WO2008077422A1

WO2008077422A1 - PROCESSING DEVICE, METHOD, AND SYSTEM USING 2n POINT FFT TO COMPUTE NON-2n POINT DFT

Info

Publication number: WO2008077422A1
Application number: PCT/EP2006/012462
Authority: WO
Inventors: Paul Van Der Arend; Zhengde Lu; Zhen Wang; Bowei Song; Yuanli Wang
Original assignee: Micronas Gmbh
Priority date: 2006-12-22
Filing date: 2006-12-22
Publication date: 2008-07-03
Also published as: CN101601031A

Abstract

The invention regards to processing device, processing method, and processing system for using 2n point FFT to compute non-2n point DFT, having at least one device, comprising a sample rate converter (1) consisting of a polyphase filter and interpolator, to implement functions of low pass filter and sample rate conversion a 2n point FFT device (2) adapted to generate 2n-point FFT results, a clip and shift device (3) adapted to clip and shift results of 2n point FFT device (2) to form non- 2n point frequency domain data, and a frequency compensation unit (4) adapted to do frequency compensation to the clipped and shifted data by multiplication to form finally results of non-2n point DFT.

Description

DESCRIPTION

Processing device, method, and system using 2ⁿ point FFT to compute non-2ⁿ point DFT

Technical Field

The invention regards to a processing method using 2ⁿ point FFT to compute non-2ⁿ point DFT according to pre-characterizing part of claim 1, to a processing device, and processing system using 2ⁿ point FFT to compute non-2ⁿ point DFT.

Background Art

The Discrete Fourier Transformation (DFT) plays an important role in the analysis, design, and implementation of discrete- time signal-processing algorithms and systems. In China Terrestrial Digital Television Broadcasting system, an IFFT/FFT (FFT: Fast Fourier Transformation, IFFT: Inverse FFT) apparatus is indispensable for the Time Domain Synchronous- Orthogonal Frequency Division Multiplex (TDS-OFDM) modem to transmit and receive data.

For 2ⁿ-point DFT, a radix-2 or radix-4 FFT can be used efficiently. But for non-2ⁿ point DFT, such as running in 3780- point IFFT/FFT processor, which is a crucial part in TDS-OFDM, ordinary FFT algorithms used in 2ⁿ point DFT cannot be applied directly. The alternative way is, described as follows, by discomposing 3780 into 9x7x3x5x4, and using Winograd Fourier transform algorithm for computing the 7, 9, 3, 5, 4-point DFT, and Good-Thomas prime factor algorithm. An algorithm and its implementation for 3780-point IFFT/FFT are proposed in "Ter- restrial digital multimedia/television broadcasting system", CN 00123597.4.

Fig. 8 shows a general OFDM system with N sub-carriers, where N point IFFT/FFT processors play core roles in OFDM modulation/demodulation processes. A data stream of data d to be transmitted via multi-path channel 56 radio link is inputted into a serial/parallel device 50. Serial/parallel device 50 multiplexes data onto N sub-carriers. Data on such N sub- carriers are provided to a QAM modulator 51 modulating data. QAM modulator 51 sends modulated data X(k) to an N point IFFT device 52. Fourier transformed data x (n) are provided via n data lines to a device 53 inserting a guard interval into stream of Fourier transformed data. Data outputted by this device 53 are forwarded to a parallel/serial device 54 multiplexing these data onto one single data line. Data stream of data outputted by parallel/serial device 54 are forwarded to a D/A and transmit filter device 55 (D/A: Digital/Analogue) . Digital/Analogue converted and filtered data are sent via an antenna A using the multi-path channel 56 from transmitting device an antenna A of a receiving device. In receiving device received data are filtered and analogue/digital converted by a receive filter and an analogue/digital converter device 57. Filtered and converted data are forwarded to a device 58 for removing guard interval. A second section of this device is constructed as serial/parallel device 59 for multiplexing data x' (n) onto n data lines. These multiplexed data x' (n) are forwarded to an N point FFT device 60 outputting Fourier transformed data X' (k) . These Fourier transformed data X' (k) are forwarded to an equalizer 61. After equalization data are provided to a QAM demodulation device 62 for demodulating data on N sub-carriers. Demodulated data are forwarded to a paral- lel/serial device 63 to demultiplex data and to output data d*.

