Abstract:
An AM neighboring interference removing method and circuit is provided which can select only a desired AM modulation wave even if an interference AM modulation wave is partially superposed upon the desired AM modulation wave. An AM modulation wave desired to be received is multiplied at multipliers by local oscillation signals having frequencies 3fc/2 and fc/2 where fc is the carrier frequency of a neighboring interference AM modulation wave. High frequency components contained in the outputs of the multipliers are removed by low-pass filters. Of the outputs of the low-pass filters, the carrier frequency of the neighboring interference wave is fc/2 and the AM carrier frequencies of the AM stereo modulation wave are (fc/2+fα) and (fc/2−fα), where fα is a difference frequency between the AM carrier frequency of the AM stereo modulation wave and the carrier frequency of the neighboring interference wave. A subtractor subtracts the output of one of the low-pass filter from the output of the other to thereby cancel out the neighboring interference wave. This subtraction signal is passed through a low-pass filter having a cut-off frequency of fc/2 to derive only the AM stereo modulation wave.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a method of selecting, during an AM broadcast reception, only a desired AM modulation wave on a desired channel by removing another AM modulation wave on a neighboring channel, and to an AM neighboring interference removing circuit executing such a method. 
   2. Description of the Related Art 
   An interchannel band width of an AM broadcast is set, for example, to 9 kHz in Japan, and an AM modulation side band width is permitted up to 7.5 kHz. An AM modulation wave from a remote site or an overseas country may superpose, particularly in a midnight, upon a neighboring channel of a desired channel. In such a case, a desired AM modulation wave with a superposed neighboring AM modulation wave is demodulated and a user listens to the demodulated sounds in a radio interference state, or the desired AM modulation wave is demodulated through SSB. 
   However, it is difficult to listen to demodulated signals in a radio interference state. If demodulation through SSB is used and a desired channel is AM stereo broadcast, a user cannot listen to demodulated signals in a stereo state from the reason of the operation principle. 
   SUMMARY OF THE INVENTION 
   It is an object of the present invention to provide an AM neighboring interference removing method capable of selecting only a desired AM modulation wave even if an interfering AM modulation wave partially superposes upon the desired wave, and an AM neighboring interference removing circuit. 
   According to one aspect of the present invention, A method of removing AM neighboring interference of an AM receiver, is provided which comprises the steps of: multiplying an AM modulation wave desired to be received by a signal having a frequency higher by a predetermined frequency than a carrier frequency of an interference AM modulation wave causing neighboring interference and by another frequency lower by the predetermined frequency than the carrier frequency of the interference AM modulation wave; removing high frequency components from each of two multiplied signals to derive two signals, and subtracting one of the two derived signals from the other to obtain a subtraction signal; and removing high frequency components higher than a predetermined frequency from the subtraction signal to obtain the AM modulation wave desired to be received. 
   With this AM neighboring interference removing method, first an AM modulation wave desired to be received is multiplied by a signal having a frequency higher by a predetermined frequency than a carrier frequency of an interference AM modulation wave causing neighboring interference and by another frequency lower by the predetermined frequency than the carrier frequency of the interference AM modulation wave, to obtain two multiplied signals. Next, high frequency components are removed from each of the two multiplied signals. One of the two multiplied signals with the high frequency components being removed is subtracted from the other to obtain a subtraction signal. Lastly, high frequency components higher than a predetermined frequency are removed from the subtraction signal to obtain the AM modulation wave desired to be received. 
   According to another aspect of the invention, an AM neighboring interference removing circuit for removing AM neighboring interference of an AM receiver, is provided which comprises: a first local oscillator for generating an oscillation output having a frequency of fp1; a second local oscillator for generating an oscillation output having a frequency of fp2; a first multiplier for multiplying an AM stereo modulation wave desired to be received, by the oscillation output from the first local oscillator; a second multiplier for multiplying the AM stereo modulation wave desired to be received, by the oscillation output from the second local oscillator; a first low-pass filter for removing high frequency components contained in an output of the first multiplier; a second low-pass filter for removing high frequency components contained in an output of the second multiplier; a subtractor for subtracting an output of the second low-pass filter from an output of the first low-pass filter; and a low-pass filter for receiving an output of the subtractor and having a cut-off frequency of fc/2, wherein fc is a carrier frequency of an interference AM modulation wave causing neighboring interference, fp1&gt;fp2, and fp1−fc=fc−fp2. 
   With this AM neighboring interference removing circuit, the AM stereo modulation wave and the interference modulation wave are frequency-converted by the first and second multipliers, and their low-frequency components are output from the first and second low-pass filters. It is assumed that a difference frequency is fα between an AM carrier frequency of the AM stereo modulation wave desired to be received and a carrier frequency of an interference AM modulation wave. Of an output from the first low-pass filter, the carrier frequency of the interference wave is fc/2 and the carrier frequency of the AM stereo modulation wave desired to be received is (fc/2−fα), and of an output from the second low-pass filter, the carrier frequency of the interference wave is fc/2 and the carrier frequency of the AM stereo modulation wave desired to be received is (fc/2+fα). The subtractor cancels out the interference wave, and the third low-pass filter selects only the AM stereo modulation wave desired to be received. In this manner, the interference wave can be removed. 
