Time domain aliasing cancellation apparatus and signal processing method thereof

A time domain aliasing cancellation method comprising an encoding method and a decoding method, said encoding method performing time domain aliasing cancellation encoding for transforming an m-th signal frame x.sub.m (n) in the time domain into an m-th signal frame X.sub.m (k) in the frequency domain, said decoding method performing time domain aliasing cancellation decoding for transforming said input frequency-domain signal frame X.sub.m (k) back to a time-domain signal frame x'.sub.m (n), said time-domain signal frames x.sub.m (n) and x'.sub.m (n) and said frequency-domain signal frame X.sub.m (k) having N terms wherein N is a positive integer number, and n, k, and m are integers, said encoding method of the time-domain aliasing cancellation method comprising the steps of

• multiplying individual terms of said input time-domain signal frame x.sub.m (n) by a modified analysis window function w.sub.E (n) for generating a first time sequence s(n) with length N expressed as:
• s(n)=x.sub.m (n)w.sub.E (n) with ##EQU61## wherein h(n) is the original analysis window function;
• rearranging said first time sequence s(n) for generating a second time sequence y(n) with length N, the first N/4 terms of said second time sequence y(n) being composed of the last N/4 terms of said first time sequence s(n), and the last 3N/4 terms of y(n) being composed of the first 3N/4 terms of s(n);
• subtracting from the first N/2 terms of said second time sequence y(n) the terms in the second half of said time sequence in reversed order for generating a third time sequence u(n) expressed as:
• u(n)=y(n)-y(N-1-n);
• performing a discrete cosine transformation on said third time sequence u(n) for generating a first frequency domain signal U(k) expressed as:
• ##EQU62## adding said first frequency sequence U(k) with neighboring terms thereof for generating a second frequency sequence Y(k) with length N/2 expressed as:
• Y(k)=U(k+1)+U(k);
• and
• rearranging said second frequency sequence Y(k) for generating said encoded output frequency sequence X.sub.m (k) with length N, the first N/2 terms of X.sub.m (k) being Y(k) multiplied by a phase factor (-1).sup.mk expressed as:
• X.sub.m (k)=(-1).sup.mk Y(k), the last N/2 terms of X.sub.m (k) being Y(k) in reversed order and multiplied by a phase factor (-1).sup.mk+1 expressed as:
• X.sub.m (k)=-(1).sup.mk+1 Y(N-k-1),
• and said decoding method comprising the steps of
• adding a phase factor of (-1).sup.mk to said frequency sequence X.sub.m (k) for generating a third frequency sequence Yr(k) expressed as Yr(k)=(-1).sup.mk X.sub.m (k);
• utilizing said third frequency sequence Yr(k) for generating a fourth frequency sequence Z(k) with length N/2, wherein Z(k)=2Yr(k-1)+2Yr(k) when k is between 1 to N/2-1, and Z(k)=2Yr(0) when k is equal to zero;
• performing an inverse discrete cosine transform on said fourth frequency sequence Z(k) for generating a fourth time sequence z(n) expressed as ##EQU63## rearranging said fourth time sequence z(n) for generating a fifth time sequence q.sub.m (n) with length N, wherein the first 1/4 of the terms of q.sub.m (n) being composed of the second half of z(n), the second N/4 terms of q.sub.m (n) being composed of the second half of z(n) in reversed order, the third N/4 terms of q.sub.m (n) being the first half of z(n) in reversed order, and the last N/4 terms of q.sub.m (n) being the first half of the fourth time sequence z(n);
• and
• multiplying said fifth time sequence q.sub.m (n) and the previous frame input time sequence q.sub.m-1 (n) by a modified synthesis window function W.sub.D (n) for generating the output time sequence x (n) expressed as ##EQU64## wherein f(n) being the original analysis window function of a coding system.

