Abstract:
A signal processing apparatus includes first and second extracting units extracting frequency components having a first frequency band and a second frequency band, respectively, from an input audio signal, a first-harmonic-component generating unit generating a first-harmonic-component signal including a frequency component whose frequency is N1 times that of the frequency component extracted in the first extracting unit, a second-harmonic-component generating unit generating a second-harmonic-component signal including a frequency component whose frequency is N2 times that of the frequency component extracted in the second extracting unit, and a combining unit combining the input audio signal, and the first- and the second-harmonic-component signals in a predetermined ratio. The first frequency band is higher than the second frequency band. N1 and N2 are positive integers, and N1 is smaller than N2.

Description:
CROSS REFERENCES TO RELATED APPLICATIONS 
       [0001]    The present invention contains subject matter related to Japanese Patent Application JP 2006-259919 filed in the Japanese Patent Office on Sep. 29, 2006, the entire contents of which are incorporated herein by reference. 
       BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to a signal processing apparatus, and more particularly, to an audio reproducing apparatus. 
         [0004]    2. Description of the Related Art 
         [0005]    A so-called minicomponent, a flat-screen television, or the like tends to have a speaker with a small diameter and a speaker box (enclosure) with a small capacity in which the speaker is placed. Accordingly, the resonance frequency f 0  of the speaker is about 100 Hz or higher in many cases. 
         [0006]    Generally, when an audio signal whose frequency is lower than or equal to the resonance frequency f 0  of a speaker is supplied to the speaker, as the frequency of the audio signal increases, the sound pressure of the fundamental frequency component decreases, and the number of frequency components (harmonic components) that cause sound distortion rapidly increases. 
         [0007]    Thus, it is difficult for an audio reproducing apparatus in which the above-mentioned speaker having a small diameter is used to sufficiently reproduce bass whose frequency is lower than or equal to the resonance frequency f 0  of the speaker. 
         [0008]    An instrumental tone includes the fundamental and its harmonics, and the tone color is decided by the ratio between the fundamental and its harmonics. Regarding audibility, even when the fundamental is not output, the output of its harmonics enables a listener to perceive the output sound as if the fundamental were output. This is psychoacoustically verified. 
         [0009]    An audio reproducing apparatus allowing a listener to experience bass using such a sensory property has been suggested.  FIG. 11  is a flow diagram of an exemplary audio reproducing apparatus using the sensory property. The exemplary audio processing apparatus includes a speaker  5  having a small diameter whose bass is to be experienced by a listener should be improved. 
         [0010]    An audio signal S 1  is supplied through an input terminal  1  to a high-pass filter  2 . As shown in part (A) of  FIG. 12 , high and midrange frequency components S 2  whose frequencies are higher than or equal to the resonance frequency f 0  of the speaker  5  are extracted from the audio signal S 1  in the high-pass filter  2  and supplied to a combining circuit  3 . Additionally, the audio signal S 1  is supplied through the input terminal  1  to a band-pass filter  7 . As shown in part (B) of  FIG. 12 , low frequency components S 7  whose frequencies are from f 0 /2 to f 0  are extracted from the audio signal S 1  in the band-pass filter  7  and supplied to a pitch shifter  8 . 
         [0011]    The pitch shifter  8  multiplies the frequencies of the low frequency components S 7  supplied thereto by two. As shown in part (C) of  FIG. 12 , harmonic components S 8  whose frequencies are from f 0  to  2   f   0  are output from the pitch shifter  8 . 
         [0012]    The harmonic components S 8  are supplied to the combining circuit  3  to be combined with the high and midrange frequency components S 2 , and the combining circuit  3  outputs an audio signal S 3  including the intensified harmonic components S 8  of the low frequency components S 7 , as shown in part (D) of  FIG. 12 . This audio signal S 3  is supplied through a power amplifier  4  to the speaker  5 . Accordingly, a sound having the frequency characteristic shown in part (D) of  FIG. 12 , i.e., a sound of the audio signal S 3  including the intensified harmonic components S 8  of the low frequency components S 7 , is output from the speaker  5 . 