In transmitter side the modulated frequency domain data before IFFT is X(k), getting the Fourier transformed time domain data x(n) after N point IFFT. In receiver side, the received and multiplexed time domain data is x' (n) , getting the Fourier transformed frequency domain data X' (k) after N point FFT. If there is no distortion through the channel and modulation/demodulation process, multiplexed time domain data x' (n) in receiver device is the same as Fourier transformed time domain data x (n) in transmitter device, and Fourier transformed frequency domain data X' (k) in receiver device should be the same as modulated frequency domain data X(k) in transmitter device, too.

DFT of N point data sequence is defined as

Inverse DFT of N point data sequence is defined as

x(n)=±-YX(k)W-^nk «= 0,l,-,tf-l. (2;

Nf₀

Using fast algorithms for the above formulas to do DFT and inverse DFT, the result will be fine, such as N is an integer power of 2. However, if N is not a 2ⁿ number, finding a hardware efficient fast algorithm is not easy, if for example N is 3780. What's more, these fast algorithms for non-2ⁿ point DFT are not general to any point FFT.

Thus, to use 2ⁿ point FFT to calculate non-2ⁿ point DFT become a natural consideration. But, in use of 2ⁿ point FFT, one must keep in mind that these 2ⁿ point FFT results should be con- verted to non-2ⁿ point DFT results with negligible precision loss and no significant calculation burden added.

There are many variations to calculate A^ppoint DFT, where N is not 2ⁿ number. To compute an N -point DFT when N is composite that is, when N = NiN₂, the common method decomposes the problem using Cooley-Tukey algorithm, which first computes Ni transforms of size N₂, and then computes N₂ transforms of size Ni. The decomposition is applied recursively to both the Ni- and N₂-point DFTs until the problem can be solved using several algorithms in combination, including a variation of Cooley- Tukey, a prime factor algorithm, and a split-radix algorithm.

When N is a prime number, decomposes an N-point problem into three (N-I) -point problems using Rader's algorithm. It then uses the Cooley-Tukey decomposition described above to compute the (N-I) -point DFTs.

For a given composite number N There are many ways to decompose it. Take N = 3780as an example, decomposition can be done as following

3780 = 60x63; 60 = 3x5x4, 63 = 9x7,

3780 = 63x60; 63 = 3x3x7, 60 = 4x5x3,

3780 = 20x189; 20 = 4x5, 189 = 9x3x7, and so on.

In existing solutions, a possible implementation of 3780 IFFT/FFT is showed as Fig. 9, which discloses one possible implementation of 3780 IFFT/FFT. Input data are forwarded to a first block 70. Within this block 70 input data are forwarded to a first sub-block 71 providing a 7 points WFTA (Winograd Fourier Transform Algorithm) . Thereafter this data are for- warded to a further block 72 providing a 9 points WFTA. Afterwards, data are provided to an unscrambling device 73. Un^¬ scrambled data outputted out of this first block 70 are forwarded to a rotator multiplier device 74. Rotated data are forwarded to a second block 75 providing 60 points PFA. Within this second block 75 data are forwarded at first to a sub- block 76 providing 3 points WFTA. Outputted data are forwarded to a further sub-block 77 providing 5 points WFTA. Thereafter data are forwarded to a further sub-block 78 providing 4 points WFTA. Data outputted from this sub-block 78 are forwarded to a further unscrambling device 79. Unscrambled data are provided to a recorder 80 outputting data to the output.

Basic structure of a small point (3, 4, 5, 7, 9) DFT, which apply Winograd Fourier transform algorithm, is depicted in Fig. 10. Inputted data are forwarded to a plurality of parallel arranged AC-devices. Parallel AC-devices are provided with coefficients I and control signals. Data outputted from AC- devices are forwarded to a multiplexer MUX. Multiplexed data are forwarded to a real multiplier device being controlled by a coefficient D and control device. Data outputted by multiplier device are forwarded to a plurality of parallel AC- devices being controlled individually by coefficients O and control signals. Data outputted from these AC-devices are forwarded to a further multiplexer MUX multiplexing such data onto a data output line.

