Fast Fourier transform circuit of audio processing device
A fast Fourier transform (FFT) circuit of an audio processing device configured to perform an N-points FFT and including a memory circuit and a butterfly operation unit circuit is provided. The butterfly operation unit circuit reads two points input data from the memory circuit, performs a butterfly operation for the two points input data according to a twiddle factor to generate two points output data, and writes the two points output data into the memory circuit. The butterfly operation unit circuit includes a multiplier and a plurality of adders/subtractors. The multiplier sequentially multiplies real or imaginary coefficients of one of the two points input data by real or imaginary coefficients of the twiddle factor in multiple clock cycles. The multiplier performs a multiplication once in each clock cycle. The adders/subtractors perform addition/subtraction, such that the butterfly operation unit circuit generates the two points output data.
1. A fast Fourier transform circuit of an audio processing device, configured to perform an N-points fast Fourier transform where N is a power of 2, and comprising:
a memory circuit; and
a butterfly operation unit circuit, coupled to the memory circuit, reading two points input data from the memory circuit, performing a butterfly operation for the two points input data according to a twiddle factor to generate two points output data, and writing the two points output data into the memory circuit, wherein the butterfly operation unit circuit comprises:
a multiplier, sequentially multiplying a real coefficient or an imaginary coefficient of one of the two points input data by a real coefficient or an imaginary coefficient of the twiddle factor in a plurality of clock cycles, wherein the multiplier performs a multiplication once in each of the clock cycles; and
a plurality of adder-subtractors, coupled to the multiplier, and performing an addition or a subtraction according to an output of the multiplier or a real coefficient or an imaginary coefficient of the other one of the two points input data, such that the butterfly operation unit circuit generates the two points output data,
wherein the clock cycles comprise a first clock cycle and a second clock cycle, the multiplier multiplies the real coefficient of one of the two points input data by one of the real coefficient and the imaginary coefficient of the twiddle factor in the first clock cycle to generate a first multiplication output, and the multiplier multiplies the imaginary coefficient of one of the two points input data by the other one of the real coefficient and the imaginary coefficient of the twiddle factor in the second clock cycle to generate a second multiplication output,
wherein the adder-subtractors comprise a first adder-subtractor and a second adder-subtractor, the first adder-subtractor performs an addition or a subtraction according to the first multiplication output and the second multiplication output in the second clock cycle to obtain a first output, and the second adder-subtractor performs an addition or a subtraction according to the first output and the real coefficient of the other one of the two points input data in the second clock cycle to obtain the real coefficient of one of the two points output data,
wherein the clock cycles comprise a third clock cycle, the second adder-subtractor performs an addition or a subtraction according to the first output and the real coefficient of the other one of the two points input data in the third clock cycle to obtain the real coefficient of the other one of the two points output data.
2. The fast Fourier transform circuit of the audio processing device according to claim 1 , further comprising:
a twiddle factor memory circuit, coupled to the butterfly operation unit circuit, and storing the twiddle factor.
3. The fast Fourier transform circuit of the audio processing device according to claim 1 , wherein the N-points fast Fourier transform is based on R points, the N-points fast Fourier transform comprises log R N level stage operations, and the butterfly operation unit circuit performs a butterfly operation N/4 times in an i th level stage operation and sequentially writes N/2 points output data generated in the i th stage operation into the memory circuit, wherein R is an integer greater than 1, and i is an integer greater than or equal to 1 and less than or equal to log R N,
wherein the N/2 points output data generated in the i th level stage operation by the butterfly operation unit circuit are not conjugate symmetric to each other, the memory circuit has (N/2+1)*2 memory addresses, and each of the memory addresses is configured to record a real coefficient or an imaginary coefficient of one of the N/2 points output data.
4. The fast Fourier transform circuit of the audio processing device according to claim 3 , wherein in the i th level stage operation, the butterfly operation unit circuit reads the two points input data from two memory addresses of the memory circuit, and overwrites the two points output data back to the two memory addresses.
