JPS5831061B2 - Single sideband frequency division multiplexing method using digital processing - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention utilizes a single sideband (hereinafter abbreviated as SSB) frequency division multiplexing (hereinafter abbreviated as FDM) method, in particular a predetermined number of baseband channel signals having a predetermined bandwidth by digital processing. The present invention relates to a single sideband frequency division multiplexing scheme with digital processing for converting to a single sideband frequency division multiplexed signal.

A predetermined number of baseband channel signals are converted into SSB-FDM.
Traditionally, analog modulators and analog bandpass filters have been used to convert signals.

However, with recent advances in digital IC technology and digital signal processing technology, it has become possible to digitally convert baseband channel signals into SSB-FDM signals.

The advantages of digital processing are that the device can be made smaller and more economical, that it can be manufactured and maintained more easily, and that its operating characteristics can be improved and their characteristics can be made more uniform.

Another major advantage that cannot be overlooked is that it facilitates interconnection between digital time division multiplexing (abbreviated as TDM) communication networks, which are rapidly expanding and developing, and analog frequency division multiplexing communication networks.

How to digitally obtain SSB-FDM and FDM
There are already several known examples of methods for mutually converting between TDM and TDM.

For example, the following documents show typical examples thereof.

Publication “IEEE TR-AN” published in December 1971
SACTIONS ON COMMUNICATION
TECHNOLOGY, VOL, C0M-19, No.
6J (7) Paper published on pages 1050-1059 "Sys-tems Analysis of TD"
M-FDM Trans-1ator/Digita
l A-Type ChannelB ank” (
Reference 1) Publication “IEEE TRA-NS” published in September 1974.
ACTIONS ON CO[NICATIONS.

Paper published on pages 1199 to 1205 of VOL, C0M-22, NO, 9J “TDM-FDM Trans-
multiplexer: Digital Polyp
hase and FFT'' (Reference 2) When using digital processing technology, the overall scale of the device, and ultimately the price of the device, is determined by the number of multiplications required per unit time.

This is because multiplication is the most complicated process in digital calculations, and multiplication is an essential calculation element in configuring digital modulators and digital filters.

SUMMARY OF THE INVENTION An object of the present invention is to provide a single sideband frequency division multiplexing method using novel digital processing that requires fewer multiplications per unit time.

Another object of the present invention is to provide a single sideband frequency division multiplexing method using digital processing that minimizes the number of calculation steps.

Another object of the present invention is to provide a digitally processed single sideband frequency division multiplexing system that is compact, inexpensive, and easy to manufacture and maintain.

Yet another object of the present invention is to provide a single sideband frequency division multiplexing scheme with digital processing that facilitates the conversion of TDM signals to FDM signals.

The single sideband frequency division multiplexing method using digital processing of the present invention uses an N-channel real sample value series obtained by sampling a predetermined number (hereinafter referred to as N channels) of baseband channel signals at a frequency fS that satisfies Nyquist's sampling theorem. is input, the N-channel real sample value series is input to an N-point offset discrete inverse Fourier transformer (to be defined later) (hereinafter abbreviated as 10DFT), and the N complex output signals of the 10DFT are converted to a sampling frequency fs. The SSB-FDM signal is obtained by passing the signal through a polyphase circuit consisting of N sets of complex bandpass filters operating at 100 nm, extracting only the real part of the complex output of the polyphase circuit, and performing time division multiplexing. .

Next, the principle and configuration of the single sideband frequency division multiplexing system using digital processing according to the present invention will be explained in detail with reference to the drawings.

FIG. 1 is a diagram for explaining the principle of the single sideband frequency division multiplexing system of the present invention.

Reference letter A is a simulated frequency spectrum of a baseband channel signal having a bandwidth fs/2 (the unit of fs is Hertz, and the unit will be omitted hereinafter).

When this baseband channel signal is sampled at the frequency fs, the frequency spectrum of the sample value series becomes like the reference alphabet B, and has a periodic structure that repeats at the frequency fs.