Up to now, the drawbacks of existing solutions are obvious. Firstly, there is not a unified process to compute, such as the butterfly units in radix-4 or radix-2 2ⁿ point FFT. For each non-2ⁿ point DFT, there are different basic processing units and their computation is also irregularly. So, for every non-2^π point DFT, we have to design a different hardware archi- tecture, that is this architecture is not reusable for other point DFTs. Secondly, if N is large and only can be decomposed to many relative prime factors, the computation may be very complex and not suitable to be implemented in hardware.

Technical Problem

It is an object of the invention to provide another solution to use 2ⁿ point FFT to calculate non-2ⁿ point FFT.

Technical Solution

This object is solved by processing method using 2ⁿ point FFT to compute non-2ⁿ point DFT having features according to claim 1, by a processing device using 2ⁿ point FFT to compute non-2ⁿ point DFT having features according to claim 7, and by a processing system using 2ⁿ point FFT to compute non-2ⁿ point DFT having features according to claim 19. Preferred aspects and embodiments are subject-matter of dependent claims.

Especially, there is provided a processing device for using 2ⁿ point FFT to compute non-2ⁿ point DFT, comprising a sample rate converter, a 2ⁿ point FFT device adapted to generate 2ⁿ-point FFT results, and a frequency compensation unit adapted to form finally results of non-2ⁿ point DFT.

Further, there is provided a method for using 2ⁿ point FFT to compute non-2ⁿ point DFT, comprising method steps of sample rate conversion of input data, thereafter using 2ⁿ-point FFT to get 2ⁿ-point FFT results, and afterwards using frequency compensation to form finally results of non-2ⁿ point DFT.

Advantageous Effects Thus, there is provided another method and device or apparatus for performing a non-2ⁿ point IFFT/FFT that utilizes 2ⁿ point FFT. The architecture of this apparatus is regular and consist of components to do sample rate conversion, interpolation, 2ⁿ FFT, and frequency compensation. Complexity of this apparatus is relative low, and computed results are accurate enough to be used in TDS-OFDM system.

Thus there is presented a better solution to use 2ⁿ point FFT to calculate non-2ⁿ point FFT, take 4096 to 3780 as an example. By applying sample rate conversion, interpolation and frequency compensation, method and device provide the 3780 point IFFT/FFT results accurately in such manner that it is appropriate to TDS-OFDM modem.

Especially, sample rate converter consists of a polyphase filter and interpolator, implementing the functions of low pass filter and sample rate conversion. In other words, during sample rate conversion there is implemented a low pass filter polyphase filtering and interpolation.

Especially, a clip and shift device is adapted to clip and shift results of 2ⁿ point FFT device to form non-2ⁿ point frequency domain data, wherein frequency compensation unit is adapted to do frequency compensation to the clipped and shifted data by multiplication. This makes possible clipping and shifting results of 2ⁿ point FFT results to form non-2ⁿ point frequency domain data, wherein frequency compensation is executed to the clipped and shifted data by multiplication, forming the finally results of non-2ⁿ point DFT.

Especially, a look up table or other form of computation mechanism is adapted or used to provide scale-factor in frequency compensation unit.

Especially, processing device and method are adapted as OFDM station including China Terrestrial Digital Television Broadcasting system functionality, and are adapted to use any non-2ⁿ point DFT to complete OFDM modulation/demodulation by 2" point FFT.

Especially, input data fed to the sample rate conversion are repeated to form a cyclic sequence, the repeat length of repetition is variable but generally related to the tap counts of a polyphase filter within sample rate conversion. Especially, the repeated data are end part of the input data, which are padded to the start of the input data or vice versa.