   According to another aspect of the invention, an AM neighboring interference removing circuit for removing AM neighboring interference of an AM receiver, is provided which comprises: a first local oscillator for generating an oscillation output having a frequency of (fp1+fα); a second local oscillator for generating an oscillation output having a frequency of (fp2−fα); a third local oscillator for generating an oscillation output having a frequency of (fp2+3fα); a first multiplier for multiplying an AM stereo modulation wave desired to be received, by the oscillation output from the first local oscillator; a second multiplier for multiplying the AM stereo modulation wave desired to be received, by the oscillation output from the second local oscillator; a third multiplier for multiplying the AM stereo modulation wave desired to be received, by the oscillation output from the third local oscillator; a first low-pass filter for removing high frequency components contained in an output of the first multiplier; a second low-pass filter for removing high frequency components contained in an output of the second multiplier; a third low-pass filter for removing high frequency components contained in an output of the third multiplier; a subtractor for subtracting outputs of the second and third low-pass filters from an output of the first low-pass filter; and a band-pass filter for receiving an output of the subtractor and having a band-pass frequency in a range from (fc/2−fα) to (fc/2+fα), wherein fc and (fc+2fα) are carrier frequencies of interference AM modulation waves causing neighboring interference, being lower and higher by a frequency fα from an AM carrier frequency of the AM stereo modulation wave desired to be received, fp1&gt;fp2, and fp1−fc=fc−fp2. 
   With this AM neighboring interference removing circuit, the AM stereo modulation wave and the interference modulation wave are frequency-converted by the first, second, and third multipliers, and their low-frequency components are output from the first, second, and third low-pass filters. It is assumed that a difference frequency is fα between an AM carrier frequency of the AM stereo modulation wave desired to be received and a carrier frequency of an interference AM modulation wave. Of an output from the first low-pass filter, the carrier frequency of the AM stereo modulation wave desired to be received is fc/2 and the carrier frequencies of the neighboring interference waves are at positions higher and lower by the frequency fα from the frequency fc/2. Of an output from the second low-pass filter, the carrier frequency of the AM stereo modulation wave desired to be received is (fc/2−2fα) and the carrier frequencies of the neighboring interference waves are at positions higher and lower by the frequency fα from the frequency (fc/2−2fα). Of an output from the third low-pass filter, the carrier frequency of the AM stereo modulation wave desired to be received is (fc/2+2fα) and the carrier frequencies of the neighboring interference waves are at positions higher and lower by the frequency fα from the frequency (fc/2+2fα). The subtractor cancels out the interference wave output from the first low-pass filter, and the band-pass filter selects only the AM stereo modulation wave desired to be received, from the first-low pass filter. In this manner, the interference waves can be removed. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a block diagram showing the structure of an AM neighboring interference removing circuit according to an embodiment of the invention. 
       FIGS. 2A to 2E  are diagrams illustrating the operation of the AM neighboring interference removing circuit of the embodiment shown in  FIG. 1 . 
       FIG. 3  is a block diagram showing the structure of an AM neighboring interference removing circuit according to a first modification of the embodiment. 
       FIGS. 4A to 4F  are diagrams illustrating the operation of the AM neighboring interference removing circuit of the first modification. 
       FIGS. 5A to 5E  are diagrams illustrating the operation of an AM neighboring interference removing circuit according to a second modification of the embodiments. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Embodiments of a method and circuit for removing AM neighboring interference will be described. 
     FIG. 1  is a block diagram showing the structure of an AM neighboring interference removing circuit according to an embodiment of the invention. 
   An AM stereo modulation wave received at an AM receiver is supplied to a multiplier  3  whereat it is multiplied by an output from a local oscillator  1  having an oscillation frequency of (3/2)ωct. The received AM stereo modulation wave is also supplied to a multiplier  4  whereat it is multiplied by an output from a local oscillator  2  having an oscillation frequency of (1/2)ωct. An output of the multiplier  3  is supplied to a low-pass filter  5  whereat the high frequency components of the multiplier output are removed. An output of the multiplier  4  is supplied to a low-pass filter  6  whereat the high frequency components of the multiplier output are removed. 
   The outputs from the low-pass filters  5  and  6  are supplied to a subtractor  7  whereat the output from the low-pass filter  5  is subtracted by the output from the low-pass filter  6 . An output of the subtractor  7  is supplied to a low-pass filter  8  having a cut-off frequency of fc/2(=ωc/4π) whereat the high frequency components of the subtractor output are removed, and the signal with the removed high frequency components is output from the low-pass filter  8 . 
   The operation of the AM neighboring interference removing circuit of the embodiment constructed as above will be described. 
   An AM stereo modulation wave desired to be received and mixed with a neighboring interference wave is written by the following equation (1). 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         v 
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       = 
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               M0 
                             
