Methods and apparatus to perform windowed sliding transforms
Methods and apparatus to perform windowed sliding transforms are disclosed. An example apparatus includes a transformer to transform a first block of time-domain samples of an input signal into a first frequency-domain representation based on a second frequency-domain representation of a second block of time-domain samples of the input signal, and a windower to apply a third frequency-domain representation of a time-domain window function to the first frequency-domain representation.
1. An apparatus, comprising:
a transformer to transform a first block of time-domain samples of an input signal into a first frequency-domain representation based on a second frequency-domain representation of a second block of time-domain samples of the input signal; and
a windower to apply a third frequency-domain representation of a time-domain window function to the first frequency-domain representation, wherein the windower includes a multiplier to multiply a vector including the first frequency-domain representation and a matrix including the third frequency-domain representation, and wherein at least one of the transformer or the windower is implemented by a logic circuit.
2. The apparatus of claim 1 , further including a kernel generator to compute the matrix by computing a transform of the time-domain window function.
3. The apparatus of claim 2 , wherein the kernel generator is to set a value of a cell of the matrix to zero based on a comparison of the value and a threshold.
4. The apparatus of claim 1 , wherein the transformer computes the first frequency-domain representation based on the second frequency-domain representation using a sliding transform.
5. The apparatus of claim 1 ,
further including a kernel generator to compute the third frequency-domain representation using a discrete Fourier transform,
wherein the transformer computes the first frequency-domain representation based on the second frequency-domain representation using a sliding discrete Fourier transform, and
wherein the windower includes a multiplier to multiply a vector including the first frequency-domain representation and a matrix including the third frequency-domain representation.
6. The apparatus of claim 5 , wherein the multiplication of the vector and the matrix by the multiplier implements an equivalent of a multiplication of the time-domain window function and the first block of time-domain samples.
7. The apparatus of claim 1 , wherein the time-domain window function includes at least one of a sine window function, a slope window function, or a Kaiser-Bessel-derived window function.
8. A method, comprising:
transforming a first block of time-domain samples of an input signal into a first frequency-domain representation based on a second frequency-domain representation of a second block of time-domain samples of the input signal; and
applying a third frequency-domain representation of a time-domain window function to the first frequency-domain representation, wherein the applying the third frequency-domain representation of a time-domain window function to the first frequency-domain representation includes multiplying a vector including the first frequency-domain representation and a matrix including the third frequency-domain representation.
9. The method of claim 8 , further including transforming the time-domain window function to the third frequency-domain representation.
10. The method of claim 9 , further including setting a value of a cell of the matrix to zero based on a comparison of the value and a threshold.
11. The method of claim 8 , wherein transforming the first block of time-domain into the first frequency-domain representation includes computing a sliding discrete Fourier transform.
12. The method of claim 8 , wherein the time-domain window function includes at least one of a sine window function, a slope window function, or a Kaiser-Bessel-derived window function.
13. A non-transitory computer-readable storage medium comprising instructions that, when executed, cause a machine to:
transform a first block of time-domain samples of an input signal into a first frequency-domain representation based on a second frequency-domain representation of a second block of time-domain samples of the input signal; and
apply a third frequency-domain representation of a time-domain window function to the first frequency-domain representation, wherein the instructions, when executed, cause the machine to apply the third frequency-domain representation of the time-domain window function to the first frequency-domain representation by multiplying a vector including the first frequency-domain representation and a matrix including the third frequency-domain representation.
14. The non-transitory computer-readable storage medium of claim 13 , wherein the instructions, when executed, cause the machine to transform the time-domain window function to the third frequency-domain representation.
15. The non-transitory computer-readable storage medium of claim 14 , wherein the instructions, when executed, cause the machine to set a value of a cell of the matrix to zero based on a comparison of the value and a threshold.
16. The non-transitory computer-readable storage medium of claim 13 , wherein the instructions, when executed, cause the machine to transform the first block of time-domain into the first frequency-domain representation by computing a sliding discrete Fourier transform.
17. The non-transitory computer-readable storage medium of claim 13 , wherein the time-domain window function includes at least one of a sine window function, a slope window function, or a Kaiser-Bessel-derived window function.
18. An apparatus, comprising:
a transformer to transform a first block of time-domain samples of an input signal into a first frequency-domain representation based on a second frequency-domain representation of a second block of time-domain samples of the input signal, wherein the transformer computes the first frequency-domain representation based on the second frequency-domain representation using a sliding discrete Fourier transform;
a windower to apply a third frequency-domain representation of a time-domain window function to the first frequency-domain representation, wherein the windower includes a multiplier to multiply a vector including the first frequency-domain representation and a matrix including the third frequency-domain representation, and wherein at least one of the transformer or windower is implemented by a logic circuit; and
a kernel generator to compute the third frequency-domain representation using a discrete Fourier transform.
19. The apparatus of claim 18 , wherein the multiplication of the vector and the matrix by the multiplier implements an equivalent of a multiplication of the time-domain window function and the first block of time-domain samples.