Apparatus and method for sampling rate conversion
First Claim
1. A data processing system capable of performing a sampling frequency conversion comprising:
- a data receiving means for receiving a plurality of input data sampled at a first sampling frequency;
a discrete transforming means for performing a discrete Fourier transform (DFT) on said input data sampled at said first sampling frequency for transforming the input data to a discrete function in a second-variable-domain at said first sampling frequency by performing;
##EQU18## where N being an integer representing the number of the sampled data f(n), W1 =ej(2π
/N), and k=-(n-1)/2, . . . , (N-1)/2; and
a convoluted inverse transform means for performing a convolute inverse discrete Fourier transform (IDFT) transform for inversely transforming said discrete function in a second-variable-domain back to the time domain at a second sampling frequency for converting said input data to a set of corresponding data sampled at said second sampling frequency wherein said convolute inverse discrete Fourier transform (IDFT) transform being represented by;
##EQU19## where W2 =W1 .sup.(1/m), and m=ω
1 /ω
2 =f2 /f1 which being a ratio of said second sampling frequency for said sampled data gp to said first sampling frequency for said sampled data f(n), wherein m being any positive real number while n=0,1,2, . . . ,N-1 and where p in Equations (1-2) being a total number of the sampled data at said second sampling frequency and p={m(Tn+L)} where {K} representing an integer value of K which being smaller or equal to K and where L representing a length of a data segment which being a length of said DFT, and where T1 =0, and
space="preserve" listing-type="equation">T.sub.n =(1/m){m(T.sub.n-1 +N)-m(T.sub.n-1 +N)} (1-3)which being a remaining interval of a (n+1)th data segment after re-sampling at said second sampling frequency.
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Abstract
The present invention teaches a data processing system capable of performing a sampling frequency conversion. The data processing system includes a data receiving means for receiving a plurality of input data sampled at a first frequency. The data processing system further includes a discrete transforming means for performing a discrete transform on the input data at the first sampled frequency for transforming the input data to a discrete function in a second-variable-domain at the first sampling frequency. The data processing system further includes a convoluted inverse transforming means for inversely transforming the discrete function in a second-variable-domain back to the time domain at a second sampling frequency for converting the input data to a set corresponding data sampled at the second sampling frequency.
31 Citations
10 Claims
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1. A data processing system capable of performing a sampling frequency conversion comprising:
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a data receiving means for receiving a plurality of input data sampled at a first sampling frequency; a discrete transforming means for performing a discrete Fourier transform (DFT) on said input data sampled at said first sampling frequency for transforming the input data to a discrete function in a second-variable-domain at said first sampling frequency by performing;
##EQU18## where N being an integer representing the number of the sampled data f(n), W1 =ej(2π
/N), and k=-(n-1)/2, . . . , (N-1)/2; anda convoluted inverse transform means for performing a convolute inverse discrete Fourier transform (IDFT) transform for inversely transforming said discrete function in a second-variable-domain back to the time domain at a second sampling frequency for converting said input data to a set of corresponding data sampled at said second sampling frequency wherein said convolute inverse discrete Fourier transform (IDFT) transform being represented by;
##EQU19## where W2 =W1 .sup.(1/m), and m=ω
1 /ω
2 =f2 /f1 which being a ratio of said second sampling frequency for said sampled data gp to said first sampling frequency for said sampled data f(n), wherein m being any positive real number while n=0,1,2, . . . ,N-1 and where p in Equations (1-2) being a total number of the sampled data at said second sampling frequency and p={m(Tn+L)} where {K} representing an integer value of K which being smaller or equal to K and where L representing a length of a data segment which being a length of said DFT, and where T1 =0, and
space="preserve" listing-type="equation">T.sub.n =(1/m){m(T.sub.n-1 +N)-m(T.sub.n-1 +N)} (1-3)which being a remaining interval of a (n+1)th data segment after re-sampling at said second sampling frequency. - View Dependent Claims (2, 3, 4)
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5. A data processing system capable of performing a sampling frequency conversion comprising:
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a data receiving means for receiving a plurality of input data sampled at a first sampling frequency; a discrete transforming means for performing a discrete transform on said input data sampled at said first sampling frequency for transforming the input data to a discrete function in a second-variable-domain at said first sampling frequency; a convoluted inverse transform means for inversely transforming said discrete function in a second-variable-domain back to the time domain at a second sampling frequency for converting said input data to a set of corresponding data sampled at said second sampling frequency; and said convoluted inverse transform means for inversely transforming said discrete function in a second-variable-domain back to the time domain at a second sampling frequency further includes a smoothing window means for applying a smoothing window to said inverse transform. - View Dependent Claims (6)
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7. A data processing system capable of performing a sampling frequency conversion comprising:
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a data receiving means for receiving a plurality of input data sampled at a first sampling frequency; a discrete transforming means for performing a discrete transform on said input data sampled at said first sampling frequency for transforming the input data to a discrete function in a second-variable-domain at said first sampling frequency wherein said discrete transform means being a discrete Fourier transform (DFT) means; said DFT transform means including a first chirp transform evaluation means which further includes a first multiplication means for computing the product of f(n) to W1 -.sup.(n*n)/2 according to an Equation represented by
space="preserve" listing-type="equation">g.sub.p =f(n)W.sub.1 -.sup.(n*n)/2 ( 9-1)said first chirp transform evaluation means further includes a first convolution means for computing the convolution e(n)*W1 -.sup.(n*n)/2 according to an Equation represented by;
##EQU26## and said first chirp transform evaluation means further includes a second multiplication means for computing the product of said convolution e(n)*W1 -.sup.(n*n)/2 to W1.sup.(k*k)/2 to compute the value of F(k)according to an Equation represented by;
##EQU27## a convoluted inverse transform means for inversely transforming said discrete function in a second-variable-domain back to the time domain at a second sampling frequency for converting said input data to a set of corresponding data sampled at said second sampling frequency wherein said convolute inverse transform means being a convolute inverse discrete Fourier transform (IDFT) transform means;said convoluted inverse transform means further including a smoothing window means which being a symmetrical low pass filter for applying a smoothing window to said inverse transform; said convolute IDFT transform means further including a second chirp transform evaluation means which further includes a third multiplication means for computing the product of exp(jkω
0) to W2k*k/2 according to an Equation represented by;
##EQU28## said second chirp transform evaluation means further includes a second convolution means for computing the convolution e(K)*W2 -.sup.[(k*k)/2+(N-1)k/2] according to an Equation represented by;
##EQU29## and said second chirp transform evaluation means further includes a fourth multiplication means for computing the product of said convolution e(K)*W2 -.sup.[(k*k)/2+(N-1)k/2] to W2.sup.[-p*p/2+(n-1)**2/8] to compute the values gp which is the data sampled at said second sampling frequency according to Equation 23 an Equation represented as;
##EQU30##
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8. A method for sampling rate conversion comprising the steps of:
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(a) receiving a plurality of input data sampled at a first sampling frequency; (b) applying a DFT at said first sampling frequency to said input data to obtain a plurality of frequency-domain discrete functions by performing;
##EQU31## where N being an integer representing the number of the sampled data f(n), W1 =ej(2π
/N), and k=-(n-1)/2, . . . , (N-1)/2; and(c) applying a convoluted IDFT to transform said frequency-domain discrete functions at said first sampling frequency to a set of corresponding time-domain data at a second sampling frequency wherein said convolute inverse discrete Fourier transform (IDFT) transform being represented by;
##EQU32## where W2 =W1.sup.(1/m), and m=ω
1 /ω
2 =f2 /f1 being a ratio of said second sampling frequency for said sampled data gp to said first sampling frequency for said sampled data f(n), wherein m being any positive real number while n=0,1,2, . . . ,N-1 and where p in Equations (1-2) being a total number of the sampled data at said second sampling frequency and p={m(Tn+L)} where {K} representing an integer value of K which being smaller or equal to K and where L representing a length of a data segment which being a length of said DFT, and where T1 =0, and
space="preserve" listing-type="equation">T.sub.n =(1/m){m(T.sub.n-1 +N)-m(T.sub.n-1 +N)} (10-3)which being a remaining interval of a (n+1)th data segment after re-sampling at said second sampling frequency.