                             ) 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       c 
                                     
                                     + 
                                     ωα 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 t 
                               
                               + 
                               θ 
                             
                             } 
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             M1 
                           
                           ) 
                         
                         ⁢ 
                         
                           cos 
                           ⁡ 
                           
                             ( 
                             
                               ω 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               ct 
                             
                             ) 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         where 
                       
                     
                   
                 
                 
                   
                     
                       
                         M0 
                         = 
                           
                         ⁢ 
                         
                           1 
                           + 
                           
                             κ0 
                             · 
                             
                               vm0 
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       , 
                     
                   
                 
                 
                   
                     
                       
                         M1 
                         = 
                           
                         ⁢ 
                         
                           1 
                           + 
                           
                             κ1 
                             · 
                             
                               vm1 
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       , 
                       and 
                     
                   
                 
                 
                   
                     
                       θ 
                       = 
                         
                       ⁢ 
                       
                         
                           arctan 
                           ⁡ 
                           
                             [ 
                             
                               κ0 
                               · 
                               
                                 
                                   vs0 
                                   ⁡ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                                 / 
                                 
                                   { 
                                   
                                     1 
                                     + 
                                     
                                       κ0 
                                       · 
                                       
                                         vm0 
                                         ⁡ 
                                         
                                           ( 
                                           t 
                                           ) 
                                         
                                       
                                     
                                   
                                   } 
                                 
                               
                             
                             ] 
                           
                         
                         . 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 1 
                 ) 
               
             
           
         
       
     
   
   In the equation (1), the first term is the AM stereo modulation wave desired to be received, and the second term is the neighboring AM interference wave. The affix 0 is used for the AM stereo modulation wave desired to be received, and the affix 1 is used for the neighboring AM interference wave. κ0 is an AM modulation factor of the AM stereo modulation wave desired to be received, κ1 is an AM modulation factor of the neighboring AM interference wave, νm0(t) is a mono modulation wave of the AM stereo modulation wave desired to be received, νs0(t) is a stereo modulation wave of the AM modulation wave, νm1(t) is a modulation wave of the neighboring AM interference wave, ωc is an angular frequency (rad/s) of a neighboring AM interference carrier wave, and ωα is a difference angular frequency (rad/s) between the neighboring AM interference carrier wave and an AM modulation carrier wave desired to be received. 
   The AM stereo modulation wave desired to be received and mixed with the neighboring interference wave which is given by the equation (1) is schematically shown in  FIG. 2A . A reference character “a” in  FIG. 2A  represents the AM stereo modulation wave desired to be received, and a reference character “b” represents the neighboring AM interference wave. 
   The AM stereo modulation wave desired to be received and mixed with the neighboring interference wave is multiplied at the multiplier  3  by the output cos(3/2)ωct of the local oscillator  1 , and the high frequency components are removed by the low-pass filter  5 . An input to the low-pass filter  5  is ν(t)·cos(3/2)ωct, and an output thereof is written by the following equation (2).
 
An output of the low-pass filter  5 
 
   
     
       
         
           
             
               
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               M0 
                             
                             ) 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       
                                         - 
                                         ω 
                                       
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         c 
                                         / 
                                         2 
                                       
                                     
                                     + 
                                     ωα 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 t 
                               
                               + 
                               θ 
                             
                             } 
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             M1 
                           
                           ) 
                         
                         ⁢ 
                         
                           cos 
                           ⁡ 
                           
                             ( 
                             
                               
                                 - 
                                 1 
                               
                               / 
                               2 
                             
                             ) 
                           
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ct 
                       
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               M0 
                             
                             ) 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         c 
                                         / 
                                         2 
                                       
                                     
                                     - 
                                     ωα 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 t 
                               
                               - 
                               θ 
                             
                             } 
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             M1 
                           
                           ) 
                         
                         ⁢ 
                         
                           cos 
                           ⁡ 
                           
                             ( 
                             
                               1 
                               / 
                               2 
                             
                             ) 
                           
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ct 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 2 
                 ) 
               
             
           
         
       
     
   
   The AM stereo modulation wave desired to be received and mixed with the neighboring interference wave is also multiplied at the multiplier  4  by the output cos(1/2)ωct of the local oscillator  2 , and the high frequency components are removed by the low-pass filter  6 . An input to the low-pass filter  6  is ν(t)·cos(1/2)ωct, and an output thereof is written by the following equation (3).
 
