DE4026476A1 - Complex polyphase filter network for sampling rate change - groups in each branch folding prods. of real and imaginary parts of input signal for interpolation of decimation - Google Patents

Abstract

The filter network works with complex input and output signal and complex coeffts. for interpolation about a factor L. The complex input signal is combined with a complex pulse reply into a specified complex output signal (yr) with L branches. In each L branch, the combination products of the real and imaginary parts of the input signal are grouped with the complex branch pulse replies of a respective branch to form yiz signals. Then all L real parts and L imaginary parts are synchronously multiplexed. USE/ADVANTAGE - For frequency multiplexing esp. in cable TV or radio systems. Low-cost construction.

Description

The invention relates to a complex Polyphase filter network for changing the sampling rate according to Preamble of claim 1 and 3. Such networks are known, for example by "Advancend Topics in Signal Processing "by Lim and Oppenheim, Prentice Hall, [1], by the Essay "On the Transposition of linear Time-Varying Discrete- Time Networks and its Application to Multirate Digital Systems " by Claasen and Mecklenbräuker in Phillips Journal of Research Vol. 33, page 78-102, 1978 [2] or by the article "An Analytic Signal Approach for Transmultiplexers: Theory and Design "by Del Re and Emiliani in IEEEE Transactions on Communications, Vol. Com-30, No. 7, July 1982 from page 1623 [3], the Literature [1] indicates a polyphase structure for real ones Input and output signals and the literature reference [2] transitions, d. H. Transpositions from interpolation to decimation and vice versa.

The known filter structures have the disadvantage of a high one Effort:

• 1. At the high sampling frequency are arithmetic Operations required.
• 2. There are more than the minimum number of multiplexers (at the Interpolation) or demultiplexers (for decimation) needed.  
• 3. The filter structures are for non-recursive implementation not canonical with regard to the number of delay elements.

The invention was based on the object To specify polyphase filter network of the type mentioned at the outset, that is not very expensive.

This object was achieved with the features of claim 1 or 3. Advantageous refinements result from the Subclaims.

The polyphase filter network according to the invention has the advantage less effort. This is achieved by the number of rapid operations reduced to a minimum becomes. In addition, the number of delay elements increases the canonical, d. H. minimal possible number reduced. By this measure will be particularly very high systems Input or output sampling frequencies, e.g. B. digital Frequency multiplexer or demultiplexer for cable television or Directional radio applications in the first place or now with acceptable ones Effort can be achieved, see and compare literature reference [3]; this stems from the fact that with the invention Polyphase filter network value now uses higher sampling frequencies can be, in which are from speed Do not set up arithmetic operations or only do so with very large Have circuit work done.

Fig. 1 shows the general structure for an interpolation Polyphasenfilternetzwerk for complex input and output signals.

In Fig. 2 is a detailed block diagram for one of the 4 sub-filters an interpolation Polyphasenfilternetzwerkes is recognizable.

FIG. 3 shows the transposed filter structure of a branch filter according to FIG. 2.

FIG. 4 shows the implementation according to the invention a Polyphasenfilternetzwerkes for complex input and output signals of general branch filter structure.

In Fig. 5a and 5b summaries of the invention for a branch are, in detail removed.

Figs. 6a and 6b finally show the canonical realization of the circuit according to Fig. 5.

In Fig. 7, the well-known basic structure is removably a decimator for complex input and output signals.

Again, the Fig. 8 shows a Dezimatorrealisierung invention with general branch filter structures.

The summaries according to the invention for a branch z are drawn in FIGS. 9a and 9b, while the canonical realization of a branch filter structure for a branch z is shown in FIGS. 10a and 10b.

According to the general structure for a polyphase network according to FIG. 1, the complex input signal s = s _r + js _{i is} folded with the complex impulse response c = r + jq. The complex output signal is created

y _r + jy _i = r _* s _r - q _* s _i + j (q _* s _r + r _* s _i ).

In the case of non-recursive sub-filters (r, q) they are Implicit answers r and q are identical to the filter coefficients.  

For high values of the sampling frequencies f _A ^and f _A is the only way ^out for an implementation of the sub-filters are identical from the then two, the polyphase structure. The basic filter structure can be recursive or non-recursive. The non-recursive case is considered below.

FIG. 2 shows a non-recursive polyphase network for realizing one of the 4 sub-filters according to FIG. 1 with L branches (z = 0... L-1) and the coefficients h _i for i = 1 to k + 1, where k is the filter degree and where h _{i stands} for r _i and q _i . At high sampling frequencies, it also makes sense to replace the individual branch filters with the transposed structure according to FIG. 3. A delay element T is then respectively arranged between two partial adders.

1 Substituting the structures shown in FIG. 2 and FIG. 3 in Fig. A, so although most operations can f at the low scanning frequencies ^an _A be performed, but there remain two Addiererfunktionen at the high output sample rate and 4 Verschachtelungsmultiplexer.

In the implementation according to the invention according to FIG. 4, the increase in the sampling rate has now been pushed further back, as a result of which only 2 are required from the 4 interleaving multiplexers and, moreover, the arithmetic operations are all carried out at the low input sampling rate. The block diagram according to FIG. 4 enables use for any structures for the branch filter blocks, that is to say recursively or non-recursively. The delay elements of the branch filters, which each work on the same summation point, can be summarized if the associated r and q filters are each implemented with the structure according to FIG. 3. The configurations according to FIGS. 5a and 5b then occur for branch z. With r _z and q _z in the structure according to FIG. 3, the canonical realization of the configurations according to FIG. 5 finally results for the configurations shown in FIGS. 6a and 6b. The canonical realization results in the minimal expenditure of delay elements.

