Abstract:
System for digital sweep type spectrum analysis with up/down frequency provides measurements of frequency spectrum of complex analog baseband input signal. The signal is quantized into three levels with fs based on the bandwidth of the input signal. Four multiplexers, a first block of registers and a block of adders perform operations equivalent to complex multiplication of the quadrature components. Two complex signals with up and down shifted spectrum are produced by the adders. The quadrature components are inputted to the accumulators with reset, which act as low-pass filters and accumulate several samples at a constant frequency f LO  of the local oscillator. Levels of two accumulated complex samples are estimates of input signal spectrum in two frequency points +f LO  and −f LO . A sweep controller changes a frequency of the local oscillator from zero up to fs/2. Estimates of the input signal spectrum are generated sequentially in range −fs/2 to +fs/2.

Description:
BACKGROUND OF THE INVENTION 
     Communication systems and satellite navigation systems often need spectrum analyzers. Swept spectrum analyzers have been in use for many years, because they are less complex compared to FFT (Fast Fourier Transform) spectrum analyzers. Some analyzers have both analog and digital signal processing means. 
     U.S. Pat. No. 6,700,366, entitled “Very fast swept spectrum analyzer”, describes a system in which the signal spectrum is formed by mixing a ramping local oscillator and an input signal to generate an IF signal, the resulting IF (Intermediate Frequency) signal having a phase change with respect to the input signal, the phase change including a quadratic portion. For analysis, the IF signal is processed such that the quadratic component of the phase change is removed. IF processing circuitry includes a resolution bandwidth filter and an analog-to-digital converter. 
     U.S. Pat. No. 6,275,020, entitled “Frequency analysis method and sweep type spectrum analyzer”, describes a sweep type spectrum analyzer, where analyzing the frequency components included in the signal to be measured are based on the correspondence relation between a power of each of the intermediate frequency signals and a frequency of the main swept frequency signal, an inverse swept signal is multiplied by each intermediate frequency signal, the inverse swept signal being frequency-swept in the reverse direction to the frequency transition direction of the associated intermediate frequency signal, and a constant frequency component obtained from the results of the multiplications is extracted as a frequency spectrum. 
     U.S. Pat. No. 4,771,232, entitled “Non-interruptive spectrum analyzer for digital modems”, describes a system that provides extracting spectral data from the actual received modem signal, where multipliers are used in the digital frequency converter. 
     However, devices with analog components are not always stable and provide less accuracy compared to fully digital solutions. The present invention is intended as a simple system for full digital sweep type spectrum analysis with up/down frequency conversion, where analysis time is less than half compared to sweep type spectrum analyzers with only down frequency conversion. The system provides measurements of frequency spectrum of an input complex analog baseband signal without use of multiplication operations for frequency conversion. 
     SUMMARY OF THE INVENTION 
     The present invention is intended for creating a system for digital sweep type spectrum analysis with up/down frequency conversion. The system provides measurements of frequency spectrum of complex analog baseband input signal, where analysis time is less than half compared to sweep type spectrum analyzers with only down frequency conversion. First, a complex analog input signal is quantized into three levels (−1; 0; +1) with a sampling frequency fs agreed with the bandwidth of the input signal. Then, a block of four 9-to-1 multiplexers, a first block of registers and a block of adders perform operations that are equivalent to mathematical complex multiplication of the quadrature components of the digitized input signal and the quadrature components of the local oscillator, but without using real multiplications. 
     Two complex signals with up-shifted and down-shifted spectrum are formed at the output of the block of adders. Further, the quadrature components of these complex signals are inputted to the block of accumulators with reset, which act as low-pass filters (LPF) and accumulate several samples at a constant frequency f LO  of the local oscillator. Levels of two accumulated complex samples are estimates of the input signal spectrum in two frequency points +f LO  and −f LO . A sweep controller changes the frequency stepwise of the local frequency-tunable oscillator from zero to fs/2 by steps that compared to the LPF bandwidth, where estimates of the input signal spectrum generated sequentially in the range from −fs/2 to +fs/2. These spectral estimates are analyzed and stored using a data analysis and storing logic, where they are periodically updated and may be used, e.g., for displaying. 
     Additional features and advantages of the invention will be set forth in the description that follows, and in part will be apparent from the description, or may be learned by practice of the invention. The advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. 
    
