Merge and split discrete sine block transform method
Discrete Sine Transforms in a radix-2 block transform method enables true split and merge transform processing of equal sized data halves in the DST transform domain for enabling recursive merges and splits in DST transform domain without data degradation. Input data in the time domain or spatial domain during either the split and merge radix-2 forward transform processing is firstly transform processed followed by combinational processing. Whole transformed data is split using combinational processing into transformed data halves in the transform domain as a true split. The transformed halves are merged using combinational processing into whole merged transformed data in the transform domain. Time or spatial domain input data can be transformed into the transform domain in the form of split halves or merged whole. The split halves are merged by the merge process combinational processing and the merged whole are split by the split process combinational processing.
1. A method for split processing input data having first and second half data into first and second split sine transformed data, a sine whole transform defining first and second radix-2 sine transforms, the whole sine transform and the first and second radix-2 sine transforms are fast sine transforms, the method comprising the steps of,
whole sine transforming the input data into merged sine transformed data, the merged sine transformed data equaling the whole sine transform of the input data,
split combinational processing the merged sine transformed data into first and second split sine transformed data, the first and second split sine transformed data respectively equaling the first and second radix-2 sine transforms of the first and second half data, and
communicating the first and second split sine transformed data over a communication link to a storage device.
2. The method of claim 1 wherein,
the whole sine transform is a whole sine forward transform, and
the first and second radix-2 sine transforms are half size forward sine transforms.
3. The method of claim 1 further comprising the step of,
recursively splitting by half size combinational processing in the sine transform domain one of the first and second split sine transformed data into half size split sine transformed data, the first and second split sine transformed data being recursively successively split into successive half size split sine transformed data.
4. The method of claim 1 further comprising the steps of,
recursively splitting by half size split combinational processing in the sine transform domain one of the first and second split sine transformed data into half size split sine transformed data, the first and second split sine transformed data being recursively successively split into successive half size split sine transformed data, and
recursively merging by half size merge combinational processing in the sine transform domain two of the half size split sine transformed data into the one of the first and second split sine transformed data as double size merged sine transformed data, the double size merged sine transformed data being recursively successively merged into successive double size merged sine transformed data.
5. The method of claim 1 wherein the split combinational processing comprises at least one processing function selected from the group consisting of scaling, permutating, adding, subtracting, multiplying, dividing, or twiddle factoring.
6. The method of claim 1 wherein
the whole sine transform is S,
the radix-2 sine transforms are S/2,
the split combinational processing is [CL A ], and
[S/2,S/2]=[CL A ]S wherein the input data is first whole sine transformed by S and then split combinationally processed by [CL A ] for providing [S/2,S/2] as the first and second split sine transformed data.
7. A method for merge processing input data having first and second half data into merged sine transformed data, a whole sine transform defining the first and second radix-2 sine transforms, the whole sine transform and the first and second radix-2 sine transforms are fast sine transforms, the method comprising the steps of,
communicating the first and second half data over a communication line to a storage device,
radix-2 sine transforming respectively the first and second half data into first and second split sine transformed data, the first and second split sine transformed data respectively equaling the first and second radix-2 sine transforms of the first and second half data, the first half data being consecutive data of the input data, and the second half data being consecutive data of the input data, and
merge combinational processing the first and second split sine transformed data into the merged sine transformed data, the merged sine transformed data equaling the whole sine transform of the input data.
8. The method of claim 7 wherein,
the whole sine transform is a whole sine forward transform, and
the first and second radix-2 sine transforms are half size forward transforms.
9. The method of claim 7 further comprising the step of,
recursively merging by double size merge combinational processing in the sine transform domain two of the merged sine transformed data into double size merged sine transformed data, the double size merged sine transformed data being recursively successively merged into successive double size merged sine transformed data.
10. The method of claim 7 further comprising the step of,
recursively merging by double size merge combinational processing in the sine transform domain two of the merged sine transformed data into the double size merged sine transformed data, the double size merged sine transformed data being recursively successively merged into successive double size merged sine transformed data, and
recursively splitting by half size split combinational processing in the sine transform domain one of the first and second split sine transformed data into half size split sine transformed data, the first and second split sine transformed data being recursively successively split into successive half size split sine transformed data.