A time domain aliasing cancellation apparatus comprising an encoding device and a decoding device, said encoding device performing time domain aliasing cancellation encoding for transforming an m-th signal frame x.sub.m (n) in the time domain into an m-th signal frame X.sub.m (k) in the frequency domain, said decoding device performing time domain aliasing cancellation decoding for transforming said input frequency-domain signal frame X.sub.m (k) back to a time-domain signal frame x (n), said time-domain signal frames x.sub.m (n) and x'.sub.m (n) and said frequency-domain signal frame X.sub.m (k) having N terms wherein N is a positive integer number and n, k, and m are integers, said encoding device of the time-domain aliasing cancellation apparatus comprising:

• a modified analysis window function unit for multiplying term by term the input time-domain signal frame x.sub.m (n) with a modified analysis window function w.sub.E (n) for generating a first time sequence s(n) expressed as s(n)=x.sub.m (n)w.sub.E (N-1-n) with ##EQU65## wherein h(n) is the original analysis window function of a coding system 0<=J<=N/2-1;
• an encoding unit, rearranging said first time sequence s(n) for generating a second time sequence y(n) with length N, the first N/4 terms of said second time sequence y(n) being composed of the last N/4 terms of said first time sequence s(n), and the last 3N/4 terms of y(n) being composed of the first 3N/4 terms of s(n);
• a subtraction unit, subtracting from the N/2 terms of said second time sequence y(n) the terms in the second half of said time sequence in reversed order for generating a third time sequence v(n);
• a first buffer register with N/2 random access memory registers for storing said third time sequence signal v(n);
• a first address unit, using a first parameter as the address to select said third time sequence v(n) from said first buffer, rearranging said third time sequence v(n) for generating a fourth time sequence v'(n);
• a first sign adjustment unit, using a second parameter for adjusting the sign of each term of said fourth time sequence v'(n);
• a first digital filter for transforming said sign-adjusted fourth time sequence v'(n) into a first encoded frequency sequence Y(k), said first encoded frequency sequence Y(k) being the discrete cosine transformation of said fourth time sequence v'(n);
• and
• an output unit, using said first frequency sequence Y(k) for generating said output encoded frequency X.sub.m (k), wherein the first N/2 terms of X.sub.m (k) are Y(k) multiplied by a phase factor (-1).sup.mk expressed as X.sub.m (k)=(-1).sup.mk Y(k), and the last N/2 terms of X.sub.m (k) being Y(k) multiplied by a phase factor (-1).sup.mk+1 expressed as X.sub.m (k)=(-1).sup.mk+1 Y(k),
• said decoding apparatus comprising
• an input sign adjusting unit, using said input frequency sequence X.sub.m (k) with length N by a phase factor (-1).sup.mk, and shifting the result to the left by 1 bit to perform a multiplication by 2 for generating a second frequency sequence 2Y(k) expressed as 2Y(k)=2(-1).sup.mk X.sub.m (k);
• a second buffer with N/2 random access memory registers for storing said second frequency sequence 2Y(k);
• a second address unit, using said first parameter as the address to select each term of said second frequency sequence 2Y(k) from said second buffer, rearranging for generating a third frequency sequence Y'(k);
• a second sign adjustment unit, using said second parameter for correcting the sign of each term of said third frequency sequence Y'(k);
• a second digital filter, transforming said sign-adjusted third frequency sequence Y'(k) into a fifth time sequence y(n), said fifth time sequence y(n) being the inverse discrete cosine transformation of said third frequency sequence Y'(k);
• a reordering encoder, rearranging said fifth time sequence y(n) for generating a sixth time sequence q.sub.m (n) with length N, the first 3N/4 terms of said sixth time sequence q.sub.m (n) being composed of the last 3N/4 terms of said fifth time sequence y(n), and the last N/4 terms of said sixth time sequence q.sub.m (n) being composed of the negative of the first N/4 terms of said fifth time sequence y(n);
• and
• a modified synthesis window function unit for multiplying said fifth time sequence q.sub.m (n) and the previous input time sequence q.sub.m-1 (n) by a modified synthesis window function w.sub.D (n) for generating the output time sequence x'.sub.m (n) expressed as ##EQU66## wherein ##EQU67## and f(n) is an original synthesis window function.

