Merge and split discrete cosine block transform method
Discrete Cosine Transforms in a radix-2 block transform method enables true split and merge transform processing of equal sized data halves in the transform domain for enabling recursive merges and splits in 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. In the split transform process, whole transformed data is split using combinational processing into first and second transformed data halves in the transform domain as a true split. In the merge transform process, first and second transform halves are merged using combinational processing into a merged transformed data whole in the transform domain. In either case, 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 can be merged by the merge process combinational processing and the merged whole can be split by the split process combinational processing. The split and merge process combinational processing enable recursive splits and merges in the transform domain.
1. A method for split processing input data having first and second half data into first and second split discrete cosine transformed data, a discrete cosine whole transform defining first and second radix-2 discrete cosine transforms, the whole discrete cosine transform and the first and second radix-2 discrete cosine transforms are fast discrete cosine transforms, the method comprising the steps of,
whole discrete cosine transforming the input data into merged discrete cosine transformed data, the merged discrete cosine transformed data equaling the whole discrete cosine transform of the input data,
split combinational processing the merged discrete cosine transformed data into first and second split discrete cosine transformed data, the first and second split discrete cosine transformed data respectively equaling the first and second radix-2 discrete cosine transforms of the first and second half data, and
communicating the first and second split discrete cosine transformed data over a communication link to a storage device.
2. The method of claim 1 wherein,
the whole discrete cosine transform is a whole discrete cosine forward transform, and
the first and second radix-2 discrete cosine transforms are half size forward discrete cosine transforms.
3. The method of claim 1 further comprising the step of,
recursively splitting by half size combinational processing in the discrete cosine transform domain one of the first and second split discrete cosine transformed data into half size split discrete cosine transformed data, the first and second split discrete cosine transformed data being recursively successively split into successive half size split discrete cosine transformed data.
4. The method of claim 1 further comprising the steps of,
recursively splitting by half size split combinational processing in the discrete cosine transform domain one of the first and second split discrete cosine transformed data into half size split discrete cosine transformed data, the first and second split discrete cosine transformed data being recursively successively split into successive half size split discrete cosine transformed data, and
recursively merging by half size merge combinational processing in the discrete cosine transform domain two of the half size split discrete cosine transformed data into the one of the first and second split discrete cosine transformed data, as double size merged trnasformed data, the double size merged discrete cosine transformed data being recursively successively merged into successive double size merged discrete cosine 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 discrete cosine transform is T,
the radix-2 discrete cosine transforms are T/2,
the split combinational processing is [CL A ], and
[T/2, T/2]=[CL A ] T wherein the input data is first whole discrete cosine transformed by T and then split combinationally processed by [CL A ] for providing [T/2, T/2] as the first and second split discrete cosine transformed data.
7. A method for merge processing input data having first and second half data into merged discrete cosine transformed data, a whole discrete cosine transform defining the first and second radix-2 discrete cosine transforms, the whole discrete cosine transform and the first and second radix-2 discrete cosine transforms are fast discrete cosine transforms, the method comprising the steps of,
communicating the first and second half data over a communication line to a storage device,
radix-2 discrete cosine transforming respectively the first and second half data into first and second split discrete cosine transformed data, the first and second split discrete cosine transformed data respectively equaling the first and second radix-2 discrete cosine transforms of the first and second half data, and
merge combinational processing the first and second split discrete cosine transformed data into the merged discrete cosine transformed data, the merged discrete cosine transformed data equaling the whole discrete cosine transform of the input data.
8. The method of claim 7 wherein,
the whole discrete cosine transform is a whole discrete cosine forward transform, and
the first and second radix-2 discrete cosine 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 discrete cosine transform domain two of the merged discrete cosine transformed data into the double size merged discrete cosine transformed data, the double size merged discrete cosine transformed data being recursively successively merged into successive double size merged discrete cosine transformed data.