11. The method of claim 7 wherein the merge combinational processing comprises at least one processing function selected from the group consisting of scaling, permutating, adding, subtracting, multiplying, dividing, or twiddle factoring.
12. The method of claim 7 wherein
the whole transform is S,
the radix-2 sine transforms are S/2,
the merge combinational processing is [CL B ], and
S=[CL B ][S/2,S/2] wherein the first half data and second half input are respectively [S/2,S/2] radix-2 sine transformed into the first and second split sine transformed data and then merge combinationally processed by [CL B ] for providing the merged sine transformed data.
13. A method for split and merge processing input data having first and second half data, the split processing for processing the input data respectively into first and second split sine transformed data, the merge processing for processing the input data into merged sine transformed data, the whole sine transform defining first and second radix-2 sine transforms, the whole sine transform and the first and second radix-2 sine transforms are fast sine transforms, the method comprising the steps of,
whole sine transforming the first and second half data into the merged sine transformed data, the merged sine transformed data equaling the whole sine transform of the input data,
split combinational processing the merged sine transformed data into first and second split sine transformed data, the first and second split sine transformed data respectively equaling the first and second radix-2 sine transforms of the first and second half data,
communicating the first and second split sine transformed data over a communication line to a storage device, and
merge combinational processing the first and second split sine transformed data into the merged sine transformed data.
14. The method of claim 13 wherein,
the whole sine transform is a whole forward sine transform, and
the first and second radix-2 sine transforms are half size forward sine transforms.
15. The method of claim 13 further comprising the step of,
recursively splitting by half size split combinational processing in the sine transform domain one of the first and second split sine transformed data into half size split sine transformed data, the first and second split transformed data being recursively successively split into successive half size split sine transformed data, and
recursively merging by double size merge combinational processing in the sine transform domain two of the merged sine transformed data into double size merged sine transformed data, the double size merged sine transformed data being recursively successively merged into successive double size merged sine transformed data.
16. The method of claim 13 wherein,
the split combinational processing comprises at least one processing function selected from the group consisting of scaling, permutating, adding, subtracting, multiplying, dividing, or twiddle factoring, and
the merge combinational processing comprises at least one processing function selected from the group consisting of scaling, permutating, adding, subtracting, multiplying, dividing, or twiddle factoring.
17. The method of claim 13 wherein
the whole sine transform is S,
the radix-2 sine transforms are S/2,
the split combinational processing is [CL A ],
the merge combinational processing is [CL B ],
[S/2,S/2]=[CL A ]S wherein the input data is first whole sine transformed by S and then split combinationally processed by [CL A ] for providing [S/2,S/2] as the first and second split transformed data, and
S=[CL B ][S/2,S/2] wherein the first half input data and second half input data are respectively [S/2,S/2] radix-2 sine transformed into the first and second split sine transformed data and then merge combinationally processed by [CL B ] for providing the merged sine transformed data.
18. The method of claim 13 wherein,
the whole sine transform is S,
the radix-2 sine transforms are S/2,
the split combinational processing is [CL A ],
the merge combinational processing is [CL B ],
[S/2,S/2]=[CL A ]S wherein the input data is first whole sine transformed by S and then split combinationally processed by [CL A ] for providing [S/2,S/2] as the first and second split sine transformed data, and
S=[CL B ][S/2,S/2] wherein the first half data and second half data are respectively [S/2,S/2] radix-2 sine transformed into the first and second split sine transformed data and then merge combinationally processed by [CL B ] for providing the merged sine transformed data,
the method further comprising the steps of,
recursively splitting by half size split combinational processing in the sine transform domain one of the first and second split sine transformed data into half size split sine transformed data, the first and second split sine transformed data being recursively successively split into successive half size split sine transformed data being defined by the half size split combinational processing of the successive half size split sine transformed data, and
recursively merging by double size merge combinational processing in the sine transform domain two of the merged sine transformed data into double size merged sine transformed data, the double size merged sine transformed data being recursively successively merged into successive double size merged sine transformed data being defined by the double size merge combinational processing of the successive double size merged sine transformed data.
19. The method of claim 13 wherein,
the radix-2 sine transforms are fast sine transforms.