An output of the low-pass filter  6 =(1 +M 0)cos{(ω c/ 2+ωα) t +θ}+(1 +M 1)cos(1/2)ω ct   (3)
 
   The output of the low-pass filter  5  given by the equation (2) is schematically shown in  FIG. 2B , and the output of the low-pass filter  6  given by the equation (3) is schematically shown in  FIG. 2C . The subtractor  7  subtracts the output of the low-pass filter  6  given by the equation (3) from the output of the low-pass filter  5  given by the equation (2). An input to the subtractor  7  is a signal of ν(t)·cos(3/2)ωct−ν(t)·cos(1/2)ωct−high frequency components, and an output of the subtractor  7  is given by the following equation (4).
 
An output of the subtractor  7 =(1 +M 0)cos{(ω c/ 2−ωα) t −θ}+(1 +M 1)cos{(ω c/ 2+ωα) t+θ}   (4)
 
   The output of the subtractor  7  is schematically shown in  FIG. 2D . The low-pass filter  8  removes from the output of the subtractor  7  the second term of the equation (4) (indicated by oblique lines in  FIG. 2D ), and outputs a signal written by the following equation (5).
 
(1 +M 0)cos{(ω c/ 2−ωα) t−θ}   (5)
 
   As seen from the equation (5), the output of the low-pass filter  8  is that shown in  FIG. 2E  which is the AM stereo modulation wave desired to be received. It can be understood that the AM neighboring interference removing circuit of the embodiment can remove the neighboring interference wave and receive only the AM stereo modulation wave desired to be received. 
   In the AM neighboring interference removing circuit of this embodiment, the angular frequency of the local oscillator  1  is set to (3/2)ωc and the angular frequency of the local oscillator  2  is set to (1/2)ωc. The angular frequencies of the local oscillators  1  and  2  may be set to different frequencies so long as they satisfy the relation of (ωpf1)−ωc=ωc−(ωpf2), where (ωpf1)&gt;(ωpf2), (ωpf1) stands for the angular frequency (3/2)ωc, and (ωpf2) stands for the angular frequency (1/2)ωc. 
   A first modification of the AM neighboring interference removing circuit according to the embodiment of the invention will be described. 
     FIG. 3  is a block diagram showing the structure of the first modification of the AM neighboring interference removing circuit according to the embodiment of the invention. 
   In the first modification of the AM neighboring interference removing circuit according to the embodiment of the invention, two neighboring interference waves such as shown in  FIG. 4A  are removed respectively having frequencies higher and lower by ωα than the frequency of the AM stereo modulation wave desired to be received. 
   In the first modification of the AM neighboring interference removing circuit according to the embodiment of the invention, an AM stereo modulation wave desired to be received and mixed with neighboring interference waves is written by the following equation (6). 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         v 
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       = 
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               M1 
                             
                             ) 
                           
                           ⁢ 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ct 
                               
                               ) 
                             
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               M0 
                             
                             ) 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       c 
                                     
                                     + 
                                     ωα 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 t 
                               
                               + 
                               θ 
                             
                             } 
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             M2 
                           
                           ) 
                         
                         ⁢ 
                         
                           cos 
                           ⁡ 
                           
                             ( 
                             
                               
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 c 
                               
                               + 
                               
                                 2 
                                 ⁢ 
                                 ωα 
                               
                             
                             ) 
                           
                         
                         ⁢ 
                         t 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         where 
                       
                     
                   
                 
                 
                   
                     
                       
                         M0 
                         = 
                           
                         ⁢ 
                         
                           1 
                           + 
                           
                             κ0 
                             · 
                             
                               vm0 
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       , 
                     
                   
                 
                 
                   
                     
                       
                         M1 
                         = 
                           
                         ⁢ 
                         
                           1 
                           + 
                           
                             κ1 
                             · 
                             
                               vm1 
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       , 
                     
                   
                 
                 
                   
                     
                       
