Collaboration diagram for Complex FFT Functions:

Functions
tpt_status	tpt_cfft_f32 (f32_t *aInPlace, size_t aLogN, bool aIfftFlag)
	Processing function for the floating-point complex FFT. More...

tpt_status	tpt_cfft_f64 (f64_t *aInPlace, size_t aLogN, bool aIfftFlag)
	Processing function for the floating-point complex FFT. More...

tpt_status	tpt_cfft_q15 (q15_t *aInPlace, size_t aLogN, bool aIfftFlag)
	Processing function for the Q15 complex FFT. More...

tpt_status	tpt_cfft_q31 (q31_t *aInPlace, size_t aLogN, bool aIfftFlag)
	Processing function for the Q31 complex FFT. More...

Detailed 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.

: The algorithms only support lengths of power of 2. Therefore, the actual fftLen is 2^aLogN.

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.

Algorithm

1] forward transform

           N-1
    X[k] = sum { x[n] * W(N, kn) } for k = 0, 1, ..., N - 1
           n=0

2] inverse transform

                     N-1
    x[k] = (1 / N) * sum { X[n] * W(N, -kn) } for k = 0, 1, ..., N - 1
                     n=0

The 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 the corresponding aLogN value is [4, 5, 6, ..., 12].

: 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.

Function: Combined Radix4 Decimation in Frequency CFFT function

: 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.

: The algorithms only support lengths of power of 2. Therefore, the actual fftLen is 2^aLogN.

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.

Algorithm

1] forward transform

           N-1
    X[k] = sum { x[n] * W(N, kn) } for k = 0, 1, ..., N - 1
           n=0

2] inverse transform

                     N-1
    x[k] = (1 / N) * sum { X[n] * W(N, -kn) } for k = 0, 1, ..., N - 1
                     n=0

The 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 the corresponding aLogN value is [4, 5, 6, ..., 12].

: 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.

Function: Combined Radix4 Decimation in Frequency CFFT function

Function Documentation

◆ tpt_cfft_f32()

tpt_status tpt_cfft_f32	(	f32_t *	aInPlace,
		size_t	aLogN,
		bool	aIfftFlag
	)

Processing function for the floating-point complex FFT.

Parameters

[in,out]	aInPlace	points to the complex data buffer of size `2 * fftLen`. Processing occurs in-place.
[in]	aLogN	The fftLen is 2^aLogN.
[in]	aIfftFlag	flag that selects transform direction value = false: forward transform value = true : inverse transform

Returns

execution status

TPT_MATH_SUCCESS : Operation is successful.
TPT_MATH_ARGUMENT_ERROR : aLogN is not supported.

Parameters

[in,out]	aInPlace	points to the complex data buffer of size. `2 * fftLen`. Processing occurs in-place.
[in]	aLogN	the fftLen is 2^aLogN.
[in]	aIfftFlag	flag that selects transform direction. value = false: forward transform value = true : inverse transform

Returns

execution status

TPT_MATH_SUCCESS : Operation is successful.
TPT_MATH_ARGUMENT_ERROR : aLogN is not supported.

◆ tpt_cfft_f64()

tpt_status tpt_cfft_f64	(	f64_t *	aInPlace,
		size_t	aLogN,
		bool	aIfftFlag
	)

Processing function for the floating-point complex FFT.

Parameters

[in,out]	aInPlace	points to the complex data buffer of size `2 * fftLen`. Processing occurs in-place.
[in]	aLogN	The fftLen is 2^aLogN.
[in]	aIfftFlag	flag that selects transform direction value = false: forward transform value = true : inverse transform

Returns

execution status

TPT_MATH_SUCCESS : Operation is successful.
TPT_MATH_ARGUMENT_ERROR : aLogN is not supported.

Parameters

[in,out]	aInPlace	points to the complex data buffer of size. `2 * fftLen`. Processing occurs in-place.
[in]	aLogN	the fftLen is 2^aLogN.
[in]	aIfftFlag	flag that selects transform direction. value = false: forward transform value = true : inverse transform

Returns

execution status

TPT_MATH_SUCCESS : Operation is successful.
TPT_MATH_ARGUMENT_ERROR : aLogN is not supported.

◆ tpt_cfft_q15()

tpt_status tpt_cfft_q15	(	q15_t *	aInPlace,
		size_t	aLogN,
		bool	aIfftFlag
	)

Processing function for the Q15 complex FFT.

Processing function for the Q31 complex FFT.

Parameters

[in,out]	aInPlace	points to the complex data buffer of size `2 * fftLen`. Processing occurs in-place.
[in]	aLogN	The fftLen is 2^aLogN.
[in]	aIfftFlag	flag that selects transform direction value = false: forward transform value = true : inverse transform

Returns

execution status

TPT_MATH_SUCCESS : Operation is successful.
TPT_MATH_ARGUMENT_ERROR : aLogN is not supported.