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9. A method for sampling rate conversion comprising the steps of:
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(a) receiving a plurality of input data sampled at a first frequency; (b) performing a discrete transform on said input data at said first sampled frequency for transforming the input data to a discrete function in a second-variable-domain at said first sampling frequency wherein said discrete transform being a discrete Fourier transform (DFT) performing a first chirp transform evaluation by first computing the product of f(n) to W1 -.sup.(n*n)/2 according to an Equation represented by;
space="preserve" listing-type="equation">g.sub.p =f(n)W.sub.1 -.sup.(n*n)/2 ( 12-1)then computing the convolution e(n)*W1 -.sup.(n*n)/2 according to an Equation represented by;
##EQU33## and furthermore computing the product of said convolution e(n)*W1 -.sup.(n*n)/2 to W1.sup.(k*k)/2 to compute the value of F(k)according to an Equation represented by;
##EQU34## (c) inversely transforming said discrete function in said second-variable-domain back to the time domain at a second sampling frequency for converting said input data to a set of corresponding data sampled at said second sampling frequency wherein said convolute inverse transform being a convolute inverse discrete Fourier transform (IDFT) transform further performing a smoothing window operation by using a symmetrical low pass filter for applying a smoothing window to said inverse transform; and(d) said convolute IDFT transform step further applying a second chirp transform evaluation by first computing the product of exp(jkω
0) to W2k*k/2 according to an Equation represented by;
##EQU35## then computing the convolution e(K)*W2 -.sup.[(k*k)/2+(N-1)k/2] an Equation represented by;
##EQU36## and further includes a fourth multiplication means for computing the product of said convolution e(K)*W2 -.sup.[(k*k)/2+(N-1)k/2] to W2.sup.[-p*p/2+(n-1)**2/8] to compute the values gp which is the data sampled at said second sampling frequency according to an Equation represented as;
##EQU37## where said output sequence F(k) being re-sampled to become said sampled data gp.
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10. A digital music synthesizer system comprising:
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a data receiving and storage means for receiving and temporary storing a plurality of input data sampled at a first sampling frequency; a pitch shifting means including a discrete transforming means for performing a discrete transform on said input data at said first sampled frequency for transforming the input data to a discrete function in a second-variable-domain at said first sampling frequency wherein said discrete transform being a discrete Fourier transform (DFT) on said input data sampled at said first sampling frequency for transforming the input data to a discrete function in a second-variable-domain at said first sampling frequency by performing;
##EQU38## where N being an integer representing the number of the sampled data f(n), W1 =ej(2π
/N), and k=-(n-1)/2, . . . , (N-1)/2; andsaid pitch shifting means further including a convoluted inverse transform means performing a convolute inverse discrete Fourier transform (IDFT) transform for inversely transforming said discrete function in a second-variable-domain back to the time domain at a second sampling frequency for converting said input data to a set of corresponding data sampled at said second sampling frequency wherein said convolute inverse discrete Fourier transform (IDFT) transform being represented by;
##EQU39## where W2 =W1.sup.(1/m), and m=ω
1 /ω
2 =f2 /f1 being a ratio of said second sampling frequency for said sampled data gp to said first sampling frequency for said sampled data f(n), wherein m being any positive real number while n=0,1,2, . . . ,N-1 and where p in Equations (1-2) being a total number of the sampled data at said second sampling frequency and p={m(Tn+L)} where {K} representing an integer value of K which being smaller or equal to K and where L representing a length of a data segment which being a length of said DFT, and where T1 =0, and
space="preserve" listing-type="equation">T.sub.n =(1/m){m(T.sub.n-1 +N)-m(T.sub.n-1 +N)} (1-3)which being a remaining interval of a (n+1)th data segment after re-sampling at said second sampling frequency; and an envelop function means for performing an enveloping processing on said data at said sampling frequency whereby said data at said second sampling frequency is ready for a digital to analog conversion operation.
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Specification