# Patent

## Title
FFT and FHT engine

## Abstract

A transformation engine includes an address generator; a butterfly unit coupled to the address generator; a twiddle LUT coupled to the address generator; and a multiplier having a first input coupled to the butterfly unit and a second input coupled to the twiddle LUT.

## Background
This application is a continuation of U.S. patent application Ser. No. 10/074,629 filed Feb. 14, 2002 entitled “FFT AND FHT ENGINE,” now U.S. Pat. No. 6,957,241 the content of which is hereby incorporated by reference.


BACKGROUND
Spread spectrum techniques are well known. In a typical spread-spectrum communication system, transmitted bits are replaced by a spreading sequence, which are stored in a receiver. During transmission, received samples are correlated with the stored sequence to determine the transmitted bits. For a spread-spectrum system using Walsh Codes, the receiver would typically correlate the received samples with all possible Walsh Codes of the same length. Such an operation can be efficiently implemented using a Fast Hadamard Transform.
In another trend, OFDM transmission systems are becoming ubiquitous. The major processing elements in an OFDM communication system are the IFFT and FFT blocks at the transmitter and receiver. Considerable processing power and hardware resources are required to compute the FFT/IFFTs to make the communication system run in real-time.
FFT and FHT are usually implemented in hardware to meet the real-time processing requirements for high data throughput communication systems. Typically these are implemented as separate hardware blocks. Such separate hardware takes up chip real-estate. Moreover, having separate FFT and FHT hardware increases power consumption.
SUMMARY
In one aspect, a transformation engine includes an address generator; a butterfly unit coupled to the address generator; a twiddle LUT coupled to the address generator; and a multiplier having a first input coupled to the butterfly unit and a second input coupled to the twiddle LUT.
Implementations of the above system may include one or more of the following. The butterfly unit can compute fast fourier transform (FFT) operations. The butterfly unit can compute decimation in frequency fast fourier transform (DIF FFT) operations. The butterfly unit can also compute fast Hadamard transform (FHT) operations. The twiddle LUT contains twiddle factors set to one. Input data belonging to FHT samples are mapped to predetermined inputs. Remaining input data is set to zero. An input buffer can be coupled to the butterfly unit. An output buffer can be coupled to the multiplier.
In another aspect, a method for performing a plurality of transformations includes determining a transformation operation to be performed on data; and sharing a transformation engine between multiple transformation operations.
Advantages of the invention can include one or more of the following. The system provides a Fast Hadamard Transform engine that is fast and that shares hardware with other operations in digital radio transmitters and receivers. By making use of the similarity of operations for FFT and FHT it is possible to use the same hardware to compute FFT and FHT with a small amount of reconfiguration. For multi-mode communication system, the system supports reusing hardware blocks of one protocol to perform the computations for other protocols and thus obviates the need to provide separate hardware blocks. This sharing reduces chip area and hence the cost.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a portion of a digital receiver.
FIG. 2 shows an exemplary FHT topology.
FIG. 3 shows an exemplary FFT topology.
FIG. 4 shows an example of Radix-4 64-point FFT topology being re-used for FHT
FIG. 5 shows an exemplary Butterfly re-use pattern of the engine of FIG. 2 to perform FHT processing.
FIG. 6 shows one embodiment of a FFT/FHT engine.
FIG. 7 shows an exemplary wireless based system that uses the FFT/FHT engine.



DESCRIPTION
Reference will now be made in detail to the preferred embodiments of the invention, examples of which are illustrated in the accompanying drawings. While the invention will be described in conjunction with the preferred embodiments, it will be understood that they are not intended to limit the invention to these embodiments. On the contrary, the invention is intended to cover alternatives, modifications and equivalents, which may be included within the spirit and scope of the invention as defined by the appended claims. Furthermore, in the following detailed description of the present invention, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be obvious to one of ordinary skill in the art that the present invention may be practiced without these specific details. In other instances, well known methods, procedures, components, and circuits have not been described in detail as not to unnecessarily obscure aspects of the present invention.
FIG. 1 shows an exemplary receiver circuit 10. The receiver circuit 10 includes a receive filter 20 that receives digitized radio frequency signals. The filter 20 digitally removes signals outside of the receive frequency and provides the filtered data to an engine 30 that can handle both FFT and FHT operations. The output of the engine 30 is provided to a channel decoder 70.
FFT is usually used in orthogonal frequency division multiplexing (OFDM) receivers to perform sub-carrier demodulation. Fast Hadamard transformations are used in spread spectrum systems to de-correlate multiple codes simultaneously. FFT and FHT both have several similarities that can be exploited. Note the similarities between the Radix-4 FFT operations/topology and the FHT operations/topology used for CCK demodulation. The radix-4 FFT butterfly is given by:




  
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A Radix-4 FFT butterfly takes in 4 complex inputs and produces 4 complex outputs.
The FHT butterfly takes in two inputs and produces four outputs.