                         M2 
                         = 
                           
                         ⁢ 
                         
                           1 
                           + 
                           
                             κ2 
                             · 
                             
                               vm2 
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       , 
                       and 
                     
                   
                 
                 
                   
                     
                       θ 
                       = 
                         
                       ⁢ 
                       
                         
                           arctan 
                           ⁡ 
                           
                             [ 
                             
                               κ0 
                               · 
                               
                                 
                                   vs0 
                                   ⁡ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                                 / 
                                 
                                   { 
                                   
                                     1 
                                     + 
                                     
                                       κ0 
                                       · 
                                       
                                         vm0 
                                         ⁡ 
                                         
                                           ( 
                                           t 
                                           ) 
                                         
                                       
                                     
                                   
                                   } 
                                 
                               
                             
                             ] 
                           
                         
                         . 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 6 
                 ) 
               
             
           
         
       
     
   
   In the equation (6), the first term is the neighboring interference wave having a lower frequency, the second term is the AM stereo modulation wave desired to be received, and the third term is the neighboring AM interference wave having a higher frequency. The affix 0 is used for the AM stereo modulation wave desired to be received, and the affixes 1 and 2 are used for the neighboring AM interference wave. κ0 is an AM modulation factor of the AM stereo modulation wave desired to be received, κ1 and κ2 are AM modulation factors of the neighboring AM interference waves, νm0(t) is a mono modulation wave of the AM stereo modulation wave desired to be received, νm1(t) and νm2(t) are modulation waves of the neighboring AM interference waves, νs0(t) is a stereo modulation wave of the AM modulation wave, ωc+ωα is an angular frequency (rad/s) of the AM stereo modulation carrier wave desired to be received, (ωc) and (ωc+2ωα) are angular frequencies (rad/s) of the neighboring AM interference carrier waves, and ωα is a difference angular frequency (rad/s) between each neighboring AM interference carrier wave and an AM modulation carrier wave desired to be received. 
   The AM stereo modulation wave desired to be received and mixed with the neighboring interference waves which is given by the equation (6) is schematically shown in  FIG. 4A . A reference character “a” in  FIG. 4A  represents the AM stereo modulation wave desired to be received, a reference character “b” represents the neighboring AM interference wave indicated by coarse meshes, and a reference character “c” represents the neighboring AM interference wave indicated by fine meshes. 
   The AM stereo modulation wave desired to be received and mixed with the neighboring interference waves which is given by the equation (6) is multiplied at a multiplier  14  by an output cos{(3/2)ωc+ωα)t of a local oscillator  11 , and the multiplied output is supplied to a low-pass filter  17  whereat the frequency components of the multiplier output are removed. An input to the low-pass filter  17  is ν(t)·cos(3/2)ωc+ωα)t, and an output thereof is written by the following equation (7).
 
An output of the low-pass filter  17 
 
   
     
       
         
           
             
               
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               M1 
                             
                             ) 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       - 
                                       1 
                                     
                                     / 
                                     2 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 c 
                               
                               - 
                               ωα 
                             
                             } 
                           
                           ⁢ 
                           t 
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               M0 
                             
                             ) 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       - 
                                       1 
                                     
                                     / 
                                     2 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ct 
                               
                               + 
                               θ 
                             
                             } 
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             M2 
                           
                           ) 
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                           { 
                           
                             
                               
                                 ( 
                                 
                                   
                                     - 
                                     1 
                                   
                                   / 
                                   2 
                                 
                                 ) 
                               
                               ⁢ 
                               ω 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               c 
                             
                             + 
                             ωα 
                           
                           } 
                         
                         ⁢ 
                         t 
                       
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               M1 
                             
                             ) 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   ( 
                                   
                                     1 
                                     / 
                                     2 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 c 
                               
                               + 
                               ωα 
                             
                             } 
                           
                           ⁢ 
                           t 
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               M0 
                             
                             ) 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   ( 
                                   
                                     1 
                                     / 
                                     2 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ct 
                               
                               - 
                               θ 
                             
                             } 
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             M2 
                           
                           ) 
                         
                         ⁢ 
                         cos 
                         ⁢ 
                         
                           { 
                           
                             
                               
                                 ( 
                                 
                                   1 
                                   / 
                                   2 
                                 
                                 ) 
                               
                               ⁢ 
                               ω 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               c 
                             
                             - 
                             ωα 
                           
                           } 
                         
                         ⁢ 
                         t 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 7 
                 ) 
               
             
           
         
       
     
   
   The AM stereo modulation wave desired to be received and mixed with the neighboring interference waves which is given by the equation (6) is multiplied at a multiplier  15  by an output cos{(1/2)(ωc−ωα)t of a local oscillator  12 , and the multiplied output is supplied to a low-pass filter  18  whereat the frequency components of the multiplier output are removed. An input to the low-pass filter  18  is ν(t)·cos(1/2)ωc−ωα)t, and an output thereof is written by the following equation (8).
 