10. The method of claim 7 further comprising the step of,
recursively merging by double size merge combinational processing in the discrete cosine transform domain two of the merged discrete cosine transformed data into the double size merged discrete cosine transformed data, the double size merged discrete cosine transformed data being recursively successively merged into successive double size merged discrete cosine transformed data, and
recursively splitting by half size split combinational processing in the discrete cosine transform domain one of the first and second split discrete cosine transformed data into half size split discrete cosine transformed data, the first and second split discrete cosine transformed data being recursively successively split into successive half size split discrete cosine 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 T,
the radix-2 discrete cosine transforms are T/2,
the merge combinational processing is [CL B ], and
T=[CL B ] [T/2, T/2] wherein the first half data and second half input are respectively [T/2, T/2] radix-2 discrete cosine transformed into the first and second split discrete cosine transformed data and then merge combinationally processed by [CL B ] for providing the merged discrete cosine 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 discrete cosine transformed data, the merge processing for processing the input data into merged discrete cosine transformed data, the whole discrete cosine transform defining first and second radix-2 discrete cosine transforms, the whole discrete cosine transform and the first and second radix-2 discrete cosine transforms are fast discrete cosine transforms, the method comprising the steps of,
whole discrete cosine transforming the first and second half input data into the merged discrete cosine transformed data, the merged discrete cosine transformed data equaling the whole discrete cosine transform of the input data,
split combinational processing the merged discrete cosine transformed data into first and second split discrete cosine transformed data,
communicating the first and second split discrete cosine transformed data over a communication line to a storage device, and
merge combinational processing the first and second split discrete cosine transformed data into the merged discrete cosine transformed data.
14. The method of claim 13 wherein,
the whole discrete cosine transform is a whole forward discrete cosine transform, and
the first and second radix-2 discrete cosine transforms are half size forward discrete cosine transforms.
15. The method of claim 13 further comprising the step of,
recursively splitting by half size split combinational processing in the discrete cosine transform domain one of the first and second split discrete cosine transformed data into half size split discrete cosine transformed data, the first and second split transformed data being recursively successively split into successive half size split discrete cosine transformed data, and
recursively merging by double size merge combinational processing in the discrete cosine transform domain two of the merged discrete cosine transformed data into double size merged discrete cosine transformed data, the double size merged discrete cosine transformed data being recursively successively merged into successive double size merged discrete cosine 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 discrete cosine transform is T,
the radix-2 discrete cosine transforms are T/2,
the split combinational processing is [CL A ],
the merge combinational processing is [CL A ], [T/2, T/2]=[CL A ] T wherein the input data is first whole discrete cosine transformed by T and then split combinationally processed by [CL A ] for providing [T/2, T/2] as the first and second split transformed data, and
T=[CL B ] [T/2, T/2] wherein the first half input data and second half input data are respectively [T/2, T/2] radix-2 discrete cosine transformed into the first and second split discrete cosine transformed data and then merge combinationally processed by CL B for providing the merged discrete cosine transformed data.
18. The method of claim 13 wherein,
the whole discrete cosine transform is T,
the radix-2 discrete cosine transforms are T/2,
the split combinational processing is [CL A ],
the merge combinational processing is C[CL B ],
[T/2, T/2]=[CL A ] wherein the input data is first whole discrete cosine transformed by T and then split combinationally processed by [CL A ] for providing [T/2, T/2] as the first and second split discrete cosine transformed data, and
T=[CL B ] [T/2, T/2] wherein the first half input data and second half data are respectively [T/2, T/2] radix-2 discrete cosine transformed into the first and second split discrete cosine transformed data and then merge combinationally processed by [CL B ] for providing the merged discrete cosine transformed data,
the method further comprising the steps of,
recursively splitting by half size split combinational processing in the discrete cosine transform domain one of the first and second split discrete cosine transformed data into half size split discrete cosine transformed data, the first and second split discrete cosine transformed data being recursively successively split into successive half size split discrete cosine transformed data being defined by the half size split combinational processing of the successive half size split discrete cosine transformed data, and
recursively merging by double size merge combinational processing in the discrete cosine transform domain two of the merged discrete cosine transformed data into double size merged discrete cosine transformed data, the double size merged discrete cosine transformed data being recursively successively merged into successive double size merged discrete cosine transformed data being defined by the double size merge combinational processing of the successive double size merged discrete cosine transformed data.
19. The method of claim 13 wherein,
the radix-2 discrete cosine transforms are fast discrete cosine transforms.