         [0013]    In this case, the speaker  5  does not output the sound of the low frequency components S 7  but outputs the sound of the harmonic components S 8  whose fundamental frequency components are the low frequency components S 7 . As described above, this allows the listener to perceive the sound as if the sound of the low frequency components S 7  were output. Thus, the listener can experience the bass although the speaker  5  has a small diameter. 
         [0014]    It is regarded that in a case where the frequencies of the harmonic components S 7  are multiplied by an integer to generate the harmonic components S 8 , when the frequencies of the low frequency components S 8  are about 200 Hz or lower, the sound of the harmonic components S 8  does not make the listener feel that there is something wrong with the sound. 
         [0015]    Japanese Unexamined Patent Application Publication No. 8-213862 is given as the related art document. 
       SUMMARY OF THE INVENTION 
       [0016]    In the above-described audio reproducing apparatus, depending on the frequencies of the low frequency components S 7 , the listener may not experience the desirable bass. For example, the reproducing frequency range (frequency characteristic) of the speaker  5  is shown by the curve F 5  in part (A) of  FIG. 13 , and suppose the resonance frequency f 0  of the speaker  5  is 100 Hz. 
         [0017]    As shown in part (A) of  FIG. 13 , when the frequency of one of the low frequency components S 7  is 60 Hz, the frequency of a corresponding one of the harmonic components S 8  is 120 Hz. Because 120 Hz, the frequency of the harmonic component S 8 , is included in the reproducing frequency range F 5  of the speaker  5 , as described above, it is possible for the listener to experience the bass of the low frequency component S 7  by receiving the sound of the harmonic component S 8 . 
         [0018]    However, as shown in part (B) of  FIG. 13 , when the frequency of one of the low frequency components S 7  is 35 Hz, the frequency of a corresponding one of the harmonic components S 8  is 70 Hz. Because 70 Hz, the frequency of the harmonic component S 8 , is not included in the reproducing frequency range F 5  of the speaker  5 , it is difficult for the listener to experience the bass of the low frequency component S 7  by receiving the sound of the harmonic component S 8 . On the contrary, since the harmonic component S 8  whose frequency is lower than the resonance frequency f 0  of the speaker  5  is supplied to the speaker  5 , a distorted sound is output from the speaker  5 . 
         [0019]    Additionally, suppose the resonance frequency f 0  of the speaker  5  is 120 Hz, as shown in part (C) of  FIG. 13 . When the frequency of one of the low frequency components S 7  is 110 Hz, the frequency of a corresponding one of the harmonic components S 8  is 220 Hz. Because 220 Hz, the frequency of the harmonic component S 8 , is included in the reproducing frequency range F 5  of the speaker  5 , the sound of the harmonic component S 8  can be output from the speaker  5 . However, as described above, the upper limit of the frequency of the harmonic component S 8  whose sound does not make the listener feel that there is something wrong with the sound is about 200 Hz. Because 220 Hz, the frequency of the harmonic component S 8 , exceeds the upper limit, the sound reproduced by the speaker  5  makes the listener feel that there is something wrong with the sound. 
         [0020]    It is desirable to overcome the disadvantages described above. 
         [0021]    According to an embodiment of the present invention, there is provided a signal processing apparatus including a first extracting unit, a second extracting unit, a first-harmonic-component generating unit, a second-harmonic-component generating unit, and a combining unit. The first extracting unit is configured to extract a frequency component having a first frequency band from an input audio signal. The second extracting unit is configured to extract a frequency component having a second frequency band from the input audio signal. The first-harmonic-component generating unit is configured to generate a first-harmonic-component signal including a frequency component whose frequency is N1 times that of the frequency component extracted in the first extracting unit. The second-harmonic-component generating unit is configured to generate a second-harmonic-component signal including a frequency component whose frequency is N2 times that of the frequency component extracted in the second extracting unit. The combining unit is configured to combine the input audio signal, the first-harmonic-component signal, and the second-harmonic-component signal in a predetermined ratio. The first frequency band is higher than the second frequency band. N1 and N2 are positive integers, and N1 is smaller than N2. 