    
     
       BRIEF DESCRIPTION OF THE ATTACHED FIGURES 
       The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification and together with the description serve to explain the principles of the invention. 
       In the drawings: 
         FIG. 1  is a functional block diagram for an embodiment of a digital sweep type spectrum analyzer with up/down frequency conversion. 
         FIG. 2  is a functional diagram for a MUX block. 
         FIG. 3 a    is an example of the spectrum of a digitized complex input signal. 
         FIG. 3 b    is an example of the spectrum of the signal of a quadrature local oscillator. 
         FIG. 3 c    is a spectrum of an up converted digitized complex input signal of  FIG. 3   a.    
         FIG. 3 d    is a spectrum of a down converted digitized complex input signal of  FIG. 3   a.    
         FIG. 4  is an example of the flowchart of a primitive algorithm of estimating for the case of only sector with borders (0, π/4). 
         FIG. 5  is an example of the flowchart of the estimation algorithm when octant (0, π/4) is divided into two sectors. 
         FIG. 6  is an example of the flowchart of the estimation algorithm when octant (0, π/4) is divided into three sectors. 
         FIG. 7  is an example of the flowchart of the estimation algorithm when octant (0, π/4) is divided into four sectors. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Reference will now be made in detail to the preferred embodiments of the present invention, examples of which are illustrated in the accompanying drawings. 
       FIG. 1  shows a functional block diagram for a digital sweep type spectrum analyzer with up/down frequency conversion, which provides a frequency spectrum of an complex analog baseband input signal. 
     The analog quadrature components I in (t) and Q in (t) of the complex input signal are pre-quantized with a sampling frequency fs by two analog-to-digital converters (ADC)  10 ,  11  into three levels (−1; 0; +1):
 
 I   n   ADC =−1, if  I   in ( n*T   s )&lt;− U   L ;
 
 I   n   ADC =0, if − U   L   ≦I   in ( n*T   s )≦+ U   L ;
 
 I   n   ADC =+1, if  I   in ( n*T   s )&gt;+ U   L ;
 
 Q   n   ADC =−1, if  Q   in ( n*T   s )&lt;− U   L ;
 
 Q   n   ADC =0, if − U   L   ≦Q   in ( n*T   s )≦+ U   L ;
 
 Q   n   ADC =+1, if  Q   in ( n*T   s )&gt;+ U   L ;
 
here
 
     U L  is the preset level; 
     T s =1/f s  is the sampling period, 
     n=0, 1, 2, . . . ; 
     where sampling frequency f s  corresponds to the bandwidth B in  of the input signal (f s ≧B in ). An example of the spectrum of a digitized input signal is shown in  FIG. 3   a.    
     An example of the signal spectrum of a quadrature local oscillator (LO)  12  with the quadrature components (I LO , Q LO ) is shown in  FIG. 3 b   . A complex up-converted signal with quadrature components (I U , Q U ) and a complex down-converted signal with quadrature components (I D , Q D ) can be obtained through complex multiplication of the quadrature components (I ADC , Q ADC ) and the quadrature components (I LO , Q LO )) of LO by formulas: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             I 
                             n 
                             U 
                           
                           = 
                           
                             
                               
                                 I 
                                 n 
                                 ADC 
                               
                               · 
                               
                                 I 
                                 n 
                                 LO 
                               
                             
                             - 
                             
                               
                                 Q 
                                 n 
                                 ADC 
                               
                               · 
                               
                                 Q 
                                 n 
                                 LO 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             Q 
                             n 
                             U 
                           
                           = 
                           
                             
                               