When the SSB-FDM method according to the present method is used for the purpose of converting from TDM to FDM, since the TDM signal is a sample value series, it is input as a signal having the spectrum of the reference alphabet B from the beginning.

When a sample value series having a spectrum like reference letter B is modulated by a carrier wave of frequency fs/2, the modulated spectrum becomes like reference letter C shifted by frequency fs/2.

The sample value series of sampling frequency fs is set to frequency fs
Modulating with a /2 carrier wave is simply inverting the sign (positive/negative polarity) of the sample value series every other sample.

If n is an index indicating time, this operation is mathematically equivalent to multiplying by (-1)n.

In the present invention, in SSB-FDM of N baseband channel signals corresponding to N channels (hereinafter simply referred to as N-channel baseband channel signals), the sampling frequency after multiplexing is set to N-f8. Ru.

However, the N-channel baseband channel signals do not necessarily consist only of signals to be actually multiplexed.

That is, an arbitrary number of dummy channels may be included within the N channels.

For example, when actually converting 60 channels of baseband channel signals to a certain specified band using SSBFDM, create an appropriate number of dummy channels whose input is O, and use channels such as N-64 or N-72. It is also possible to set the value to N.

By doing so, it is possible to provide a degree of freedom in setting the sampling frequency of the multiplexed signal.

Returning to FIG. 1, the principle of this method will be explained using the case of N=4 as an example.

The first diagrams E, F and G each simulate the frequency characteristics of a complex digital bandpass filter operating at a sampling frequency N-fs having a bandwidth fs/2.

Hereinafter, the term "bandwidth of a filter" will be used to mean that sufficient attenuation can be provided outside the bandwidth.

For example, a filter designed with a pass band maximum frequency of 1.7 kHz,g and a stop band minimum frequency of 2.0 kHz is called a filter with a bandwidth of 2 kHz.

The first filter H6 has a center frequency fs/4 and the second
The filter H1 has a center frequency (5·fs)/4,
Generally, the (k+1)th filter Hk is (4+1
)・fs/4.

Although the frequency characteristic of a complex filter does not have a symmetrical structure with a symmetrical point at 1/2 of the sampling frequency like a real filter, it does have a periodic structure that repeats at each sampling frequency.

Regarding complex digital filters, please refer to the publication "IEEE TRANSACTIONS" published in September 1968.
ON AUDIO AND ELECTROACOUS
TIC8, VOL, AU-16, No. 315 of 3J
The paper published on page 320 from page ° “The Design
and Applications of Digi
talFilters with Complex C
oefficients (Reference 3).

Regarding digital filters in general, in 1969, the publication JDi published by the American company McGraw-Hil1
Digital Processing of Signa
-1sJ (Reference 4).

Now, the sample value series of the baseband channel signal of the O-th channel (hereinafter simply referred to as the O-th channel) is set to H8, the first channel is set to Hl, and the second channel is set to H.
2, assume that the third channel is input to HN-1 (-H3).

(In this case, the above-mentioned (-1)H multiplication operation is applied to the N/2nd and higher channels before input.)

When the respective outputs of N complex bandpass filters are added, the summed output becomes a signal having a spectrum as shown in FIG. 1H.

This addition output is a complex signal, and the spectrum of its real part is as shown in Figure I of N1.

This is nothing but the spectrum of a sample value series when N-channel baseband channel signals are sampled in the 0-care/fs band using SSB-FDML at a sampling frequency of N-fs.

Therefore, by using an analog low-pass filter,
If only fs is extracted, an analog FDM signal as shown in FIG. 1J can be obtained.

Furthermore, if an analog bandpass filter having a normal band Σ·fs-N-fs is used, an FDM signal multiplexed into the band -Lfs-N-fs can be obtained as shown in FIG. 1K.

Although the spectra are not arranged in the order of channel numbers at the stage of FDM in this way, there is no particular inconvenience, and if necessary, the channels can be rearranged before input.