         [0022]    In a signal processing apparatus according to an embodiment of the present invention, when a frequency of a low frequency component of an audio signal is lower than the resonance frequency f 0  of a speaker, a sound of a harmonic component of the low frequency component is output from the speaker. This allows a listener to experience the bass of the low frequency component by receiving the sound of the harmonic component. In addition, the frequency of the low frequency component is multiplied such that the frequency of the low frequency component can fall within a band between the resonance frequency f 0  of the speaker and an upper limit frequency f 1 . This prevents the listener from feeling that there is something wrong with the bass. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0023]      FIG. 1  is a flow diagram of a signal processing apparatus according to a first embodiment of the present invention; 
           [0024]      FIG. 2  includes diagrams each showing a frequency characteristic of the signal processing apparatus according to the first embodiment of the present invention; 
           [0025]      FIG. 3  includes diagrams each showing a frequency characteristic of the signal processing apparatus according to the first embodiment of the present invention; 
           [0026]      FIG. 4  is a flow diagram of a signal processing apparatus according to a second embodiment of the present invention; 
           [0027]      FIG. 5  includes diagrams each showing a frequency characteristic of the signal processing apparatus according to the second embodiment of the present invention; 
           [0028]      FIG. 6  is a flow diagram of a signal processing apparatus according to a third embodiment of the present invention; 
           [0029]      FIG. 7  includes diagrams each showing a frequency characteristic of the signal processing apparatus according to the third embodiment of the present invention; 
           [0030]      FIG. 8  illustrates waveforms describing signal processing according to the embodiments of the present invention; 
           [0031]      FIG. 9  is a flow diagram of a circuit according the embodiments of the present invention; 
           [0032]      FIG. 10  illustrates waveforms describing signal processing performed in the circuit shown in  FIG. 9 ; 
           [0033]      FIG. 11  is a flow diagram of an exemplary audio reproducing apparatus of the related art; 
           [0034]      FIG. 12  includes diagrams each showing a frequency characteristic of the audio reproducing apparatus shown in  FIG. 11 ; and 
           [0035]      FIG. 13  includes diagrams each showing a frequency characteristic of the audio reproducing apparatus shown in  FIG. 11 . 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     First Embodiment 
       [0036]      FIG. 1  is a diagram of an exemplary configuration of a signal processing apparatus, which is an audio processing apparatus, according to a first embodiment of the present invention. The signal processing apparatus includes a speaker  5  having a small diameter whose bass is to be experienced by a listener should be improved. Here, f 0  and f 1  are defined as follows: 
         [0037]    f 0 : the resonance frequency of the speaker  5 , which is about 100 Hz or lower in the first embodiment; and 
         [0038]    f 1 : the frequency of a frequency component generated by multiplying the frequency of the fundamental frequency component included in a certain signal by an integer, which produces a sound that does not make the listener feel that there is something wrong with the sound, the frequency being typically about 200 Hz. 
         [0000]    In the first embodiment, f 0 =f 1 /2 (or f 0 ≦f 1 /2). When the signal processing apparatus is a two-channel stereo apparatus or a multichannel stereo apparatus, each channel of the two-channel stereo apparatus or the multichannel stereo apparatus may have the configuration shown in  FIG. 1 . 
         [0039]    An audio signal S 1  is supplied through an input terminal  1  to a high-pass filter  2 . As shown by the solid line in part (A) of  FIG. 2 , high and midrange frequency components S 2  whose frequencies are higher than or equal to the resonance frequency f 0  of the speaker  5  are extracted from the audio signal S 1  in the high-pass filter  2  and supplied to a combining circuit  3 . Additionally, the audio signal S 1  is supplied through the input terminal  1  to a band-pass filter  11  having a pass band from f 0  to f 1 , which is from 100 Hz to 200 Hz in the first embodiment. As shown by the broken line in part (A) of  FIG. 2 , low frequency components S 11  whose frequencies are from f 0  to f 1  are extracted from the audio signal S 1  in the band-pass filter  11  and supplied through an attenuator  13  to the combining circuit  3 . 
         [0040]    Furthermore, the audio signal S 1  is supplied through the input terminal  1  to a band-pass filter  21  having a pass band from f 0 /2 to f 1 /2, which is from 50 Hz to 100 Hz in the first embodiment. As shown in part (B) of  FIG. 2 , low frequency components S 21  whose frequencies are from f 0 /2 to f 1 /2 are extracted from the audio signal S 1  in the band-pass filter  21  and supplied to a pitch shifter  22 . 
