t  ifftFlag,
uint8_t  bitReverseFlag 
)
Deprecated:
Do not use this function. It has been superseded by arm_cfft_f32 and will be removed in the future.
Parameters
[in,out]Spoints to an instance of the floating-point CFFT/CIFFT structure
[in]fftLenlength of the FFT
[in]ifftFlagflag that selects transform direction
  • value = 0: forward transform
  • value = 1: inverse transform
[in]bitReverseFlagflag that enables / disables bit reversal of output
  • value = 0: disables bit reversal of output
  • value = 1: enables bit reversal of output
Returns
execution status
Details
The parameter ifftFlag controls whether a forward or inverse transform is computed. Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated
The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.
The parameter fftLen Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.
This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.
arm_status arm_cfft_radix2_init_q15 ( arm_cfft_radix2_instance_q15 S,
uint16_t  fftLen,
uint8_t  ifftFlag,
uint8_t  bitReverseFlag 
)
Deprecated:
Do not use this function. It has been superseded by arm_cfft_q15 and will be removed
Parameters
[in,out]Spoints to an instance of the Q15 CFFT/CIFFT structure.
[in]fftLenlength of the FFT.
[in]ifftFlagflag that selects transform direction
  • value = 0: forward transform
  • value = 1: inverse transform
[in]bitReverseFlagflag that enables / disables bit reversal of output
  • value = 0: disables bit reversal of output
  • value = 1: enables bit reversal of output
Returns
execution status
Details
The parameter ifftFlag controls whether a forward or inverse transform is computed. Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated
The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.
The parameter fftLen Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.
This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.
arm_status arm_cfft_radix2_init_q31 ( arm_cfft_radix2_instance_q31 S,
uint16_t  fftLen,
uint8_t  ifftFlag,
uint8_t  bitReverseFlag 
)
Deprecated:
Do not use this function. It has been superseded by arm_cfft_q31 and will be removed in the future.
Parameters
[in,out]Spoints to an instance of the Q31 CFFT/CIFFT structure
[in]fftLenlength of the FFT
[in]ifftFlagflag that selects transform direction
  • value = 0: forward transform
  • value = 1: inverse transform
[in]bitReverseFlagflag that enables / disables bit reversal of output
  • value = 0: disables bit reversal of output
  • value = 1: enables bit reversal of output
Returns
execution status
Details
The parameter ifftFlag controls whether a forward or inverse transform is computed. Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated
The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.
The parameter fftLen Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.
This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.
void arm_cfft_radix2_q15 ( const arm_cfft_radix2_instance_q15 S,
q15_t pSrc 
)
Deprecated:
Do not use this function. It has been superseded by arm_cfft_q15 and will be removed in the future.
Parameters
[in]Spoints to an instance of the fixed-point CFFT/CIFFT structure
[in,out]pSrcpoints to the complex data buffer of size 2*fftLen. Processing occurs in-place
Returns
none
void arm_cfft_radix2_q31 ( const arm_cfft_radix2_instance_q31 S,
q31_t pSrc 
)
Deprecated:
Do not use this function. It has been superseded by arm_cfft_q31 and will be removed in the future.
Parameters
[in]Spoints to an instance of the fixed-point CFFT/CIFFT structure
[in,out]pSrcpoints to the complex data buffer of size 2*fftLen. Processing occurs in-place
Returns
none
void arm_cfft_radix4_f32 ( const arm_cfft_radix4_instance_f32 S,
float32_t pSrc 
)
Deprecated:
Do not use this function. It has been superseded by arm_cfft_f32 and will be removed in the future.
Parameters
[in]Spoints to an instance of the floating-point Radix-4 CFFT/CIFFT structure
[in,out]pSrcpoints to the complex data buffer of size 2*fftLen. Processing occurs in-place
Returns
none
arm_status arm_cfft_radix4_init_f32 ( arm_cfft_radix4_instance_f32 S,
uint16_t  fftLen,
uint8_t  ifftFlag,
uint8_t  bitReverseFlag 
)
Deprecated:
Do not use this function. It has been superceded by arm_cfft_f32 and will be removed in the future.