Especially, frequency data output from 2ⁿ point FFT are clipped and shifted according to

X'(k) = X(k\ k = 0,\,--,floor(^^) and

where N₁ is a non-2ⁿ point number, N₂ is a 2ⁿ point number,

N₂>N,, and X(k) is the output of 2ⁿ point FFT, wherein according to preferred embodiment the clipped position is changed. Due to the symmetrical property of FFT and low pass filter and, one can change the clipped position slightly.

Especially, the clipped and shifted data out from 2ⁿ point FFT are scaled by a scale factor, which corresponds to the frequency response of polyphase filter and interpolator of sample rate conversion. Especially, the frequency compensation implements operation

X(k)= X'(k)IH(k),

where X(k) is the final result of non-2ⁿ point DFT, H(k) is the frequency response of polyphase filter and interpolator.

Further, there is provided a processing system for using 2ⁿ point FFT to compute non-2ⁿ point DFT, having at least one such device and/or being adapted to execute such method, comprising a sample rate converter consisting of a polyphase filter and interpolator, to implement functions of low pass filter and sample rate conversion, a 2ⁿ point FFT device adapted to generate 2ⁿ-point FFT results, a clip and shift device adapted to clip and shift results of 2ⁿ point FFT device to form non-2ⁿ point frequency domain data, and a frequency compensation unit adapted to do frequency compensation to the clipped and shifted data by multiplication to form finally results of non- 2ⁿ point DFT.

Especially, such processing system have a design of OFDM systems, including China Terrestrial Digital Television Broadcasting system, using a non-2ⁿ point DFT to complete OFDM modulation/demodulation by 2ⁿ point FFT

Especially, such device, method and/or processing system are adapted to use 4096 point FFT to compute 3780 point DFT.

Description of Drawings

An embodiment will be disclosed in more details with respect to enclosed drawing. There are shown in: Fig. 1 a block diagram of device for computation of 3780 DFT by 4096 FFT,

Fig. 2 diagrams illustrating the conversion of different point DFTs,

Fig. 3 a block diagram of polyphase filter used for LPF and sample rate conversion,

Fig. 4 an illustration of sample rate conversion,

Fig. 5 a flow of the MATLAB program used to compute fre^¬ quency response,

Fig. 6 an example frequency responses of polyphase filter and interpolator,

Fig. 7 constellation of transmitted data and demodulated data,

Fig. 8 a general OFDM system with N sub-carriers, where

N point IFFT/FFT processors play core roles in OFDM modulation/demodulation processes,

Fig. 9 a possible implementation of 3780 IFFT/FFT, and

Fig. 10 an implementation of small point WFTA.

Mode for Invention

Fig. 1 and 2 shows the basic ideas for conversion of different point DFTs. This method apply ideal low pass filter (LPF) and sample rate conversion (SRC) to complete conversion of different point DFTs. For Ni point time domain sampled data, first they are extended to form a periodic sequence with Ni as the period. Ni corresponds to the symbol period T of continuous OFDM signal. After ideal low pass filter, according to sampling theorem, the continuous time domain signal x' (t) can be reconstructed by equation

where T_si is sampling time interval, ω_c is the cut-off frequency of this ideal low pass filter, and x'(t) = x(t), t e [0, T) , and T = N- T_Λ .

For sample rate conversion, provide N₂ > N₁ , sampling interval

is changed to T₂=T₁ — N^L, and t = nT₂, H = O, I,---, N₂ is substituted

N₂ to the above formula, getting N₂ point time domain sampled data. These newly acquired data are used to do N₂ point DFT, getting the frequency domain dataX(£) . There are some important properties OfX(A:), which can be used to compute N₁ point DFT result X(k) from X(k) easily.

The frequency interval between two successive points of X{k) and X(k) is the same, that is

1/(TZN₁) _ i ₌ i/(r/N₂) 1 N₁ T N₂ The following relationship for the frequency domain data of X(k) and X(k) is hold:

X(k) = cX(k) , k = 0, 1, ^{■ ■}•, floor-(^-^) X(N, -k) = cX(N₂ -k), k = 1, ^■ ••, cez7(^—^)

Otherwise

X(k) = 0.

In above equations, cis a constant.