  
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The FHT butterfly takes in two inputs and produces four outputs. By inspection of the matrices, it can be seen that FHT butterfly results if x(2)=x(3)=0 in the FFT matrix.
A 64 point Radix-4 FFT has three stages. Each stage uses 16 butterflies. Each stage produces 64 outputs. The total number of input samples is 64 and the total number of output samples is 64. The 8 point FHT used in 802.11b has three stages. The first stage has 4 butterflies, the second stage has 8 butterflies and the final stage has 16 butterflies. The first stage produces 16 outputs, the second stage produces 32 outputs and the final stage produces 64 outputs.
The 64 point Radix-4 FFT takes in 64 complex inputs and produces 64 complex outputs, an example of which is shown in FIG. 3, a black-box view of the 64 point complex FFT. Internally, the operations are performed using Radix-4 butterflies and the outputs of the butterflies are multiplied by twiddle factors. As described in more detail below, the circuit of FIG. 6 reduces the area and cost by re-using the computation blocks of one receiver for performing the computations for the other. The FFT engine is reused for FHT by incorporating the following changes:
1. Set all twiddle factors equal to 1
2. Map the FHT samples to appropriate inputs
3. Set the rest of the inputs to zero.
Turning now to one implementation of the system, a Fast Hadamard Transform (FHT) takes in 8 inputs. Here the inputs of the FFT block are denoted {x0, x1, . . . , x63}. A set of samples {a0, a1, . . . a7} for FHT is mapped to the FFT inputs {x0, . . . x63} using the following table. The rest of the FFT inputs are set to zero.














Input for FHT
FFT ports









A0
X0



A1
X32



A2
X8



A3
X40



A4
X2



A5
X34



A6
X10



A7
X42










The butterflies of Radix 4 FFT can be re-used for FHT if the intermediate values are properly routed between the butterflies. The butterfly re-use pattern for FHT is given in FIG. 5. The circles show butterflies of the 64-point Radix-4 FFT. The circles in gray are re-used for FHT.
FIG. 2 shows an exemplary Fast Hadamard Transform topology. This topology shows 1⁄4th of the structure for a Fast Hadamard transform for input vector length 8. There are 8 inputs and 16 outputs. The same structure is repeated 4 times with different values of 2 to obtain the 64 output values.
FIG. 3 shows an exemplary 64-point Radix 4, Decimation in Frequency FFT structure with 64 inputs and 64 output. FIG. 4 shows the application of the 64-point Radix-4 FFT structure of FIG. 3 in computing a Fast Hadamard transform for input vector length 8 of FIG. 2. The mapping between the FFT input ports and the FHT input signals is given in Table 1. The dashed lines in FIG. 4 indicate the data flow for FHT. It can be seen from the figures that four of the FFT butterflies are re-used in the first stage, 8 of them in the second stage and 16 of them in the third stage. FIG. 5 shows an exemplary butterfly re-use pattern for re-using the Radix-4 DIF FFT engine for the computation of FHT. The circles represent the butterflies and the dark circles are re-used.
FIG. 6 shows the exemplary engine 30 that can be programmably selected as an FFT engine or an FHT engine. The engine 30 has an input buffer 32 that receives data to be processed. The input buffer 32 is driven by an address generator 34. The output of the input buffer 32 is received by a butterfly unit 36. The output of the butterfly unit 36 is provided to a P/S unit 38. The address generator 34 also drives the P/S unit 38. The output of the P/S unit 38 is provided to one input of a complex multiplier 40, while a second input of the complex multiplier 40 receives the output of a twiddle LUT 42. The address generator 34 also drives the address input of the twiddle LUT 42. The output of the multiplier is saved in an output buffer 44 whose address input is driven by the address generator 34. The output of the output buffer 44 is presented to the channel decoder 70.
FIG. 7 shows a block diagram of an exemplary multi-mode wireless receiver which implements two protocols for non-simultaneous operation. Protocol 1 uses FFT algorithm for reception and Protocol 2 uses FHT algorithm. Radio signals are fed to an analog to digital (A/D) converter 70 and an A/D converter 90. The output of the A/D converter 70 is provided to a first receive filter 72, whose output is provided to a synchronizing circuit 74. The output of the synchronizing circuit 74 is provided to the combined FFT/FHT engine 30 (FIG. 6). The output of the FFT/FHT engine 30 is provided to first and second channel decoders 76 and 96, respectively. Correspondingly, the output of the A/D converter 90 is provided to a second receive filter 92, whose output is provided to a second synchronizing circuit 94, which in turn drives a second input of the combined FFT/FHT engine 30. A digital signal processor 80 coordinates and controls the filter, synchronizing circuit, combined FFT/FHT engine 30, and the channel decoders to provide output data.
As shown in FIG. 7, separate hardware blocks are used for the filtering and synchronization operation for these protocols. However, the FFT and FHT block is shown as shared between the protocols thus reducing the hardware requirement. A DSP core controls the operation of these hardware blocks. It also selects the mode of operation of the combined FFT-FHT block.
Although the invention has been shown and described with respect to certain preferred embodiments, it is obvious that equivalents and modifications will occur to others skilled in the art upon the reading and understanding of the specification. The present invention includes all such equivalents and modifications, and is limited only by the scope of the following claims.