An output of the low-pass filter  18 =(1 +M 1)cos{(1/2)ω c+ωα}t +(1 +M 0)cos[{(1/2)ω c+ 2 ωα}t +θ]+(1 +M 2)cos{(1/2)ω c+ 3 ωα}t   (8)
 
   The AM stereo modulation wave desired to be received and mixed with the neighboring interference waves which is given by the equation (6) is multiplied at a multiplier  16  by an output cos{(1/2)ωc+3ωα)t of a local oscillator  19 , and the multiplied output is supplied to a low-pass filter  19  whereat the frequency components of the multiplier output are removed. An input to the low-pass filter  19  is ν(t)·cos(1/2)ωc+3ωα)t, and an output thereof is written by the following equation (9).
 
An output of the low-pass filter  19 =(1 +M 1)cos{(1/2)ω c− 3 ωα}t +(1 +M 0)cos{(1/2)ω c− 2ωα) t +θ}+(1 +M 2)cos{(1/2)ω c−ωα}t   (9)
 
   The output of the low-pass filter  17  given by the equation (7) is schematically shown in  FIG. 4B , the output of the low-pass filter  18  given by the equation (8) is schematically shown in  FIG. 4C , and the output of the low-pass filter  19  given by the equation (9) is schematically shown in  FIG. 4D . A subtractor  20  subtracts the outputs of the low-pass filters  18  and  19  given by the equations (8) and (9) from the output of the low-pass filter  17  given by the equation (7). With this subtraction, the first term of the equation (7) and the first term of the equation (8) are cancelled out, and the third term of the equation (7) and the third term of the equation (9) are cancelled out, so that a signal given by the following equation (1) is output from the subtractor  20 .
 
An input to the subtractor  20 =ν( t )·cos{(3/2)ω c+ωα}t −ν( t )·cos{(1/2)ω c−ωα ) t −ν( t )·cos{(1/2)ω c+ 3ωα) t −high frequency components at each term.
 
An output of the subtractor  20 =(1 +M 0)cos{(1/2)ω ct −θ}+(1 +M 0)cos[{(1/2)ω c+ 2 ωα}t +θ]+(1 +M 2)cos{1/2)ω c+ 3ωα) t +(1 +M 1)cos{1/2)ω c− 3ωα) t +(1 +M 0)cos[{(1/2)ω c− 2ωα} t+θ]   (10)
 
   The output of the subtractor  20  given by the equation (10) is schematically shown in  FIG. 4E . The subtraction output given by the equation (10) is supplied to a band-pass filter  21  having a band-path width of from (1/2)fc−fα to (1/2)fc+fα to remove the frequency components other than the band-path width. An output of the band-pass filter  21  is given by the following equation (11). A hatched portion in  FIG. 4E  is a frequency range other than the band-path width of the band-pass filter.
 
(1 +M 0)cos{(1/2)ω ct−θ}   (11)
 
   The output of the band-pass filter given by the equation (11) is schematically shown in  FIG. 4F . Only the AM stereo modulation wave desired to be received can therefore be selected. 
   A second modification of the AM neighboring interference removing circuit according to the embodiment of the invention will be described. 
   In the second modification of the AM neighboring interference removing circuit according to the embodiment of the invention, two neighboring interference waves such as shown in  FIG. 5A  are removed having frequencies higher respectively by ωα and 2ωα than the frequency of the AM stereo modulation wave desired to be received. 
   In the second modification of the AM neighboring interference removing circuit according to the embodiment of the invention, an AM stereo modulation wave desired to be received and mixed with neighboring interference waves is written by the following equation (12). 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         v 
                         ⁡ 
                         
                           ( 
                           t 
                           ) 
                         
                       
                       = 
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               M0 
                             
                             ) 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       ω 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       c 
                                     
                                     - 
                                     
                                       2 
                                       ⁢ 
                                       ωα 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 t 
                               
                               + 
                               θ 
                             
                             } 
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               M1 
                             
                             ) 
                           
                           ⁢ 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   ω 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   c 
                                 
                                 - 
                                 ωα 
                               
                               ) 
                             
                           
                           ⁢ 
                           t 
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             M2 
                           
                           ) 
                         
                         ⁢ 
                         
                           cos 
                           ⁡ 
                           
                             ( 
                             
                               ω 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               ct 
                             
                             ) 
                           