         [0041]    The pitch shifter  22 , which will be described in more detail below, multiplies the frequencies of the low frequency components S 21  supplied thereto by two. Accordingly, as shown in part (C) of  FIG. 2 , second harmonic components S 22  whose frequencies are from f 0  to f 1  are output from the pitch shifter  22  and supplied through an attenuator  23  to the combining circuit  3 . 
         [0042]    In addition, the audio signal S 1  is supplied through the input terminal  1  to a band-pass filter  41  having a pass band from f 0 /4 to f 1 /4, which is from 25 Hz to 50 Hz in the first embodiment. As shown by the solid line in part (D) of  FIG. 2 , low frequency components S 41  whose frequencies are from f 0 /4 to f 1 /4 are extracted from the audio signal S 1  in the band-pass filter  41  and supplied to a pitch shifter  42 . 
         [0043]    The pitch shifter  42  multiplies the frequencies of the low frequency components S 41  supplied thereto by four. Accordingly, as shown by the broken line in part (D) of  FIG. 2 , fourth harmonic components S 42  whose frequencies are from f 0  to f 1  are output from the pitch shifter  42  and supplied through an attenuator  43  to the combining circuit  3 . 
         [0044]    As shown in part (E) of  FIG. 2 , an audio signal S 3  is generated in the combining circuit  3  by combining the low frequency components S 11 , the second harmonic components S 22 , and the fourth harmonic components S 42 , which are supplied to the combining circuit  3  through the attenuators  13 ,  23 , and  43 , respectively, with the high and midrange frequency components S 2  in a predetermined ratio. The audio signal S 3  is supplied through a power amplifier  4  to the speaker  5 . 
         [0045]    In the above-described configuration, after the audio signal S 1  is supplied to the input terminal  1 , the frequencies of the low frequency components S 21  and S 41  are multiplied by two and four in the pitch shifters  22  and  42  to generate the second and fourth harmonic components S 22  and S 42 , respectively. Then, the second and fourth harmonic components S 22  and S 42  are combined with the high and midrange frequency components S 2 . Thus, the audio signal S 3  having a frequency characteristic shown in part (E) of  FIG. 2  is generated from the audio signal S 1  and supplied to the speaker  5 . 
         [0046]    Although the speaker  5  negligibly outputs the sound of the fundamental frequency components whose frequencies are lower than or equal to the resonance frequency f 0 , the speaker  5  outputs the sound of the second and fourth harmonic components S 22  and S 42 . As described above, this allows the listener to perceive the sound as if the sound were output at the frequencies lower than or equal to the resonance frequency f 0 . As a result, the listener can experience the bass although the speaker  5  has a small diameter. 
         [0047]    In the above case, for example, as shown in part (A) of  FIG. 3 , in a case where the frequency of one of the low frequency components S 21  (the frequency of one of the low frequency components S 41 ) is 35 Hz, when a corresponding one of the second harmonic components S 22  (shown by the broken line) is generated from the low frequency component S 21 , the frequency of the second harmonic component S 22  is twice the frequency of the low frequency component S 21 , which is 70 Hz. It is difficult for the speaker  5  to reproduce the sound of the second harmonic component S 22  at 70 Hz. The same case is shown in part (B) of  FIG. 13 . 
         [0048]    However, in the signal processing apparatus shown in  FIG. 1 , in the case where the frequency of the low frequency component S 21  is 35 Hz, the frequency of the low frequency component S 21 , i.e., the low frequency component S 41 , is supplied through the band-pass filter  41  to the pitch shifter  42 , and the pitch shifter  42  generates a corresponding one of the fourth harmonic components S 42 . The frequency of the fourth harmonic component S 42  (shown by the solid line) is four times that of the low frequency component S 41 , which is 140 Hz, and the fourth harmonic component S 42  is supplied to the combining circuit  3 . Accordingly, even when the frequency of the low frequency component S 21  is 35 Hz, the listener can experience the bass corresponding to the low frequency component S 21  by receiving the sound of the fourth harmonic component S 42  whose frequency is four times that of the low frequency component S 21 . 