                                 I 
                                 n 
                                 ADC 
                               
                               · 
                               
                                 Q 
                                 n 
                                 LO 
                               
                             
                             + 
                             
                               
                                 Q 
                                 n 
                                 ADC 
                               
                               · 
                               
                                 I 
                                 n 
                                 LO 
                               
                             
                           
                         
                       
                     
                   
                   } 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             I 
                             n 
                             D 
                           
                           = 
                           
                             
                               
                                 I 
                                 n 
                                 ADC 
                               
                               · 
                               
                                 I 
                                 n 
                                 LQO 
                               
                             
                             + 
                             
                               
                                 Q 
                                 n 
                                 ADC 
                               
                               · 
                               
                                 Q 
                                 n 
                                 LQO 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             Q 
                             n 
                             D 
                           
                           = 
                           
                             
                               
                                 - 
                                 
                                   I 
                                   n 
                                   ADC 
                                 
                               
                               · 
                               
                                 Q 
                                 n 
                                 LQO 
                               
                             
                             + 
                             
                               
                                 Q 
                                 n 
                                 ADC 
                               
                               · 
                               
                                 I 
                                 n 
                                 LQO 
                               
                             
                           
                         
                       
                     
                   
                   } 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     The implementation of equations (1) and (2) would require four real multiplications:
 
 R   n   II   =I   n   ADC   ·I   n   LQO ,  (3)
 
 R   n   QQ   =Q   n   ADC   ·Q   n   LQO ,  (4)
 
 R   n   IQ   =I   n   ADC   ·Q   n   LQO ,  (5)
 
 R   n   QI   =Q   n   ADC   ·I   n   LQO ,  (6)
 
     In the present invention, the values R n   II , R n   QQ , R n   IQ , R n   QI  are produced without using multiplication by a MUX block  13  comprising four 9-to-1 multiplexers operating in accordance with the combined logic table 
     
       
         
               
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
             
           
               
                   
               
               
                   
                 Outputs 
               
             
          
           
               
                   
                 Select inputs 
                 MUX 1 
                 MUX 2 
                 MUX 3 
                 MUX 4 
               
             
          
           
               
                   
                 I ADC   
                 Q ADC   
                 R II   
                 R QQ   
                 R IQ   
                 R QI   
               
               
                   
               
             
          
           
               
                 1) 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 2) 
                 0 
                 +1 
                 0 
                  Q LO   
                 0 
                  I LO   
               
               
                 3) 
                 0 
                 −1 
                 0 
                 −Q LO   
                 0 
                 −I LO   
               
               
                 4) 
                 +1 
                 0 
                  I LO   
                 0 
                  Q LO   
                 0 
               
               
                 5) 
                 −1 
                 0 
                 −I LO   
                 0 
                 −Q LO   
                 0 
               
               
                 6) 
                 +1 
                 +1 
                  I LO   
                  Q LO   
                  Q LO   
                  I LO   
               
               
                 7) 
                 −1 
                 −1 
                 −I LO   
                 −Q LO   
                 −Q LO   
                 −I LO   
               
               
                 8) 
                 +1 
                 −1 
                  I LO   
                 −Q LO   
                  Q LO   
                 −I LO   
               
               
                 9) 
                 −1 
                 +1 
                 −I LO   
                  Q LO   
                 −Q LO   
                  I LO   
               
               
                   
               
             
          
         
       
     
     An example of a logic diagram for MUX block is shown in  FIG. 2 . 
     Zero number is supplied to data inputs 1, 2, 3 of the multiplexer 1, to the data inputs 1, 4, 5 of the multiplexer 2, to data inputs 1, 2, 3 of the multiplexer 3 and to data inputs 1, 4, 5 of the multiplexer 4. 
     Component I LO  is supplied to data inputs 4, 6, 8 of the multiplexer 1 and to the data inputs 2, 6, 9 of the multiplexer 4. 
     Component I LO  with the opposite sign is supplied to data inputs 5, 7, 9 of the multiplexer 1 and to the data inputs 3, 7, 8 of the multiplexer 4. 
     Component Q LO  is supplied to data inputs 2, 6, 9 of the multiplexer 2 and to the data inputs 4, 6, 8 of the multiplexer 3. 
     Component Q LO  with the opposite sign is supplied to data inputs 3, 7, 8 of the multiplexer 2 and to the data inputs 5, 7, 9 of the multiplexer 3. 
     The real numbers R n   II , R n   QQ , R n   IQ , R n   QI  are written into the first block of registers  14 , comprising four registers. 
     A block of adders  15  produces a complex up-converted signal with quadrature components (I n   U , Q n   U ) and a complex down-converted signal with quadrature components (I n   D , Q n   D ) by the following formulas: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             I 
                             n 
                             U 
                           