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         where 
                       
                     
                   
                 
                 
                   
                     
                       
                         M0 
                         = 
                           
                         ⁢ 
                         
                           1 
                           + 
                           
                             κ0 
                             · 
                             
                               vm0 
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       , 
                     
                   
                 
                 
                   
                     
                       
                         M1 
                         = 
                           
                         ⁢ 
                         
                           1 
                           + 
                           
                             κ1 
                             · 
                             
                               vm1 
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       , 
                     
                   
                 
                 
                   
                     
                       
                         M2 
                         = 
                           
                         ⁢ 
                         
                           1 
                           + 
                           
                             κ2 
                             · 
                             
                               vm2 
                               ⁡ 
                               
                                 ( 
                                 t 
                                 ) 
                               
                             
                           
                         
                       
                       , 
                       and 
                     
                   
                 
                 
                   
                     
                       θ 
                       = 
                         
                       ⁢ 
                       
                         
                           arctan 
                           ⁡ 
                           
                             [ 
                             
                               κ0 
                               · 
                               
                                 
                                   vs0 
                                   ⁡ 
                                   
                                     ( 
                                     t 
                                     ) 
                                   
                                 
                                 / 
                                 
                                   { 
                                   
                                     1 
                                     + 
                                     
                                       κ0 
                                       · 
                                       
                                         vm0 
                                         ⁡ 
                                         
                                           ( 
                                           t 
                                           ) 
                                         
                                       
                                     
                                   
                                   } 
                                 
                               
                             
                             ] 
                           
                         
                         . 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 12 
                 ) 
               
             
           
         
       
     
   
   In the equation (12), the first term is the AM stereo modulation wave desired to be received, the second term is the neighboring interference wave having a lower frequency, and the third term is the neighboring AM interference wave having a higher frequency. The affix 0 is used for the AM stereo modulation wave desired to be received, and the affixes 1 and 2 are used for the neighboring AM interference waves. κ0 is an AM modulation factor of the AM stereo modulation wave desired to be received, κ1 and κ2 are AM modulation factors of the neighboring AM interference waves, νm0(t) is a mono modulation wave of the AM stereo modulation wave desired to be received, νm1(t) and νm2(t) are modulation waves of the neighboring AM interference waves, νs0(t) is a stereo modulation wave of the AM modulation wave, (ωc−2ωα) is an angular frequency (rad/s) of the AM stereo modulation carrier wave desired to be received, (ωc−ωα) and (ωc) are angular frequencies (rad/s) of the neighboring AM interference carrier waves, and ωα and 2ωα are difference angular frequencies (rad/s) between each neighboring AM interference carrier wave and an AM modulation carrier wave desired to be received. 
   The AM stereo modulation wave desired to be received and mixed with the neighboring interference waves is schematically shown in  FIG. 5A . A reference character “a” in  FIG. 5A  represents the AM stereo modulation wave desired to be received, reference characters “b” and “c” represent the neighboring AM interference waves one of which is indicated by meshes. 
   The AM stereo modulation wave desired to be received and mixed with the neighboring interference waves which is given by the equation (12) is multiplied by an output cos{(3/2)ωc+ωα)t of a local oscillator  11 , and the multiplied output is supplied to a first low-pass filter whereat the frequency components of the multiplied output are removed. An input to the first low-pass filter is ν(t)·cos(3/2)ωc+ωα)t, and an output thereof is written by the following equation (13).
 
An output of the first low-pass filter
 
   
     
       
         
           
             
               
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               M0 
                             
                             ) 
                           
                           ⁢ 
                           
                             cos 
                             ⁡ 
                             
                               [ 
                               
                                 
                                   
                                     { 
                                     
                                       
                                         
                                           ( 
                                           
                                             
                                               - 
                                               1 
                                             
                                             / 
                                             2 
                                           
                                           ) 
                                         
                                         ⁢ 
                                         ω 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         c 
                                       
                                       - 
                                       
                                         2 
                                         ⁢ 
                                         ωα 
                                       
                                     
                                     } 
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 θ 
                               
                               ] 
                             
                           
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               M1 
                             
                             ) 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   ( 
                                   
                                     
                                       - 
                                       1 
                                     
                                     / 
                                     2 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 c 
                               
                               - 
                               ωα 
                             
                             } 
                           
                           ⁢ 
                           t 
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             M2 
                           
                           ) 
                         
                         ⁢ 
                         
                           cos 
                           ⁡ 
                           
                             ( 
                             
                               
                                 - 
                                 1 
                               
                               / 
                               2 
                             
                             ) 
                           
