Apparatus and method for sampling rate conversion

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 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.

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 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 W.sub.1 -.sup.(n*n)/2 according to an Equation represented by
• 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)*W.sub.1 -.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)*W.sub.1 -.sup.(n*n)/2 to W.sub.1.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(jk.omega..sub.0) to W.sub.2.sup.k*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)*W.sub.2 -.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)*W.sup.2 -.sup.[(k*k)/2+(N-1)k/2] to W.sub.2.sup.[-p*p/2+(n-1)**2/8] to compute the values g.sub.p which is the data sampled at said second sampling frequency according to Equation 23 an Equation represented as:
• ##EQU30##

A method for sampling rate conversion comprising the steps of:

• (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), W.sub.1 =e.sup.j(2.pi./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 W.sub.2 =W.sub.1.sup.(1/m), and m=.omega..sub.1 /.omega..sub.2 =f.sub.2 /f.sub.1 being a ratio of said second sampling frequency for said sampled data g.sub.p 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 T.sub.1 =0, and
• 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.

A method for sampling rate conversion comprising the steps of:

• (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 W.sub.1 -.sup.(n*n)/2 according to an Equation represented by:
• g.sub.p =f(n)W.sub.1 -.sup.(n*n)/2 ( 12-1)
• then computing the convolution e(n)*W.sub.1 -.sup.(n*n)/2 according to an Equation represented by:
• ##EQU33## and furthermore computing the product of said convolution e(n)*W.sub.1 -.sup.(n*n)/2 to W.sub.1.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(jk.omega..sub.0) to W.sub.2.sup.k*k/2 according to an Equation represented by:
• ##EQU35## then computing the convolution e(K)*W.sub.2 -.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)*W.sub.2 -.sup.[(k*k)/2+(N-1)k/2] to W.sub.2.sup.[-p*p/2+(n-1)**2/8] to compute the values g.sub.p 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 g.sub.p.

A digital music synthesizer system comprising:

• 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), W.sub.1 =e.sup.j(2.pi./N), and k=-(n-1)/2, . . . , (N-1)/2;
• and
• said 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 W.sub.2 =W.sub.1.sup.(1/m), and m=.omega..sub.1 /.omega..sub.2 =f.sub.2 /f.sub.1 being a ratio of said second sampling frequency for said sampled data g.sub.p 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 T.sub.1 =0, and
• 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.