In the case of FIG. 1J, the direction of the spectrum of each channel is equal to the direction of the baseband spectrum, and in the case of FIG. 1, spectral inversion has occurred.

Depending on the use or field of application, a spectral arrangement opposite to that of J and K in FIG. 1 may be desirable.

In this case, the above-mentioned (-1)n multiplication operation may be performed only on channels with numbers less than N/2, contrary to the above.

Furthermore, from a signal having a spectrum as shown in Figure 1,
Obtaining signals with spectra like those shown in Figure 1 J and K is not practical because it requires an analog filter with extremely steep cut-off characteristics, but if the part of the filter that corresponds to the cut-off region is used as a dummy channel, , this problem can be easily solved.

That is, in the example shown in Figure 1 J, the second channel is a dummy,
In the example shown in FIG. 1, the 0th channel and the 2nd channel may each be made dummy.

The present invention basically uses such a process to achieve SSB.
- The purpose is to obtain an FDM signal, and the calculation operations for this purpose can be performed extremely efficiently as explained below with the help of formulas.

As a preparation, first the complex filter Hk is transformed into a Z transfer function H
k(Z) to show that Hk(Z) can be derived from a real low-pass filter.

Here, the sampling period of the multiplexed signal is I/(N-
fs) 2T/N, Z is Z=exp(j2π
fT/N).

Z −1 is an operator indicating a delay of one sample.

Therefore, the delay of one sample of the baseband channel can be expressed as z-N.

A complex bandpass filter Hk(Z) having a band width of fs can be created by considering a real low-pass filter G(Z) having a bandwidth and frequency-shifting the real low-pass filter G(Z).

In other words, the center frequency of Hk(Z) is (
4 +1) fs/4, the filter G(Z
) is subjected to a frequency shift of (+1 to 4)·fs/4, the following is obtained.

/Next, as explained in Figure 1, note that although the filter Hk(Z) operates at the sampling frequency N-fs, the input is only given at the sampling frequency fs. .

In such a case, Hk (Z) can be realized by being decomposed into N sets of filters operating at the sampling frequency fs.

FIG. 2 is a diagram for explaining that such decomposition is possible.

Since it is easy to expand from a real filter to a complex filter, first consider the real low-pass filter G(Z) defined earlier.

FIG. 2A is a block diagram showing a real low-pass filter G(Z), in which reference numeral 1 is an input signal terminal of sampling frequency fs, reference numeral 3 is an output terminal at which an output of sampling frequency N-fs appears, and Number 2 is the transfer function G (
Z) respectively.

Now, when an impulse is applied to terminal 1, the output of terminal 3 (
It is assumed that the impulse response (impulse response) is as shown in FIG. 2C.

If two filters with different configurations can be configured so that their impulse responses are completely equal, their transfer functions will be the same, and they can be treated as mathematically completely equivalent filters.

In Figure 2B, reference numerals 21.22.23 and 2
4 are N (N-4 in this case) filters that operate at the sampling frequency fs.

The transfer functions of these filters will be expressed as Gi(ZN).

Filter Gi(ZN) can be defined as a filter whose impulse response is a value obtained by sampling the impulse response of (G (Z)·Zl) at frequency fs.

That is, Go(zN)tGl(zN). G2 (ZN)
The impulse responses of and G3 (ZN), as shown in FIG. 2 D, E, F, and G, are values obtained by sampling the impulse response shown in FIG. 2 C advanced by i.

Conversely, to obtain the impulse response in Figure 2C from the impulse responses shown in Figures E, F, and G in Figure 2, the impulse response in Figure 2E is delayed by one sample based on the impulse response in Figure 2, and the impulse response in Figure 2E is delayed by one sample. The impulse response in FIG. 2F may be delayed by 2 samples, the impulse response in FIG. 2G may be delayed by 3 samples, and these may be synthesized.

Reference numeral 25 in FIG. 2B is a TDM circuit that performs such time division multiplexing.