A time domain aliasing cancellation signal processing method comprising an encoding method and a decoding method, said encoding method performing time domain aliasing cancellation encoding for transforming an m-th sequence x.sub.m (n) in the time domain into an m-th sequence X.sub.m (k) in the frequency domain, said decoding method performing time domain aliasing cancellation decoding for transforming said input frequency-domain sequence X.sub.m (k) back to an output sequence x'.sub.m (n), said time-domain sequences x.sub.m (n) and x.sub.m '(n) and said frequency-domain sequence X.sub.m (k) having N terms wherein N is a positive integer number, and n, k, and m are integers, said encoding method of the time domain aliasing cancellation method comprising the steps of:

• multiplying a modified analysis window function w.sub.E (n) term by term with said input time domain signal frame x.sub.m (n) for generating a first time sequence s(n) expressed as s(n)=x.sub.m (n)w.sub.E (N-1-n) with ##EQU68## wherein h(n) being an original analysis window function, 0<=J<=N/2-1;
• rearranging said first time sequence s(n) for generating a second time sequence y(n) with length N, the first N/4 terms of said second time sequence y(n) being composed of the last N/4 terms of said first time sequence s(n), and the last 3N/4 terms of y(n) being composed of the first 3N/4 terms of s(n);
• subtracting from the first N/2 terms of said second time sequence y(n) the terms in the second half of said time sequence in reversed order for generating a third time sequence v(n);
• storing said third time sequence signal v(n) in a first buffer with N/2 registers;
• using a first parameter as the address to select said third time sequence v(n) from said first buffer, rearranging said third time sequence v(n) for generating a fourth time sequence v'(n);
• using a second parameter for adjusting the sign of each term of said fourth time sequence v'(n);
• filtering and transforming said sign-adjusted fourth time sequence v'(n) into a first encoded frequency sequence Y(k), said first encoded frequency sequence Y(k) being the discrete cosine transformation of said fourth time sequence v'(n);
• and
• reordering said first frequency sequence Y(k) for generating said output encoded frequency X.sub.m (k), wherein the first N/2 terms of X.sub.m (k) being Y(k) multiplied by a phase factor (-1).sup.mk expressed as
• X.sub.m (k)=(-1).sup.mk Y(k)
• wherein the last N/2 terms of X.sub.m (k) being Y(k) multiplied by a phase factor (-1).sup.mk+1 expressed as
• X.sub.m (k)=(-1).sup.mk+1 Y(k),
• said decoding procedure comprising the steps of
• multiplying said input frequency sequence X.sub.m (k) with length N by a phase factor (-1).sup.mk, and shifting the result to the left by 1 bit to perform a multiplication by 2 for generating a second frequency sequence 2Y(k) expressed as 2Y(k)=2(-1).sup.mk X.sub.m (k);
• storing said 2nd frequency sequence 2Y(k) in a second buffer with N/2 RAM registers;
• using said first parameter as the address to select each term of said second frequency sequence 2Y(k) from said second buffer registers and rearrange order thereof for generating a third frequency sequence Y'(k);
• using said second parameter for correcting the sign of each term of said third frequency sequence Y'(k);
• filtering and transforming said sign-adjusted third frequency sequence Y'(k) into a fifth time sequence y(n), said fifth time sequence y(n) being the inverse discrete cosine transformation of said third frequency sequence Y'(k);
• rearranging said fifth time sequence y(n) for generating a sixth time sequence q.sub.m (n) with length N, the first 3N/4 terms of said sixth time sequence q.sub.m (n) being composed of the last 3N/4 terms of said fifth time sequence y(n), and the last N/4 terms of said sixth time sequence q.sub.m (n) being composed of the negative of the first N/4 terms of said 5th time sequence y(n);
• multiplying said fifth time sequence q.sub.m (n) and the previous input time sequence q.sub.m-1 (n) by a modified synthesis window function W.sub.D (n) for generating the output time sequence x.sub.m '(n) expressed as ##EQU69## wherein ##EQU70## and f(n) is an original synthesis window function.