         [0049]    Additionally, for example, as shown in part (B) of  FIG. 3 , in a case where the frequency of one of the low frequency components S 41  (the frequency of one of the low frequency components S 21 ) is 60 Hz, when a corresponding one of the fourth harmonic components S 42  (shown by the broken line) is generated from the low frequency component S 41 , the frequency of the fourth harmonic component S 42  is four times that of the low frequency component S 41 , which is 240 Hz, and exceeds an upper limit frequency f 1  (≅200 Hz) used in combining harmonic components. Thus, when this fourth harmonic component S 42  is supplied to the speaker  5 , the listener feels that there is something wrong with the sound reproduced by the speaker  5 . The same case is shown in part (C) of  FIG. 13 . 
         [0050]    However, in the signal processing apparatus shown in  FIG. 1 , in the case where the frequency of the low frequency component S 41  is 60 Hz, the low frequency component S 41 , i.e., the low frequency component S 21 , is supplied through the band-pass filter  21  to the pitch shifter  22 , and the pitch shifter  22  generates a corresponding one of the second harmonic components S 22 . The frequency of the second harmonic component S 22  (shown by the solid line) is twice that of the low frequency component S 21 , which is 120 Hz, and the second harmonic component S 22  is supplied to the combining circuit  3 . Accordingly, even when the frequency of the low frequency component S 41  is 60 Hz, the listener can experience the bass corresponding to the low frequency component S 41  by receiving the sound of the second harmonic component S 22  whose frequency is twice that of the low frequency component S 41 . 
         [0051]    In addition, as shown in parts (A) and (E) of  FIG. 2 , because the low frequency components S 11  included in the original audio signal S 1  are intensified, the listener can naturally perceive the bass. 
       Second Embodiment 
       [0052]      FIG. 4  is a diagram of an exemplary configuration of a signal processing apparatus according to a second embodiment of the present invention. In the second embodiment, it is possible for the listener to effectively experience the bass even when f 0 &gt;f 1 /2. As in the case of the signal processing apparatus shown in  FIG. 1 , the high and midrange frequency components S 2  and the low frequency components S 11  are extracted from the audio signal S 1  and supplied to the combining circuit  3 . 
         [0053]    The input audio signal S 1  is supplied to a band-pass filter  21 . As shown by the broken line in part (A) of  FIG. 5 , the low frequency components S 21  whose frequencies are from f 0 /2 to f 1 /2 are extracted from the audio signal S 1  in the band-pass filter  21  and supplied to the pitch shifter  22 . As shown by the sold line in part (A) of  FIG. 5 , the second harmonic components S 22  whose frequencies are twice those of the low frequency components S 21 , i.e., the second harmonic components S 22  whose frequencies are from f 0  to f 1 , are output from the pitch shifter  22  and supplied through the attenuator  23  to a combining circuit  62 . 
         [0054]    Furthermore, the input audio signal S 1  is supplied to a band-pass filter  41 . As shown by the broken line in part (A) of  FIG. 5 , the low frequency components S 41  whose frequencies are from f 0 /4 to f 1 /4 are extracted from the audio signal S 1  in the band-pass filter  41  and supplied to the pitch shifter  42 . As shown by the sold line in part (A) of  FIG. 5 , the fourth harmonic components S 42  whose frequencies are four times those of low frequency components S 41 , i.e., the fourth harmonic components S 42  whose frequencies are from f 0  to f 1 , are output from the pitch shifter  42  and supplied through the attenuator  43  to the combining circuit  62 . 
         [0055]    As shown in part (B) of  FIG. 5 , a combined signal S 62  is generated in the combining circuit  62  by combining the second harmonic components S 22  and the fourth harmonic components S 42  and supplied to a low-pass filter  63 . The low-pass filter  63  has a frequency characteristic, for example, shown by the curve F 63  in part (C) of  FIG. 5 . More specifically, the frequency characteristic is that the resonance frequency f 0  is used as the cut-off frequency and input signal components are substantially removed at the upper limit frequency f 1 . 