If we include this operation and express the transfer function from terminal 1 to terminal 3 in Figure 2 B in general, then A and B in Figure 2 will have the following answer, so the same impulse response will hold true. .

The complex bandpass filter Hk(Z) can also be decomposed as shown in equation (2).

Since the complex bandpass filter Hk(Z) is related to the real low-pass filter G(Z) by equation (1), equation (1)
By substituting equation (2) into , Hk (force can be expressed as

In equation (3), Gi(-jZN) is the transfer function by substituting -jZ for 2 in the transfer function of the real low-pass filter Gi(ZN) operating at the sampling frequency fs defined by equation (2). A complex bandpass filter with a sampling frequency fs in which a function is defined, the center frequency of which is equal to fs/4.

Let us now consider the properties of G.(ZN), and therefore Gi(-jZN).

The impulse response of Gi(ZN) is (G(Z)・zi)
Since it is equal to the impulse response of sampled at frequency fs, if G(Z) is a low-pass filter that passes only the band below fs/2, the in-band amplitude characteristics of G・(ZN) are equal for all i. .

Further, the in-band phase characteristic of Gi(zN)/Go(zN) has a linear phase characteristic of 1.2πfi eJ−H yo.

In this way, G and (Z) have the same amplitude characteristic for all i, and only the phase characteristic has a linear phase characteristic with a slope proportional to i.

This also applies to the complex filter G-(-jZ).

H-(-jZ) is simply the zero frequency point of G,(Z) moved to fs/4.

Because of this property, the Gi(-jZN) complex band filter bank will be referred to as a polyphase (POLYPHASE) circuit.

First, let the sample value sequence of the baseband channel signal of the channel be xk (nT), and its Z transformation be Xk (ZN
), the sample value sequence of the complex FDM signal shown in FIG. 1H is y(nT/N), and its Z transformation is Y(Z), then y
For (n T/N) = o ~ (N-1), X
Since k(nT) is passed through a filter Hk and its output is added, the following is obtained.

Here, since equation (6) is similar to the inverse discrete Fourier transform equation, this operation is defined as the inverse offset discrete Fourier transform (IODFT).

While the discrete Fourier inverse transform is to obtain the time series Ai from the Fourier spectrum Xk, Equation (6) does not have such a meaning.

It should be added that the term "inverse Fourier transform" was used for equation (6) simply because of the similarity of the operations.

Based on equations (5) and (6), a first embodiment of the digitally processed single sideband frequency division multiplexing system of the present invention can be obtained as shown in FIG.

In Figure 3, reference numbers 31.32.33°...
...and 3N is the input terminal and reference number 3 of the sample value series xk (nT) when the N-channel baseband channel signal is sampled at the frequency fs.
0 is the sample value series when sampling the SSB-FDM signal at frequency N-fs, that is, y(nT/
N) is the output terminal of the real part yre a 1 (nT/N).

Reference numeral 300 is a preprocessing circuit that performs the aforementioned (-1) H multiplication operation on the input sample value series Xk(nT) as necessary.

Hereinafter, the output of the preprocessing circuit will be expressed as xk (nT).

where the reference numeral 310 is the previously defined N-point l0DFT
It is a calculation circuit.

l0DFT calculation circuit generally has N complex input terminals Xo
, Xt...;・XN-1 and N complex output terminals (A
o, A1. ...... AN-1).

Since the input signal xk(nT) is a real signal, 0 is input to the imaginary part input terminal of the input terminals.

Reference numbers 331, 332, 333. . . . and 33N are the complex bandpass filters Go(
-jZN) G1 (-jZN), G2 (-jZN),...
... and GN-1 (jZN), and together form a polyphase circuit.

Only the real part of the complex output of each filter Gi(-jZN) is used.

Reference numeral 390 is a time division multiplex (TDM) circuit.

Equations (5) and (6) are obtained by the method of the embodiment shown in FIG.
) is calculated and an SSB-FDM signal is obtained.