Parameters
[in,out]Spoints to an instance of the floating-point CFFT/CIFFT structure
[in]fftLenlength of the FFT
[in]ifftFlagflag that selects transform direction
  • value = 0: forward transform
  • value = 1: inverse transform
[in]bitReverseFlagflag that enables / disables bit reversal of output
  • value = 0: disables bit reversal of output
  • value = 1: enables bit reversal of output
Returns
execution status
Details
The parameter ifftFlag controls whether a forward or inverse transform is computed. Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated
The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.
The parameter fftLen Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.
This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.
arm_status arm_cfft_radix4_init_q15 ( arm_cfft_radix4_instance_q15 S,
uint16_t  fftLen,
uint8_t  ifftFlag,
uint8_t  bitReverseFlag 
)
Deprecated:
Do not use this function. It has been superseded by arm_cfft_q15 and will be removed in the future.
Parameters
[in,out]Spoints to an instance of the Q15 CFFT/CIFFT structure
[in]fftLenlength of the FFT
[in]ifftFlagflag that selects transform direction
  • value = 0: forward transform
  • value = 1: inverse transform
[in]bitReverseFlagflag that enables / disables bit reversal of output
  • value = 0: disables bit reversal of output
  • value = 1: enables bit reversal of output
Returns
execution status
Details
The parameter ifftFlag controls whether a forward or inverse transform is computed. Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated
The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.
The parameter fftLen Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.
This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.
arm_status arm_cfft_radix4_init_q31 ( arm_cfft_radix4_instance_q31 S,
uint16_t  fftLen,
uint8_t  ifftFlag,
uint8_t  bitReverseFlag 
)
Deprecated:
Do not use this function. It has been superseded by arm_cfft_q31 and will be removed in the future.
Parameters
[in,out]Spoints to an instance of the Q31 CFFT/CIFFT structure.
[in]fftLenlength of the FFT.
[in]ifftFlagflag that selects transform direction
  • value = 0: forward transform
  • value = 1: inverse transform
[in]bitReverseFlagflag that enables / disables bit reversal of output
  • value = 0: disables bit reversal of output
  • value = 1: enables bit reversal of output
Returns
execution status
Details
The parameter ifftFlag controls whether a forward or inverse transform is computed. Set(=1) ifftFlag for calculation of CIFFT otherwise CFFT is calculated
The parameter bitReverseFlag controls whether output is in normal order or bit reversed order. Set(=1) bitReverseFlag for output to be in normal order otherwise output is in bit reversed order.
The parameter fftLen Specifies length of CFFT/CIFFT process. Supported FFT Lengths are 16, 64, 256, 1024.
This Function also initializes Twiddle factor table pointer and Bit reversal table pointer.
void arm_cfft_radix4_q15 ( const arm_cfft_radix4_instance_q15 S,
q15_t pSrc 
)
Deprecated:
Do not use this function. It has been superseded by arm_cfft_q15 and will be removed in the future.
Parameters
[in]Spoints to an instance of the Q15 CFFT/CIFFT structure.
[in,out]pSrcpoints to the complex data buffer. Processing occurs in-place.
Returns
none
Input and output formats:
Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process. Hence the output format is different for different FFT sizes. The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT:
CFFTQ15.gif
Input and Output Formats for Q15 CFFT
CIFFTQ15.gif
Input and Output Formats for Q15 CIFFT
void arm_cfft_radix4_q31 ( const arm_cfft_radix4_instance_q31 S,
q31_t pSrc 
)
Deprecated:
Do not use this function. It has been superseded by arm_cfft_q31 and will be removed in the future.
Parameters
[in]Spoints to an instance of the Q31 CFFT/CIFFT structure
[in,out]pSrcpoints to the complex data buffer of size 2*fftLen. Processing occurs in-place
Returns
none
Input and output formats:
Internally input is downscaled by 2 for every stage to avoid saturations inside CFFT/CIFFT process. Hence the output format is different for different FFT sizes. The input and output formats for different FFT sizes and number of bits to upscale are mentioned in the tables below for CFFT and CIFFT:
CFFTQ31.gif
Input and Output Formats for Q31 CFFT
CIFFTQ31.gif
Input and Output Formats for Q31 CIFFT