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regading PWI-ZFE speech coder

Started by ravichandra reddy August 29, 2003
hi,
i completed my M.tech in DSP. I did my project on " Implementation of Mixed
Multi-Band PrototypeWaveform Interpolation-Zinc Function Excitation
(MMBE-PWI-ZFE) Speech coder.
here i used Zinc pulses i used for reconstructing the speech signal at the
decoder instead of normal Dirac delta pulses".

Here I got one doubt, " why can't we use pureSinc or Cosc signal".
and I am giving the full details of ZINC function.please clarrify it .

Zinc Basis Functions

[Sukkar89] suggest that a signal representation based on "orthogonal
function decomposition" can be done via a set of basis functions that
have similar characteristics to the signal being modeled. The "zinc
basis functions" are proposed to model LPC excitation signals (that
are inherently band-limited and pulse-type). The zinc function is
defined as:

Z(t) = A Sinc(t) + B Cosc(t),
where Sinc(t) = [sin(2*pi*fc*t)]/(2*pi*fc*t) and
and Cosc(t)= [1 - cos(2*pi*fc*t)]/(2*pi*fc*t)

here A,B and fc (cut-off frequency) are constants. Time shifted zinc
functions: Z(t-k) = A Sinc(t-k) + B Cosc(t-k).

Each Zinc function is itself composed of orthogonal functions
Sinc(t-k) and Cosc(t-k), for any value of k. It can be proved the
orthogonal set of (weighted) zinc functions can fully span the space
of all band-limited signals.
r(t) = sum{Z(t)} = sum { A Sinc(t-nT) + B Cosc(t-nT) }, where k=nT.

An upsampled residual y(n) is computed. The goal is to optimally
represent y(n) with a finite order zinc function model yz(n). A mean
sq error L between y(n) and yz(n) is minimized to compute the
parameters A and B giving an optimal p-order model corresponding
to the P smallest values of L.

It has been shown that for the same order, the zinc function model is
superior to the Fourier series model (for voiced signals). Unvoiced
signals are represented using white noise source. Zinc funtions are
shown to closely model the perceptually important pitch pulses with a
relatively low-order model. Several techniques are proposed to
minimize the "roughness" heard in the synthetic speech, due to
secondary pitch pulses in the excitation.

thanks in advance.
ravichandra

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Hi ravi,

One simple explanation of using both sinc and cosc functions to model
a signal is that these two functions are respectively evn and odd
function. Thus, sinc function is more suitable to model the even part
of the signal and cosc the odd part.
Using only one of them leads to the use of a much higher order to
reach the same approximation in case when you use both functions.

BTW, is it possible to have a copy of your project report ?

Best regards