That is, in the preprocessing circuit 300, ≧7 or k
The baseband channel signal Xk (ZN
) is the input terminal X of the l0DFT calculation circuit.

, Xl, . . . and the real part of XN-1.

The 10DFT calculation circuit calculates equation (6) for i-0 to (N-1), and outputs the complex output to output terminal A.

, Ai, . . . and AN l.

The l0DFT calculation may be performed for N points within a time period of T=1/fs.

The output A, (ZN) obtained from the l0DFT calculation circuit is
Next, a complex bandpass filter Gi (-jZN) 331 .

332, ...... and 33N, and the formula (5
) in Gi(-jZN):Ai(ZN义S) is calculated.

In the TDM circuit 390, zl
If the calculation of equation (5) is completed by adding after giving a delay of

What we need here is the real part yreal(
nT/N), the complex bandpass filter 331 .
332, 333. It is sufficient to take out only the output real part of . . . and 33N and perform TDM.

The preprocessing circuit 300 simply applies -1) to the input sample values.
Since it is only multiplied by n, if the input sample value is expressed as a two's complement number, a two's complement circuit is installed and
All that is required is to operate the two's complement circuit for each sample, or to prohibit its operation.

If the input sample value is displayed as polarity/absolute value,
Even simpler is to invert the polarity bit every other sample.

The l0DFT calculation circuit only needs to calculate equation (6), and can be constructed from a multiplication circuit and an addition circuit. However, when N can be expanded into a product of prime numbers, an operation called frequency thinning or time thinning is used. FFT
The amount of multiplication can be significantly reduced by using an arithmetic technique known as urier transform.

There are many documents regarding FFT, and for example, the above-mentioned document 4 provides a detailed explanation, and its application is easy.

It is also known that by utilizing the fact that the input is a real value, the amount of calculation can be halved compared to the case of general complex manual input.

Furthermore, if formula (6) is modified, Ai (ZN) is 2π, independent of k and the calculation result of the usual inverse discrete Fourier transform (IDFT).

It can be seen that it can be obtained by multiplying the unique phase offset eJ by 1.

FIG. 4 shows a second embodiment of the present invention in which the calculation of the offset discrete Fourier inverse transform is divided into two stages as described above, and reference numeral 3100 indicates an IDFT calculation circuit, and reference numeral 31
01.3102.3103...and 31ON is ej
It is a phase offset circuit that multiplies by '%.

The other components have the same configuration as the corresponding ones in FIG.

In addition, phase offset circuits 3101, 3102, 310
3. ...and 31ON is a complex bandpass filter 33L3
It goes without saying that the same result can be obtained in principle even if it is placed after 32°, 333, . . . and 33N.

Next, complex bandpass filters 331, 332, 333 . . . are components of the polyphase circuit. ... and 33N will be explained in detail.

First, filter G(Z) with sampling frequency N'fs
After a standard for in-band transmission characteristics and out-of-band attenuation is given, a filter G(Z) that satisfies the standard is designed.

It is assumed that the design result is given as a transfer function consisting of M poles and M zeros.

That is, this transfer function G (Z) is given by the following equation (8).

becomes.

Here, (1-x) ”-(1+x+x2+...+
If the equation (8) is rearranged using the identity x'')(1-x×1, G(Z) can be expressed as the following equation.

Comparing equation (2) and equation (9), GO(ZN
)1 < i≦N-1, Gi(ZN) is as follows, and it can be seen that if G(Z) is given, Go(ZN) and G·(ZN) can be designed.

Complex bandpass filter G.

(-jZN) and G1 (-jZN) can be obtained by substituting =jZ in place of Z in equations 00) and 0υ.

The denominator of equation 00) and αυ can generally be expressed as a product of quadratic equations (a linear equation can also be considered a special case of a quadratic equation).

It is well known that a real filter having a transfer function F(ker(1+B1Z-1+B2Z-2)-1) whose denominator is a quadratic expression and whose numerator is 1 can be realized by the circuit shown in FIG. 5A.