There are now two special cases, each with half of all Additional blocks are not required. In the first case a real or imaginary input signals and a complex output signal there are no blocks that are not fed and therefore not required are. In the second case, a complex one Input signals and a real or imaginary Output signals are eliminated from all blocks, which are not would calculate required output signal.

In the case of a polyphase filter network with sampling rate reduction, it is only necessary to transpose an interpolation arrangement conjugate complex, ie hermetically. The basic structure for this is shown in the arrangement according to FIG. 7. The complex input signal s _r + js _i is folded with the complex impulse response and, after decimation, is combined accordingly to form the output signal y _r + jy _i .

A decimator implementation according to the invention shows the hermetic transposition of the structures according to FIG. 4, the structure according to FIG. 8. This structure is not canonical, ie the number of delay elements is 4k instead of the canonical number 2k, k = filter degree. The ratio of the input sampling rate to the output sampling rate is mentioned here for distinction M.

A canonical realization of the structure according to FIG. 8 can be achieved in exactly the same way as with the interpolator. The substructures according to FIGS. 5a and 5b are equally present in FIGS. 4 and 8 and can be implemented in accordance with the structure according to FIGS .

Another canonical implementation is obtained if the substructures according to FIGS. 9a and 9b are combined and the polyphase branch filters are constructed in the same way as the branch filters according to FIG. 2. This non-recursive implementation variant is again identical in the same way to the interpolation case according to FIG. 4 and decimation case according to FIG. 8 applicable.

Claims (6)

1. Poly phase filter network for changing the sampling rate, with complex input and output signal and complex coefficients, for interpolation by the factor L, the complex input signal s = s _r + js _{i being} folded with the complex impulse response c = r + jq to form the complex output signal y _r + jy _i = r _* s _r - q _* s _i + j (q _* s _r + r _* s _i ), with L branches, characterized in that
that in each of the L branches the convolution products of the real part and the imaginary part of the input signal with the complex branch impulse responses c _z = r _z + jq _{z of} the branch z in question, with z = 0,. . . , L-1, can be summarized as follows: y _rz = s _{r *} r _z - s _{i *} q _z undy _iz = s _{r *} q _z + s _{i *} r _{z and} that then all L real parts y _rz to y _r and all L imaginary parts y _iz to y _{i are} multiplexed synchronously ( FIG. 4). 2. Polyphase filter network according to claim 1, using non-recursive branch filter structures of grade k, characterized in that
that the folding operations in the L branches each with k + 1 coefficients q _z , 1. . . . . q _z , k + 1 andr _z , 1. . . . . r _z , k + 1 ensure that for the real part y _rz the part-product pairs with the same indication _{r *} r _{z, k + 1} . . . . . . s _{r *} r _{z, 1} and (-s _i ) _* q _{z, k + 1} . . . (-s _i ) _* q _{z, 1 are} added, the partial sums are then each delayed via a delay element with the delay time of a cycle time T and the output signals of the delay elements are each added to the partial sums with the next lower index ( FIG. 6a),
that for the imaginary part a _iz the partial product pairs with the same indication _{r *} q _{z, k + 1} . . . . . s _{r *} q _{z, 1} ands _{i *} r _{z, k + 1} . . . . . s _{i *} r _{z, 1 are} added, the partial sums are then each delayed via a delay element with the delay time of a clock time T and the output signals of the delay elements are each added to the partial sums with the next lower index ( FIG. 6b). 3. Polyphase filter network with a change in sampling rate, with complex input and output signal and complex coefficients, for decimation by the factor M, the complex input signal s = s _r + js _{i being} folded with the complex impulse response c = r + jq to form the complex output signal y _r + jy _i = r _* s _r - q _* s _i + j (q _* s _r + r _* s _i ), with M branches, characterized in that the real part and imaginary part of the input signal are each demultiplexed into M branches and
that in each of the M branches the convolution products of the real part and the imaginary part of the input signal with the complex branch impulse responses c _z = r _z + jq _{z of} the branch z in question, with z = 0,. . . , M-1, can be summarized as follows: y _rz = s _{r *} r _z - s _{i *} q _z y _iz = s _{r *} q _z + s _{i *} r _{z and} that then all real subtotals y _rz to y _r and all imaginary partial sums y _iz to y _{i can be} added up ( FIG. 8). 4. Polyphase filter network according to claim 3, using non-recursive branch filter structures of grade k, characterized in that
that in the M branches the demultiplexed branch filter signals for the real part s _rz and for the imaginary part s _{iz are} each delayed in a chain of k delay elements T,
that the input and output signals of each delay element in the M branches each with k + 1 coefficients q _{z, 1st} . . . q _{z, 1 + k} and r _{z, 1} . . . . r _{z, 1 + k are} folded,
that the convolution products resulting from the real part s _rz with r _{z, 1} . . . . r _{z, 1 + k} , the real _subtotals y _rz1 , the convolution products, which result from the imaginary part s _iz with q _{z, 1} . . . . q _{z, 1 + k} emerge, to the real partial sums y _rz2 , the convolution products that result from the real part s _rz with q _{z, 1} . . . . q _{z, 1 + k} emerge for the imaginary partial sums y _iz2 and the convolution _{products resulting} from the imaginary part s _iz with r _{z, 1} . . . . r _{z, 1 + k} emerge, are combined to form the imaginary partial sums y _iz1 ( _FIGS . 10a, 10b). 5. polyphase filter network according to claim 3 or 4, characterized characterized in that formation and addition of the partial sums in one single adder.   6. polyphase filter network according to claim 3 or 4, characterized characterized in that formation and addition of the partial sums in one distributed adder.