Thus obviously, N₂point DFT will be used to compute N₁ (Ni < N₂) . Just following steps has to be taken: Ni point time domain data x (n) are extended repetitively (Fig. 2 (b) ) . Low pass filter and sample rate conversion is used (Fig. 2 (c)) to acquire N₂ point time domain data (Fig. 2 (d) ) . After sampling (Fig. 2 (e) ) , N₂ point FFT will be done to get first frequency domain data X(k) (Fig. 2 (f)) . First frequency domain data

X(k) is clipped and shifted, then multiplied by a constant factor to get clipped and shifted data X(k) .

In Fig. 2 diagram illustrate the conversion of different point DFTs. There is shown in method applied to different data signals (Fig. 2 (a)) on left side , and on right side of Fig, 2, respectively.

However, in real hardware implementation, the time domain data x(n) sequence can not be repeated infinitely. Further, a de- signable low pass filter should be proposed instead of an ideal low pass filter. Basing on this method there will be de- scribed an example device or apparatus to compute non-2ⁿ point DFT by 2ⁿ point FFT using 4096 to 3780 samples.

Preferred embodiment uses a polyphase filter 4 and a linear interpolator 8 to do low pass filtering and sample rate conversion. In a first section providing sample rate converter 1 3780 time domain data x (n) are up sampled to 4096 time domain data x(n) . Then, up sampled data x(«) are transformed using 4096 point FFT in a second section providing a fast Fourier transformation device 2 to get first frequency domain data

X(k) . First frequency domain data X{k) are clipped and shifted in a third section providing a clip and shift device 3. By clipping and shifting result of 4096 point FFT is changed to intermediate 3780 point frequency domain data X' (k) . At last, these intermediate 3780 point frequency data X' (k) are multiplied in a frequency compensation section in a multiplication device 5 by a frequency compensation factor to acquire final 3780-point FFT frequency domain data X(k).

Fig. 3 discloses block diagram of polyphase filter used for LPF and sample rate conversion showing some further aspects when compared with Fig. 1.

There is shown the process flow of sample rate conversion for the LPF (low pass filter) polyphase filter. The 3780 time domain data x (n) are feed to an input buffer 11 sequentially. Input buffer 11 has length L. After 3780 data blocks are finished, first 2L+2 data of time domain data x (n) is repeated to feed to input buffer 11 again. The length L is variable. A control logic uses data in input buffer 11 and these coefficients from look up table 12 to compute the up-sampled data x_Os (n) adjacent to the positions of converted 4096 up sampled data. Then there is applied interpolation algorithm to acquire the 4096 up sampled time domain data x(n) as output data of this section.

Fig. 4 illustrates the sample rate conversion process and data of such sample rate conversion. Ni time domain data x (n) are converted to interpolated N₂ time domain data x(«) . Related to inputted time domain data x(n) , the position of up sampled time domain data x(«) should be fractional. Its position can be calculated by equation

pos = pos₀+n - N^J-, « = 0,1, ,N₂-I :6i

N,

where poso is the initial position for n = 0. Using above equation (6), the related positions of x(n) are determined to adjacent up-sampled data x_OΞ (n) accurately. Interpolation algorithm is used to compute x(n) . Generally speaking, linear interpolation is enough.

As to the design of polyphase filter, equation (3) can be used directly, i.e. SIΝC function can be used to compute the coefficients of polyphase filter components. There is another easy way to design polyphase filter, applying a filter design toolbox of MATLAB being commercial software of MathWorks, Inc. In this system, these coefficients will be stored m a look up table (LUT), a ROM implemented in hardware.

Take 4096 to 3780 as an example, after obtain the converted 4096 time domain data x(ή) , one can do 4096 FFT to get the frequency domain data X(Ic) . Then, clip and shift such data to get the result of 3780 point DFT. However, as we know the poly phase filter is not an idea low pass filter, causing some amplitude loss and phase shift to the frequency domain data. Thus interpolation is done.