In FIG. 5A, reference numeral 51 is an input terminal, reference numeral 53 is an adder, reference numerals 54 and 55 are one-sample delay circuits, reference numerals 56 and 57 are coefficient multiplication circuits for multiplying -B2 and B1, respectively; Reference numerals 52 each indicate an output terminal.

In the real filter F(Z), the complex filter F(-jZ) in which Z is replaced with -jZ is F(jZ)""(1+jB
1Z-1B2z-2)-1, and can be realized by a circuit as shown in FIG. 5B.

In FIG.
30 and 531 are adders, reference numerals 540, 541 .
550 and 551 are one sample delay circuits, reference numbers 560, 56L, 570 and 571 are B2, respectively;
Coefficient multiplier circuits for multiplying B2, Bl, and -B1 and reference numerals 520 and 521 represent real and imaginary output terminals, respectively.

The molecules of GO (JZ') and Gi (-jZN) can be realized in a circuit form called a direct form as shown in FIG.

In FIG. 6, reference numerals 610 and 611 are respectively a real part input terminal and an imaginary part input terminal, and reference numeral 63
0 and 631 are respectively tapped delay circuits for M samples, reference numbers 6410, 6411゜6420.642
1. 6430, 6431.6440°6441. 6
450,6451.6460,646L6470.64
80 and 6481 are coefficient multiplication circuits, reference numerals 650 and 651 are adders and reference numerals 620 and 621
represent the real part output terminal and the imaginary part output terminal, respectively.

In the circuit shown in FIG. 6, when only the output of the real part or the imaginary part is required, the number of coefficient multiplication circuits can be halved.

It goes without saying that the denominators of Go (-jzN) and Gi (-jZN) can also be expanded into direct forms as shown in FIG.

Further, it is also possible to use a filter construction method known as a standard form in which both the numerator and denominator are expanded into Z polynomials.

The standard type has the advantage of requiring only half the number of delay circuits.

Conversely, the Z polynomial in the numerator is factorized and expressed as a product of quadratic equations (including linear equations), and the entirety of Go (-jZN) and Gi (-jZN) is expressed as a cascade of biquadratic filters. It can also be expressed.

The TDM circuit 390 in which N filters in a polyphase circuit operate in parallel can be configured extremely easily, and therefore no special explanation is required.

It may be the case that each filter in the polyphase is actually implemented by multiplexing hardware consisting of only one filter.

In this case, the filter output itself is time-division multiplexed, and there is no need to connect a TDM circuit as hardware to the output of the polyphase circuit.

However, in this case, the input to the polyphase circuit or the input to the offset discrete Fourier inverse transformer, or
This means that the TDM circuit is working at the stage of the baseband channel itself.

In fact, if the baseband channel signal itself is TDMed, then the offset discrete Fourier inverse transformer and the polyphase circuit need only be operated at N multiple speeds.

As mentioned above, in digital processing, N digital filters do not necessarily mean N hardware filters.

In reality, one hardware filter often acts as N filters.

It is assumed that the N filters of the present invention include cases realized by such multiple use.

As described above, the single sideband frequency division multiplexing method of the present invention adds a real sample value sequence of frequency fs of N channels to an N-point offset inverse discrete Fourier transform (IODFT), and outputs N complex outputs of this l0DFT. is added to a polyphase circuit consisting of N complex bandpass filters, and by time-division multiplexing only the real part of the complex output of this polyphase circuit, an actual sample value series of the frequency N'fs of the SSB-FDM signal is obtained. It is characterized by

In this way, the baseband channel signal is converted to SSB-F
In order to convert the input base punt channel signal into a DM signal, the present invention only requires two calculation steps of a 10DFT and a poly-phase circuit. ) does not require any extra operations.

The fact that the number of calculation steps is reduced in this way means that
This brings about great advantages, such as reducing the number of man-hours for device design, reducing the number of man-hours for manufacturing, inspection and maintenance, reducing the accumulation of calculation errors, and significantly improving operating characteristics.