Input and output formats:: Internally input is downscaled 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:

Input and Output Formats for Q15 CFFT
aLogN	CFFT Size	Input format	Output format	Number of bits to upscale
4	16	1.15	5.11	4
5	32	1.15	6.10	5
6	64	1.15	7.9	6
7	128	1.15	8.8	7
8	256	1.15	9.7	8
9	512	1.15	10.6	9
10	1024	1.15	11.5	10
......

Input and Output Formats for Q15 CIFFT
aLogN	CFFT Size	Input format	Output format	Number of bits to upscale
4	16	1.15	5.11	0
5	32	1.15	6.10	0
6	64	1.15	7.9	0
7	128	1.15	8.8	0
8	256	1.15	9.7	0
9	512	1.15	10.6	0
10	1024	1.15	11.5	0
......

Parameters

[in,out]	aInPlace	points to the complex data buffer of size. `2 * fftLen`. Processing occurs
[in]	aLogN	the fftLen is 2^aLogN.
[in]	aIfftFlag	flag that selects transform direction value = false: forward transform value = true : inverse transform

Returns

execution status

TPT_MATH_SUCCESS : Operation is successful.
TPT_MATH_ARGUMENT_ERROR : aLogN is not supported.

Input and output formats:: Internally input is downscaled 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:

Input and Output Formats for Q31 CFFT
aLogN	CFFT Size	Input format	Output format	Number of bits to upscale
4	16	1.31	5.27	4
5	32	1.31	6.26	5
6	64	1.31	7.25	6
7	128	1.31	8.24	7
8	256	1.31	9.23	8
9	512	1.31	10.22	9
10	1024	1.31	11.21	10
......

Input and Output Formats for Q31 CIFFT
aLogN	CFFT Size	Input format	Output format	Number of bits to upscale
4	16	1.31	5.27	0
5	32	1.31	6.26	0
6	64	1.31	7.25	0
7	128	1.31	8.24	0
8	256	1.31	9.23	0
9	512	1.31	10.22	0
10	1024	1.31	11.21	0
......

◆ tpt_cfft_q31()

tpt_status tpt_cfft_q31	(	q31_t *	aInPlace,
		size_t	aLogN,
		bool	aIfftFlag
	)

Processing function for the Q31 complex FFT.

Parameters

[in,out]	aInPlace	points to the complex data buffer of size `2 * fftLen`. Processing occurs in-place.
[in]	aLogN	The fftLen is 2^aLogN.
[in]	aIfftFlag	flag that selects transform direction value = false: forward transform value = true : inverse transform

Returns

execution status

TPT_MATH_SUCCESS : Operation is successful.
TPT_MATH_ARGUMENT_ERROR : aLogN is not supported.

Input and output formats:: Internally input is downscaled 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:

Input and Output Formats for Q31 CFFT
aLogN	CFFT Size	Input format	Output format	Number of bits to upscale
4	16	1.31	5.27	4
5	32	1.31	6.26	5
6	64	1.31	7.25	6
7	128	1.31	8.24	7
8	256	1.31	9.23	8
9	512	1.31	10.22	9
10	1024	1.31	11.21	10
......

Input and Output Formats for Q31 CIFFT
aLogN	CFFT Size	Input format	Output format	Number of bits to upscale
4	16	1.31	5.27	0
5	32	1.31	6.26	0
6	64	1.31	7.25	0
7	128	1.31	8.24	0
8	256	1.31	9.23	0
9	512	1.31	10.22	0
10	1024	1.31	11.21	0
......

Parameters

[in,out]	aInPlace	points to the complex data buffer of size. `2 * fftLen`. Processing occurs
[in]	aLogN	the fftLen is 2^aLogN.
[in]	aIfftFlag	flag that selects transform direction value = false: forward transform value = true : inverse transform

Returns

execution status

TPT_MATH_SUCCESS : Operation is successful.
TPT_MATH_ARGUMENT_ERROR : aLogN is not supported.

Input and output formats:: Internally input is downscaled 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:

Input and Output Formats for Q31 CFFT
aLogN	CFFT Size	Input format	Output format	Number of bits to upscale
4	16	1.31	5.27	4
5	32	1.31	6.26	5
6	64	1.31	7.25	6
7	128	1.31	8.24	7
8	256	1.31	9.23	8
9	512	1.31	10.22	9
10	1024	1.31	11.21	10
......

Input and Output Formats for Q31 CIFFT
aLogN	CFFT Size	Input format	Output format	Number of bits to upscale
4	16	1.31	5.27	0
5	32	1.31	6.26	0
6	64	1.31	7.25	0
7	128	1.31	8.24	0
8	256	1.31	9.23	0
9	512	1.31	10.22	0
10	1024	1.31	11.21	0
......