         [0056]    Accordingly, harmonic components S 63  (hatched portion) including the second and fourth harmonic components whose sound does not make the listener feel that there is something wrong with the sound are extracted from the combined signal S 62  in the low-pass filter  63  and supplied to the combining circuit  3 . The audio signal S 3  is output from the combining circuit  3  and supplied though the power amplifier  4  to the speaker  5 . 
         [0057]    In the above-described configuration, as in the case of the signal processing apparatus shown in  FIG. 1 , the pitch shifters  22  and  42  generate the second harmonic components S 22  whose frequencies are twice those of the low frequency components S 21  and the fourth harmonic components S 42  whose frequencies are four times those of the low frequency components S 41 . Then, the second and fourth harmonic components S 22  and S 42  are combined with the high and midrange frequency components S 2 . As described above, this allows the listener to perceive the sound as if the sound were output from the speaker  5  at the frequencies lower than or equal to the resonance frequency f 0 . As a result, the listener can experience the bass although the speaker  5  has a small diameter. 
         [0058]    Furthermore, although, in the combining circuit  3 , the harmonic components S 63 , which includes the second and fourth harmonic components, are combined with the high and midrange frequency components S 2 , the levels of the harmonic components S 63  are reduced in the low-pass filter  63  as the frequencies of the harmonic components S 63  approach the upper limit frequency f 1 . This can reduce the listener&#39;s feeling that there is something wrong with the sound even when the harmonic components S 63  include a frequency component whose frequency exceeds the upper limit frequency f 1 . As a result, even when f 0 &gt;f 1 /2, the sound does not make the listener feel that there is something wrong with the sound, so that the listener can experience the bass. 
       Third Embodiment 
       [0059]      FIG. 6  is a diagram of an exemplary configuration of a signal processing apparatus according to a third embodiment of the present invention. As in the case of the signal processing apparatus shown in  FIG. 1 , the audio signal S 1  is supplied through the input terminal  1  to the high-pass filter  2 . The high and midrange frequency components S 2  whose frequencies are higher than or equal to the resonance frequency f 0  of the speaker  5  are extracted from the audio signal S 1  in the high-pass filter  2  and supplied to the combining circuit  3 . Additionally, the audio signal S 1  input from the input terminal  1  is supplied to a low-pass filter  10  having a pass band which is lower than or equal to the upper limit frequency f 1  that is 200 Hz in the third embodiment. Low frequency components S 10  whose frequencies are lower than or equal to the upper limit frequency f 1  are extracted from the audio signal S 1  in the low-pass filter  10 . The low frequency components S 10  are supplied through the attenuator  13  to the combining circuit  3  and combined with the high and midrange frequency components S 2  in a predetermined ratio. 
         [0060]    Furthermore, as in the case of the signal processing apparatus shown in  FIG. 1 , the second and fourth harmonic components S 22  and S 42  are generated by using the band-pass filters  21  and  41  and the pitch shifters  22  and  42 , supplied to the combining circuit  3  through the attenuators  23  and  43 , respectively, and combined with the high and midrange frequency components S 2  in a predetermined ratio. 
         [0061]    As shown in part (A) of  FIG. 7 , the audio signal S 3  is generated in the combining circuit  3  by combining the low frequency components S 10 , the second harmonic components S 22 , and the fourth harmonic components S 42 , which are supplied to the combining circuit  3  through the attenuators  13 ,  23 , and  43 , respectively, with the high and midrange frequency components S 2  in a predetermined ratio. 
         [0062]    The audio signal S 3  is supplied to a low-frequency cut filter  6 . As shown in part (B) of  FIG. 7 , an audio signal S 6  is generated in the low-frequency cut filter  6  by removing deep low frequency components having a negative effect on the speaker  5  with a small diameter from the audio signal S 3 ; when the deep low frequency components are supplied to the speaker  5 , the normal bass is not output but components (harmonic components) that cause sound distortion are output in high volume from the speaker  5 . The audio signal S 6  is supplied through the power amplifier  4  to the speaker  5 . 