Furthermore, if the method of the present invention is used, SSB-
It is possible to obtain an FDM signal, and therefore the device can be made smaller and lower in price.

Next, the amount of multiplication per unit time in the method of the present invention will be specifically explained.

For this reason, consider performing SSB-FDM on 60 channels of baseband channel signals to a band of 8 to 248 kHz.

Add 4 dummy channels to the 60-channel signal to obtain N-64.

Baseband channel signal is 300-3400 Hg
Assume that the telephone band is sampled at a frequency fs = 8 kHz.

In this case, while using the configuration of the embodiment shown in FIG.
The 4-point IDFT is calculated by applying the radix-2 real number manual FFT algorithm.

Also, considering the order M=8 as a polyphase circuit,
Assume that the circuit is constructed from the circuits shown in FIGS. 5B and 5C.

Furthermore, since the coefficient multiplier associated with the imaginary part output in FIG. 5C is unnecessary, it is considered to be removed.

Under these conditions, the number of real multiplications required per 8kHz for the 64-point IDFT, phase offset circuit, and polyphase circuit is 166 and 256, respectively.
and 1536 times.

The total number of required multiplications per second is 15.664X106
Calculated as times/second.

This value is about 0% smaller than the 19.392×10 6 times/sec of the multiplication circuit of the method described in Document 2.

In addition, in the above explanation, (4
The basic idea was to obtain a complex bandpass filter Hk(Z) by performing a frequency shift of fs/4 (k+1) fs/4, but even if the frequency shift is (+3 to 4) fs/4, the first
The characteristics of Hk(Z) shown in Figures D-G simply change to the right f s
Accordingly, the complex FDM signal in FIG. 1 (2) can only be shifted to the right by f s /2, and if you take its real part, it becomes SSB-FDM.
There is no difference in the fact that the spectrum of the signal can be obtained.

In this case, the filter Gi(-jZN) of the polyphase circuit is
FT, 2π.

The phase offset ej□1 is the phase offset.

It just changes to j' 3 i. Filter Gi(-j
Conversion from ZZ)N to filter Gi(jZΣ is performed using filter Gi(-
jZN) to the right by f s /2.

[Brief explanation of drawings]

FIG. 1 is a diagram for explaining the present invention in detail, FIG. 2 is a diagram for explaining the present invention, FIG. 3 is a diagram showing the first embodiment of the present invention, and FIG. 4 is a diagram for explaining the present invention. FIG. 5 is a diagram for explaining the cyclic part of the complex band filter used in the present invention, and FIG. 6 is a diagram showing the acyclic part of the complex band filter used in the present invention. It is a figure for explaining. In Figures 3 and 4, reference numerals 31°32,
33. . . . and 3N are input terminals for N-channel baseband channel sample value series, reference number 300.
is a preprocessing circuit, reference numeral 310 is an offset discrete Fourier inverse transformer, reference numerals 331, 332, . . . , and 3
3N is a complex bandpass filter that constitutes a polyphase circuit;
Reference numeral 390 is a TDM circuit, reference numeral 30 is an output terminal, reference numeral 3100 is a discrete Fourier inverse transformer, and reference numerals 3101, 3102, 3103, . ...and 31
ON each indicates a phase offset circuit.

Claims (1)

[Claims] 1 Offset discrete Fourier that is supplied as input with a real sample value sequence when N baseband channel signals including an arbitrary number of dummy baseband channels are sampled at sampling frequency f8, and outputs N complex sample value sequences. Inverse converter and bandwidth f8/2
A polyphase circuit composed of N complex bandpass filters whose center frequency is an odd multiple of f,/4, and N complex bandpass filters obtained by cascading the offset discrete Fourier inverse transformer and the polyphase circuit. Output sampling frequency N
- A single sideband frequency division multiplexing system using digital processing, characterized in that the system comprises means for outputting an f8 time division multiplexed signal.