                           = 
                           
                             
                               R 
                               n 
                               II 
                             
                             - 
                             
                               R 
                               n 
                               QQ 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             Q 
                             n 
                             U 
                           
                           = 
                           
                             
                               R 
                               n 
                               IQ 
                             
                             + 
                             
                               R 
                               n 
                               QI 
                             
                           
                         
                       
                     
                   
                   } 
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             I 
                             n 
                             D 
                           
                           = 
                           
                             
                               R 
                               n 
                               II 
                             
                             + 
                             
                               R 
                               n 
                               QQ 
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             Q 
                             n 
                             D 
                           
                           = 
                           
                             
                               R 
                               n 
                               IQ 
                             
                             + 
                             
                               R 
                               n 
                               QI 
                             
                           
                         
                       
                     
                   
                   } 
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     A spectrum of the up-converted signal with the quadrature components (7) is shown in  FIG. 3 c    and a spectrum of the down converted signal with the quadrature components (8) is shown in  FIG. 3 d   . Thus, a MUX block  13 , a local quadrature oscillator  12 , a first block of registers and a block of adders perform the role of a dual up/down frequency converter. 
     The complex samples (7) and (8) are inputted to a block of accumulators  16  comprising four accumulators with reset, which accumulates M samples (M&gt;&gt;1) at a constant frequency of the local oscillator: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           I 
                           m 
                           
                             U 
                             , 
                             A 
                           
                         
                         = 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               0 
                             
                             
                               i 
                               = 
                               
                                 M 
                                 - 
                                 1 
                               
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             
                               i 
                               + 
                               
                                 
                                   ( 
                                   
                                     m 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                                 · 
                                 M 
                               
                             
                             U 
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           Q 
                           m 
                           
                             U 
                             , 
                             A 
                           
                         
                         = 
                         
                           
                             ∑ 
                             
                               i 
                               = 
                               0 
                             
                             
                               i 
                               = 
                               
                                 M 
                                 - 
                                 1 
                               
                             
                           
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             Q 
                             
                               i 
                               + 
                               
                                 
                                   ( 
                                   
                                     m 
                                     - 
                                     1 
                                   
                                   ) 
                                 
                                 · 
                                 M 
                               
                             
                             U 
                           
                         
                       
                     
                   
                 
                 } 
               
               ⁢ 
               
                 
 
               
               ⁢ 
               
                 
                   
                     
                       
                         I 
                         m 
                         
                           D 
                           , 
                           A 
                         
                       
                       = 
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             0 
                           
                           
                             i 
                             = 
                             
                               M 
                               - 
                               1 
                             
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           I 
                           
                             i 
                             + 
                             
                               
                                 ( 
                                 
                                   m 
                                   - 
                                   1 
                                 
                                 ) 
                               
                               · 
                               M 
                             
                           
                           D 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         Q 
                         m 
                         
                           D 
                           , 
                           A 
                         
                       
                       = 
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             0 
                           
                           
                             i 
                             = 
                             
                               M 
                               - 
                               1 
                             
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           Q 
                           
                             i 
                             + 
                             
                               
                                 ( 
                                 
                                   m 
                                   - 
                                   1 
                                 
                                 ) 
                               
                               · 
                               M 
                             
                           
                           D 
                         
                       
                     
                   
                 
               
             
             } 
           
         
       