         [0063]    In the above-described configuration, although the speaker  5  negligibly outputs the sound of the low frequency components S 10 , the speaker  5  outputs the sound of the second and fourth harmonic components S 22  and S 42  of the low frequency components S 10 . As described above, this allows the listener to perceive the sound as if the sound of the low frequency components S 10  were output. As a result, the listener can experience the bass although the speaker  5  has a small diameter. 
         [0064]    Furthermore, as shown in part (B) of  FIG. 7 , because some of the low frequency components S 10  remain in the audio signal S 6 , the listener can naturally experience the bass. In addition, the deep low frequency components having a negative effect on the speaker  5  with a small diameter are removed from the low frequency components S 11  in the low-frequency cut filter  6 . Thus, a case where components (harmonic components) that cause sound distortion are output in high volume, although the normal bass is negligibly output from the speaker  5 , does not occur. 
       Examples of Pitch Shifters  22  and  42   
       [0065]    The second harmonic components S 22  whose frequencies are twice the frequencies of the low frequency components S 21  and the fourth harmonic components S 42  whose frequencies are four times the frequencies of the low frequency components S 41  can be generated by a method illustrated in  FIG. 8 . Suppose that digital data DA that can be digital to analog (D/A) converted into data representing one cycle of a sinusoidal signal SA as shown in part (A) of  FIG. 8  is stored in a memory. A symbol • indicates a sampling point of the digital data DA. A period TA is one period of the sinusoidal signal SA, and a period  1 /fc is one sampling period. 
         [0066]    When the digital data DA is read from the memory, by reading the digital data DA on a sample by sample basis at a clock frequency fc which is the same frequency as used in writing, data representing one period of the sinusoidal signal SA can be obtained in the period TA. 
         [0067]    Similarly, when the digital data DA is read from the memory, as shown in part (B) of  FIG. 8 , by reading the digital data DA from every other address of the memory at a clock frequency fc which is the same frequency as used in the writing and performing the reading twice, data representing two periods of a sinusoidal signal SB whose frequency is twice that of the sinusoidal signal SA can be obtained in the period TA. That is, the second harmonic component SB having a frequency twice that of the sinusoidal signal SA can be obtained in the period TA. 
         [0068]    Moreover, when the digital data DA is read from the memory, as shown in part (C) of  FIG. 8 , by reading the digital data DA from every four addresses of the memory at a clock frequency fc which is the same frequency as used in the writing and performing the reading four times, data representing four periods of a sinusoidal signal SC whose frequency is four times that of the sinusoidal signal SA can be obtained in the period TA. That is, the fourth harmonic component SC having a frequency four times that of the sinusoidal signal SA can be obtained in the period TA. 
         [0069]    The pitch shifters  22  and  42  may have, for example, the configuration shown in  FIG. 9 . Referring to  FIG. 9 , a memory  22 M, for example, including a ring buffer, has a substantially sufficient number of addresses (substantially sufficient capacity). It is assumed that the low frequency components S 21  are described by a waveform shown in part (A) of  FIG. 10 , digital data D 21  is obtained by performing analog to digital (A/D) conversion of the data described by the waveform, and the sampling frequency (clock frequency) for the A/D conversion is fc. 
         [0070]    A point at which the sign of the digital data D 21  (the low frequency components S 21 ) changes, for example, from negative to positive, is defined as a point tx. A period between a certain point tx and the next point tx, i.e., one period of the low frequency components S 21 , is defined as a period Tx. 
         [0071]    Referring to  FIG. 9 , the digital data D 21  is supplied through an input terminal  22 A to the memory  22 M. As shown in part (A) of  FIG. 10 , the digital data D 21  is written on a sample by sample basis in respective addresses of the memory  22 M. Accordingly, the period Tx shown in  FIG. 10  corresponds to the period TA shown in  FIG. 8 , and part (A) of  FIG. 10  corresponds to part (A) of  FIG. 8 . 
         [0072]    The digital data D 21  is simultaneously written to and read from the memory  22 M. For the sake of simplicity, referring to  FIG. 10 , the period Tx is used as a writing cycle and a reading cycle, and the writing and reading are simultaneously performed in the period Tx. 