5. A fast Fourier transform circuit of an audio processing device, configured to perform an N-points fast Fourier transform where N is a power of 2, and comprising:
a memory circuit; and
a butterfly operation unit circuit, coupled to the memory circuit, reading two points input data from the memory circuit, performing a butterfly operation for the two points input data according to a twiddle factor to generate two points output data, and writing the two points output data into the memory circuit, wherein the butterfly operation unit circuit comprises:
a multiplier, sequentially multiplying a real coefficient or an imaginary coefficient of one of the two points input data by a real coefficient or an imaginary coefficient of the twiddle factor in a plurality of clock cycles, wherein the multiplier performs a multiplication once in each of the clock cycles; and
a plurality of adder-subtractors, coupled to the multiplier, and performing an addition or a subtraction according to an output of the multiplier or a real coefficient or an imaginary coefficient of the other one of the two points input data, such that the butterfly operation unit circuit generates the two points output data,
wherein the clock cycles comprise a first clock cycle and a second clock cycle, the multiplier multiplies the real coefficient of one of the two points input data by one of the real coefficient and the imaginary coefficient of the twiddle factor in the first clock cycle to generate a first multiplication output, and the multiplier multiplies the imaginary coefficient of one of the two points input data by the other one of the real coefficient and the imaginary coefficient of the twiddle factor in the second clock cycle to generate a second multiplication output,
wherein the adder-subtractors comprise a first adder-subtractor and a second adder-subtractor, the first adder-subtractor performs an addition or a subtraction according to the first multiplication output and the second multiplication output in the second clock cycle to obtain a first output, and the second adder-subtractor performs an addition or a subtraction according to the first output and the imaginary coefficient of the other one of the two points input data in the second clock cycle to obtain the imaginary coefficient of one of the two points output data,
wherein the clock cycles comprise a third clock cycle, the second adder-subtractor performs an addition or a subtraction according to the first output and the imaginary coefficient of the other one of the two points input data in the third clock cycle to obtain the imaginary coefficient of the other one of the two points output data.
6. A fast Fourier transform circuit of an audio processing device, configured to perform an N-points fast Fourier transform where N is a power of 2, and comprising:
a plurality of radix-2 butterfly operation circuits, wherein each of the radix-2 butterfly operation circuits performs steps of: receiving input data, and performing a butterfly operation for the input data according to one twiddle factor of M twiddle factors to generate output data, wherein the butterfly operation comprises a plurality of additions and subtractions and a plurality of multiplications decomposed based on a complex operation, and M is a positive integer less than N/2,
wherein each of the radix-2 butterfly operation circuits sequentially perform the additions or the subtractions and the multiplications in a plurality of clock cycles, and the multiplication is performed at most once in each of the clock cycles,
wherein one single multiplier is used in each of the radix-2 butterfly operation circuits to perform the multiplications,
wherein each of the radix-2 butterfly operation circuits further comprises:
a memory circuit, configured to store the input data and the output data, and having (N/2+1)*2 memory addresses, wherein each of the memory addresses is configured to record a real coefficient or an imaginary coefficient of one of N/2 points output data.
7. The fast Fourier transform circuit of the audio processing device according to claim 6 , wherein each of the radix-2 butterfly operation circuits further comprises:
a plurality of adder-subtractors, coupled to the multiplier, and performing an addition or a subtraction according to an output of the multiplier or a real coefficient or an imaginary coefficient of the input data, such that the butterfly operation unit circuit generates the output data.
8. The fast Fourier transform circuit of the audio processing device according to claim 6 , further comprising:
a read-only memory, coupled to each of the radix-2 butterfly operation circuits, and storing the M twiddle factors, wherein M is equal to N/4.
9. The fast Fourier transform circuit of the audio processing device according to claim 6 , wherein at least part of the radix-2 butterfly operation circuits constitute one or more butterfly operation circuits having a radix greater than 2.