Method to compensate frequency loss bases on the fact that the polyphase filter and interpolation compose a time-invariant linear system. There is a frequency transform function H(k) for this time-invariant linear system. A frequency domain signal X(k) through this system becomes transformed signal Y(k) according to

Y(k) = H(k)- X(k) . (7)

After getting transformed signal Y(k), real DFT result X(k) should be known. If the real DFT results X(k) is known. X(k) can be obtained by the expression

X(k) = Y(k)/H(k) . (8)

In fact, just 1/H(k) need to be calculated. Fig. 5 illustrates the MATLAB program flow to calculate \lH{k) for conversion of 4096 to 3780 DFT. Fig. 5 disclose a flow of the MATLAB program used to compute frequency response. 3780 frequency domain data are set to constant, i.e. 1 with C(k) = 1, k = 0,1,... ,3779 (Sl). Then 3780 IFFT is done to get the time domain data x (n) , n = 0,1,..., 3779 (S2). After sample rate conversion, low pass filter polyphase filter and interpolation there are provided time domain data x(n) , n = 0, 1 ,...., 4095 (S3). Then 4096 FFT is done, followed by clipping and shifting to get transformed signal Y(k),n = 0,1,... ,3779 (S4). Thereafter, 1/H(k) = C(k)Y(k), k = 0,1, ...,3779 is calculated (S5) . Fig. 6 shows example frequency responses of such polyphase filter and interpolator. Left side shows amplitude response |H(k) I and right side shows phase response angle (H (k)). Factually, the details of the frequency response depend on the design of polyphase filter and interpolation method used. Besides the details, there are some common properties of the frequency responses. The phase responses are linear. The amplitude responses far from middle point (1890) are almost constant.

Base on preceding analysis, the processing system used to compute non-2ⁿ point DFT by 2ⁿ point FFT especially consists of the following main components. Sample rate converter 1, consist of LPF polyphase filter and interpolator. Further, there is used a 2ⁿ-point FFT unit, which use Radix-2, Radix-4 or other method to compute FFT. The frequency compensation unit uses complex multiplier and look up table.

Fig. 1 gives the block diagram of this processing system, taking 4096 FFT to 3780 DFT as an example.

Two points should be noticed, firstly in clip and shift process in clip and shift device 3, due to the symmetrical property of the designed low pass filter and FFT algorithm, if not clip in the middle of the data sequence, but some variation of several points exists, it does not matter much. Secondly, the look up table can be simplified for frequency compensation significantly by applies the common properties of H(k) described above.

Finally, take 4096 to 3780 as an example again. Using MATLAB is preferred to generate OFDM signals with 3780 QPSK modulated sub-carriers. Then present processing system will be used to demodulate these OFDM signals. The results will be compared with transmitted signals, and EVM (error vector magnitude) in dB as gauge.

The compare results with different Taps and up-sample times are given in the Table listing up EVM of OFDM modulated signals after 4096 to 3780 DFT conversions.

Fig. 7 shows constellations of transmitted data and demodulated data. OFDM demodulation is implemented by present method. Taps = 41, Up sample times = 100.

Thus, there is provided a unified method to do any non-2ⁿ point DFT by using 2ⁿ point FFT. The structure of this processing system is very regular, and easy to implement in VLSI (Very Large Scale Integration) . Compare to other methods to do any non-2ⁿ point DFT, generally speaking, present method cost less ASIC gates (ASCI: Application Specific Integrated Circuit) and memory usage. Combined with 2ⁿ point FFT any-point DFT can be done. Thus, present method and device can be used in OFDM systems, which utilize the bandwidth of channel adaptively.

Claims

1. Processing device for using 2ⁿ point FFT to compute non-2ⁿ point DFT, comprising

- a sample rate converter (1),

- a 2ⁿ point FFT device (2) adapted to generate 2ⁿ-point FFT results, and

-a frequency compensation unit (4) adapted to form finally results of non-2ⁿ point DFT.

2. Processing device according to claim 1, wherein sample rate converter (3) consists of a polyphase filter and interpo^¬ lator, implementing the functions of low pass filter and sample rate conversion.