         [0073]    As in a manner similar to that shown in part (B) of  FIG. 8 , the digital data D 21  written in the memory  22 M is read from every other address of the memory  22 M at a clock frequency fc which is the same frequency as used in the writing, and the reading is performed twice in the period Tx, whereby digital data D 22  is obtained. By performing D/A conversion of this digital data D 22  read from the memory  22 M, the second harmonic components S 22  whose frequencies are twice those of the original low frequency components S 21  can be obtained. 
         [0074]    Similarly, the low frequency components S 41  are A/D converted to generate digital data, and this digital data is written in the memory  22 M. The written digital data is read in a manner similar to that shown in part (C) of  FIG. 8 . That is, the digital data is read from every four addresses of the memory  22 M at a clock frequency fc which is the same frequency as used in the writing, and the reading is performed four times in the period Tx. By performing D/A conversion of the digital data read from the memory  22 M, the fourth harmonic components S 42  whose frequencies are four times those of the original low frequency components S 41  can be obtained. 
       CONCLUSION 
       [0075]    In the above-described signal processing apparatuses, even when the frequencies of the low frequency components are lower than the resonance frequency f 0  of the speaker  5 , the second harmonic components S 22  and the fourth harmonic components S 42  whose frequencies are higher than the resonance frequency f 0  of the speaker  5  are generated in the pitch shifters  22  and  42 , respectively, combined with the high and midrange frequency components S 2 , and supplied to the speaker  5 . Thus, the listener can experience the bass although the speaker  5  has a small diameter. 
         [0076]    Additionally, in order to generate the harmonic components, the frequencies of the low frequency components are multiplied by two or four such that the frequencies of the harmonic components can fall within the band between the resonance frequency f 0  of the speaker  5  and the upper limit frequency f 1 . This prevents the listener from feeling that there is something wrong with the bass. 
         [0077]    Furthermore, as shown in part (B) of  FIG. 7 , since some of the original low frequency components S 10  remain in the audio signal S 6 , the listener can naturally experience the bass. In addition, the deep low frequency components having a negative effect on the speaker  5  with a small diameter are removed from the low frequency components S 10  in the low-frequency cut filter  6 . Thus, the case where the components that cause sound distortion are output in high volume, although the normal bass is not output from the speaker  5 , does not occur. 
         [0078]    For example, because the relationship between third harmonic components and the fundamental frequency components is not an octave, the sound of the third frequency components makes the listener feel that there is something wrong with the sound. In contrast, the second or fourth harmonic components have frequencies higher by an octave or two octaves than those of the fundamental frequencies. Thus, the sound of the second or fourth frequency components does not make the listener feel that there is something wrong with the sound. 
       Other Embodiments 
       [0079]    In the above descriptions, the signal system in which the output audio signal S 6  is generated from the input audio signal S 1  is realized by digital signal processing using a digital signal processor (DSP) or dedicated hardware. For example, the band-pass filter  21  and the pitch shifter  22  may share a memory, or the band-pass filter  21  and the band-pass filter  41  may share a memory. For example, when the band-pass filter  21  processes digital data representing one cycle and supplies the result of the processing to the pitch shifter  22 , the band-pass filter  21  and the pitch shifter  22  may share a buffer memory. 
         [0080]    Additionally, in the foregoing descriptions, as shown in  FIG. 10 , the pitch shifter  22  performs multiplication by two in units of cycles of the input digital data D 21  (the low frequency components S 21 ). Similarly, the pitch shifter  22  may perform multiplication by two in units of certain periods. This allows processing of data represented by a waveform such that the end of a waveform in a certain period can be continuously connected to the beginning of a waveform in the next period. 
         [0081]    Furthermore, low frequency components having considerably low frequencies may be recorded in, for example, a compact disc (CD) or a super audio CD (SACD). In order that the listener can experience the bass of the low frequency components, not only second and fourth harmonic components but also eighth, sixteenth, and thirty-second harmonic components and the like may be combined with an original audio signal. More specifically, the harmonic components whose frequencies do not exceed the upper limit frequency f 1  and are N (N=2n where n=an integer from 1 to 6) times the frequency of the frequency component of bass that the listener wants to experience may be combined with the original audio signal. 
         [0082]    It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and alterations may occur depending on design requirements and other factors insofar as they are within the scope of the appended claims or the equivalents thereof.