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ct 
                       
                     
                   
                 
                 
                   
                     
                       = 
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             M0 
                           
                           ) 
                         
                         ⁢ 
                         
                           cos 
                           [ 
                           
                             
                               
                                 { 
                                 
                                   
                                     
                                       ( 
                                       
                                         1 
                                         / 
                                         2 
                                       
                                       ) 
                                     
                                     ⁢ 
                                     ω 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     c 
                                   
                                   + 
                                   
                                     2 
                                     ⁢ 
                                     ωα 
                                   
                                 
                                 } 
                               
                               ⁢ 
                               t 
                             
                             - 
                             θ 
                             + 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           
                             ( 
                             
                               1 
                               + 
                               M1 
                             
                             ) 
                           
                           ⁢ 
                           cos 
                           ⁢ 
                           
                             { 
                             
                               
                                 
                                   ( 
                                   
                                     1 
                                     / 
                                     2 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 ω 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 ct 
                               
                               + 
                               ωα 
                             
                             } 
                           
                           ⁢ 
                           t 
                         
                         + 
                       
                     
                   
                 
                 
                   
                     
                         
                       ⁢ 
                       
                         
                           ( 
                           
                             1 
                             + 
                             M2 
                           
                           ) 
                         
                         ⁢ 
                         
                           cos 
                           ⁡ 
                           
                             ( 
                             
                               1 
                               / 
                               2 
                             
                             ) 
                           
                         
                         ⁢ 
                         ω 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         ct 
                       
                     
                   
                 
               
             
             
               
                 ( 
                 13 
                 ) 
               
             
           
         
       
     
   
   The AM stereo modulation wave desired to be received and mixed with the neighboring interference waves which is given by the equation (12) is multiplied by an output cos{(1/2)ωct of a local oscillator, and the multiplied output is supplied to a second low-pass filter whereat the frequency components of the multiplied output are removed. An input to the second low-pass filter is ν(t)·cos(1/2)ωct, and an output thereof is written by the following equation (14).
 
An output of the second low-pass filter=(1 +M 0)cos[{(1/2)ω c −2 ωα}t+θ ]+(1 +M 1)cos{(1/2)ω c−ωα}t +(1 +M 2)cos{(1/2)ω ct   (14)
 
   The output of the first low-pass filter given by the equation (13) is schematically shown in  FIG. 5B , and the output of the second low-pass filter given by the equation (14) is schematically shown in  FIG. 5C . A first subtractor subtracts the output of the second low-pass filter given by the equation (14) from the output of the first low-pass filter given by the equation (13). With this subtraction, the third term of the equation (13) and the third term of the equation (14) are cancelled out, so that a signal given by the following equation (15) is output from the first subtractor.
 
An input to the first subtractor=ν(t)·cos(3/2)ω ct−ν ( t )·cos(1/2)ω ct −high frequency components
 
An output of the first subtractor=(1 +M 0)cos[{(1/2)ω c−ωα}t−θ ]+(1 +M 1)cos{(1/2)ω c+ωα}t −(1 +M 0)cos[{(1/2)ω c− 2ωα} t+θ ]−(1 +M 1)cos{1/2)ω c−ωα ) t   (15)
 
   The output of the first subtractor given by the equation (15) is schematically shown in  FIG. 5D . The subtraction output given by the equation (15) is supplied to a third low-pass filter having a cut-off frequency of (1/2)fc to remove the high frequency components. An output of the third low-pass filter is given by the following equation (16). A hatched portion in  FIG. 4D  is a high frequency range to be cut off by the third low-pass filter.
 
An output of the third low-pass filter=−(1 +M 0)cos[{(1/2)ω c− 2 ωα}t+θ ]−(1 +M 1)cos{(1/2)ω c−ωα}t   (16)
 
   The output of the third low-pass filter given by the equation (16) is schematically shown in  FIG. 5E . One of the neighboring interference waves can therefore be removed. The AM stereo modulation wave desired to be received and mixed with the other of the neighboring interference waves is supplied to the AM neighboring interference removing circuit of the embodiment of the invention to thereby remove the remaining neighboring interface wave with similar operations to the embodiment. Only the AM stereo modulation wave desired to be received can therefore be selected. 
   Even if a number of neighboring interference waves are superposed, all the waves can be removed by using a combination of the embodiment and the first and second modifications of the AM neighboring interference removing circuit of the invention. 
   As described so far, according to the embodiment method and circuit of removing AM interference, even an AM stereo modulation wave can be listened by a user as clear sounds without any neighboring interference waves which are conventionally listened as noises.