     
     The resultant values I m   U,A , Q m   U,A , I m   D,A , Q m   D,A  are divided by a coefficient 2 K  (2 K ≦M) by shifting in K bits toward LSBs and are written into four registers of the second block of registers  17 , i.e.:
 
 I   m   U,K   =I   m   U,A /2 K ,
 
 Q   m   U,K   =Q   m   U,A /2 K ,
 
 I   m   D,K   =I   m   D,A /2 K ,
 
 Q   m   D,K   =Q   m   D,A /2 K ,
 
     Then all four accumulators are reset to zero; wherein the secondary sampling frequency becomes equal to F M =fs/M (down sampling by an integer factor, M). 
     A level detector  18  produces an estimate of vector length V m   U , V m   D  with complex quadrature samples (I m   U,K , Q m   U,K ) and (I m   D,K , Q m   D,K ) respectively of the second block of registers using an algorithm as described below. The level {circumflex over (V)} m   U  is an estimate of the input signal spectrum at frequency point −f LO  and level {circumflex over (V)} m   D  is an estimate of the input signal spectrum at frequency point +f LO . Exact values of V m   U , V m   D  can be calculated by formulas based on the Pythagorean theorem:
 
 V   m   U =√{square root over (( I   m   U,K ) 2 +( Q   m   U,K ) 2 )}
 
 V   m   D =√{square root over (( I   m   D,K ) 2 +( Q   m   D,K ) 2 )}.
 
     Calculations based on the Pythagorean theorem require a lot of computationally intensive operations. However, an estimate of the vector length with acceptable accuracy can be obtained using relatively simple algorithms. In this case, the level detector produces a rough estimate of vector length for each input vector using the following successive steps:
         a) forming auxiliary vector with orthogonal components (X, Y), where X=max(|x|, |y|), Y=min(|x|, |y|), x, y—orthogonal components of the input vector V; where the auxiliary vector located in the (0, π/4) octant;   b) finding in the (0, π/4) octant a preset sector which contains the auxiliary vector;   c) selecting a linear equation corresponding to the sector found;   d) solving the linear equation with preset coefficients.       

     This approach is illustrated using an example of preselected octant with borders (0, π/4). The auxiliary vector with orthogonal components (X, Y), where X=max(|x|, |y|), Y=min(|x|, |y|), x, y are orthogonal components of input vector, has the same length as the input vector and is located in octant (0, π/4). 
       FIG. 4  shows an example of the flowchart of a simple algorithm of estimating for the case of only sector (S=1) with borders (0, π/4). A Ve estimate of V vector length is:
 
 Ve=X+C   1   *Y/D   1 ,
 
     here C 1  and D 1  are the preset constant numbers. 
     For example, when C 1  and D 1  are preset
 
 C   1 =21,  D   1 =64,
 
     the Ve estimate has an maximum error ε max =100*|V−Ve|/V=5.68%. 
       FIG. 5  shows an example of the flowchart of the estimation algorithm when octant (0, π/4) is divided into two (S=2) sectors: 
     θ 1  with borders (0, arctan (B 1 /A 1 )) and 
     θ 2  with borders (arctan (B 1 /A 1 ), π/4); 
     here A 1  and B 1  are the preset constants. 
     And Ve estimate of V vector length is: 
     Ve=X+C 1 *Y/D 1  for the θ 1  sector, and 
     Ve=X+C 2 *Y/D 2  for the θ 2  sector; 
     here C 1 , D 1  and C 2 , D 2  are the preset constant numbers. 
     For example, if the following parameters are preset
 