## Claims

1. An apparatus comprising:
a transformation circuit configured to perform a transformation operation based on an operating mode, wherein the transformation circuit is configured to perform a fast Hadamard transform (FHT) operation in a first operating mode and a fast Fourier transform (FFT) operation in a second operating mode, wherein the transformation circuit includes:
a fast Fourier transform (FFT) circuit configured to perform an FFT operation in the second operating mode; and
an input buffer coupled to provide FHT samples to at least one, but not all, inputs of the FFT circuit in the first operating mode, wherein the transformation circuit is configured to perform the FHT operation using the FFT circuit and the FHT samples provided by the input buffer.

2. The apparatus of claim 1, wherein the FFT circuit is configured to receive at least two inputs and produce at least four outputs.

3. The apparatus of claim 1, wherein the apparatus is configured, when performing the FHT operation, to set all twiddle factors to a value of one, and to map FHT samples for the FHT operation to selected inputs of the FFT circuit.

4. The apparatus of claim 1, further comprising a digital signal processor (DSP) configured to control the transformation circuit.

5. The apparatus of claim 1, wherein the FFT circuit is an M point, radix N butterfly unit, wherein M and N are integer values.

6. The apparatus of claim 5, wherein M=64 and N=4.

7. The apparatus of claim 1, wherein the transformation circuit further includes:
a twiddle lookup table (LUT) configured to store twiddle factors; and
a multiplier circuit coupled to receive twiddle factors from the twiddle LUT and outputs from the FFT circuit.

8. A receiver comprising:
a filter configured to receive incoming digitized radio frequency (RF) signals and to provide filtered data as an output;
a transformation circuit coupled to the filter to receive the filtered data and configured to perform a fast Fourier transform (FFT) operation or a fast Hadamard transform (FHT) operation on the filtered data based on an operating mode of the transformation circuit, wherein the transformation circuit includes:
a fast Fourier transform (FFT) circuit configured to perform an FFT operation in a first operating mode;
an input buffer coupled to provide FHT samples to at least one, but not all, inputs of the FFT circuit in a second operating mode to permit the transformation circuit to perform the FHT operation using the FFT circuit and the provided FHT samples; and

a channel decoder coupled to an output of the transformation circuit.

9. The receiver of claim 8, further comprising a synchronization unit coupled between the filter and the transformation circuit.

10. The receiver of claim 8, further comprising a digital signal processor (DSP) coupled to the filter and the transformation circuit.

11. The receiver of claim 10, wherein the DSP is configured to control the transformation circuit to perform the FFT operation and the FHT operation.

12. The receiver of claim 8, wherein the receiver comprises a multi-mode wireless receiver.

13. The receiver of claim 8, wherein the transformation circuit is configured to perform the FFT operation in an orthogonal frequency division multiplexing mode.

14. The receiver of claim 13, wherein the transformation circuit is configured to perform the FHT operation in a spread spectrum mode.

15. The receiver of claim 8, wherein the FFT circuit is an M point, radix N butterfly unit, wherein M and N are integer values.

16. The receiver of claim 15, wherein M=64 and N=4.

17. The receiver of claim 8, wherein the transformation circuit is configured to perform the FFT operation when the receiver is operating according to a first communication protocol, and further configured to perform the FHT operation when the receiver is operating according to a second communication protocol.

18. The receiver of claim 8, wherein the transformation circuit further includes:
a twiddle lookup table (LUT) configured to store twiddle factors; and
a multiplier circuit coupled to receive twiddle factors from the twiddle LUT and outputs from the FFT circuit.

19. A method comprising:
performing a first transformation operation in a transformation circuit, wherein the first transformation operation comprises a fast fourier transform (FFT) operation performed by a Fast Fourier Transform (FFT) circuit when the transformation circuit is operating in a first mode; and
performing a second transformation operation in the transformation circuit, wherein the second transformation operation comprises a fast Hadamard transform (FHT) operation performed by the FFT circuit when the transformation circuit is operating in a second mode, wherein performing the FHT operation includes a buffer providing FHT samples to at least one, but not all, inputs of the FFT circuit to permit the FFT circuit to perform the FHT operation using the provided FHT samples.

20. The method of claim 19, further comprising setting input data to zero for remaining ones of the inputs of the FFT circuit.

21. The method of claim 19, wherein the butterfly unit is an M point, radix N butterfly unit, wherein M and N are integer values.

22. The method of claim 17, wherein M=64 and N=4.

23. The method of claim 19, further comprising:
providing the outputs of the FFT circuit to a multiplier;
providing twiddle factors from a twiddle lookup table (LUT) to the multiplier; and
multiplying the outputs of the FFT circuit by the twiddle factors.