3. Processing device according to claim 1 or 2, comprising a clip and shift device (3) adapted to clip and shift results of 2ⁿ point FFT device (2) to form non-2ⁿ point frequency domain data .

4. Processing device according to claim 3, wherein frequency compensation unit (4) adapted to do frequency compensation to the clipped and shifted data by multiplication.

5. Processing device according to any preceding claim, wherein a look up table (6) or other form of computation mechanism is adapted to provide scale-factor in frequency compensation unit (4) .

6. Processing device according to any preceding claim, adapted as OFDM station including China Terrestrial Digital Television Broadcasting system functionality, and adapted to use any non-2ⁿ point DFT to complete OFDM modulation/demodulation by 2ⁿ point FFT.

7. Method for using 2ⁿ point FFT to compute non-2ⁿ point DFT, comprising method steps of

- sample rate conversion of input data (1),

- thereafter using 2ⁿ-point FFT to get 2ⁿ-point FFT results, and

-afterwards using frequency compensation to form finally results of non-2ⁿ point DFT.

8. Method according to claim 7, wherein during sample rate conversion there is implemented a low pass filter polyphase filtering and interpolation.

9. Method according to claim 7 or 8, comprising clipping and shifting results of 2ⁿ point FFT results to form non-2ⁿ point frequency domain data.

10. Processing device according to claim 9, wherein frequency compensation is executed to the clipped and shifted data by multiplication, forming the finally results of non-2ⁿ point DFT.

11. Method according to anyone of claims 7 to 10, wherein a non-2ⁿ point DFT is performed to complete OFDM modulation/demodulation by 2ⁿ point FFT according to China Terrestrial Digital Television Broadcasting system functionality.

12. Method according to anyone of claims 7 to 11, wherein input data feed to the sample rate conversion are repeated to form a cyclic sequence, the repeat length (L) of repetition is variable but generally related to the tap counts of a polyphase filter within sample rate conversion.

13. Method according to claim 12, wherein the repeated data are end part of the input data, which are padded to the start of the input data or vice versa.

14. Method according to anyone of claims 7 to 13, wherein frequency data output from 2ⁿ point FFT are clipped and shifted according to

where N₁ is a non-2ⁿ point number, N₂ is a 2ⁿ point number, N₂>N,, and X(K) is the output of 2ⁿ point FFT.

15. Method according to claim 14, wherein the clipped position is changed.

16. Method according to anyone of claims 14 or 15, wherein the clipped and shifted data out from 2ⁿ point FFT are scaled by a scale factor (q(t)), which corresponds to the frequency response of polyphase filter and interpolator of sample rate conversion.

17. Method according to anyone of claims 7 to 16, wherein a look up table or other form of computation mechanism is used to provide scale-factor in frequency compensation.

18. Method according to claim 17, wherein the frequency compensation implement operation X(k) = X'(k)/H(k) ,

where X(Ji) is the final result of non-2ⁿ point DFT, H(k) is the frequency response which is used to compensate the loss of all the process before the compensation block, which include polyphase filter and interpolator, 2^Λn point fft, clip and shift.

19. Processing system for using 2ⁿ point FFT to compute non-2ⁿ point DFT, having at least one device according to any of claims 1 to 6 and/or adapted to execute method according to any of claims 7 to 18, comprising

- a sample rate converter (1) consisting of a polyphase filter and interpolator, to implement functions of low pass filter and sample rate conversion,

- a 2ⁿ point FFT device (2) adapted to generate 2ⁿ-point FFT results,

- a clip and shift device (3) adapted to clip and shift results of 2ⁿ point FFT device (2) to form non-2ⁿ point frequency domain data, and

-a frequency compensation unit (4) adapted to do frequency compensation to the clipped and shifted data by multiplication to form finally results of non-2ⁿ point DFT.

20. Processing system according to claim 19, having a design of OFDM systems, including China Terrestrial Digital Television Broadcasting system, using a non-2ⁿ point DFT to complete OFDM modulation/demodulation by 2ⁿ point FFT

21. Processing system according to claim 20, using 4096 point FFT to compute 3780 point DFT.