 A   1 =93,  B   1 =64,
 
 C   1 =1,  D   1 =4,
 
 C   2 =47,  D   2 =128,
 
     the Ve estimate has maximum error ε max =3.45%. 
       FIG. 6  shows an example of the flowchart of the estimation algorithm when octant (0, π/4) is divided into three (S=3) sectors: 
     θ 1  with borders (0, arctan (B 1 /A 1 )), 
     θ 2  with borders (arctan (B 1 /A 1 ), arctan (B 2 /A 2 )) and 
     θ 3  with borders (arctan (B 2 /A 2 ), π/4); 
     here A 1 , B 1  and A 2 , B 2  are the preset constant numbers. 
     and Ve estimate of V vector length is: 
     Ve=X+C 1 *Y/D 1  for the θ 1  sector, 
     Ve=X+C 2 *Y/D 2  for the θ 2  sector and 
     Ve=X+C 3 *Y/D 3  for the θ 3  sector; 
     here C 1 , D 1 , C 2 , D 2  and C 3 , D 3  are the preset constant numbers. 
     For example, if the following parameters are preset
 
 A   1 =7,  B   1 =4,
 
A 2 =81, B 2 =64,
 
 C   1 =7,  D   1 =32,
 
C 2 =5, D 2 =16,
 
 C   3 =49,  D   3 =128,
 
     the Ve estimate has maximum error ε max =2.37%. 
       FIG. 7  shows an example of the flowchart of the estimation algorithm when octant (0, π/4) is divided into four (S=4) sectors: 
     θ 1  with borders (0, arctan (B 1 /A 1 )), 
     θ 2  with borders (arctan (B 1 /A 1 ), arctan (B 2 /A 2 )), 
     θ 3  with borders (arctan (B 2 /A 2 ), arctan (B 3 /A 3 )) and 
     θ 4  with borders (arctan (B 3 /A 3 ), π/4); 
     here A 1 , B 1 , A 2 , B 2  and A 3 , B 3  are the preset constant numbers, and Ve estimate of V vector length is: 
     Ve=X+C 1 *Y/D 1  for the θ 1  sector, 
     Ve=X+C 2 *Y/D 2  for the θ 2  sector, 
     Ve=X+C 3 *Y/D 3  for the θ 3  sector, and 
     Ve=X+C 4 *Y/D 4  for the θ 4  sector; 
     here C 1 , D 1 , C 2 , D 2 , C 3 , D 3  and C 4 , D 4  are the preset constant numbers. 
     For example, if the following parameters are preset (the constants were chosen empirically):
 
 A   1 =257 , B   1 =128,
 
 A   2 =95,  B   2 =64,
 
A 3 =19, B 3 =16,
 
 C   1 =25,  D   1 =128,
 
 C   2 =35,  D   2 =128,
 
 C   3 =43,  D   3 =128,
 
 C   4 =25,  D   4 =64,
 
     the Ve estimate has maximum error ε max =1.89%. 
     The higher the S value, the greater the potential accuracy of estimate of vector length. 
     All dividers are multiple of two in the above examples; therefore, the division operation can be performed with help of the shift operation. 
     A data analysis and collection logic  19  that receives spectrum data from the level detector output executes an analysis of data and sequentially stores them within one scanning period after which the spectrum data is updated, the spectral data may be used, e.g., for a display. 
     A sweep and data collection controller  20  sends a sweep signal to the frequency control input of LO to control the LO by stepwise changing of frequency in the range (0, fs/2), sequentially setting N&gt;&gt;1 of equidistant frequency values fn=fs*(2n−1)/4N, where n=1, 2, . . . , N; wherein each accumulator of the block of accumulators accumulates M samples at each frequency fn: M=floor[k*N] (The floor function is also called the “greatest integer” or “entier” function, see, for example, http:**en.wikipedia.org/wiki/Floor_and_ceiling_functions), where constant k is selected from the range (0.5, . . . , 5.0); wherein the spectrum analyzer forms 2N of spectrum points in the range (−fs/2, +fs/2) during each sweep period. The sweep controller synchronizes the spectrum analyzer sweep to the recirculating memory of a data analysis and storing logic. 
     Having thus described the invention, it should be apparent to those skilled in the art that certain advantages of the described apparatus have been achieved. 
     It should also be appreciated that various modifications, adaptations, and alternative embodiments thereof may be made within the scope and spirit of the present invention. The invention is further defined by the following claims.