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# polyscale() - Signal Processing

```b = polyscale(a,alpha) scales
the roots of a polynomial in the z-plane, where a is a vector containing the polynomial
coefficients and alpha is the scaling factor.If alpha is a real value in the range [0 1], then the roots of a are
radially scaled toward the origin in the z-plane.
Complex values for alpha allow arbitrary changes
to the root locations.```

### Syntax

`b = polyscale(a,alpha)`

### Example

```Roots of UnityOpen This Example
Express the solutions to the equation
as the roots of a polynomial. Plot the roots in the complex plane.
pp = [1 0 0 0 0 0 0 -1];
zplane(pp,1)

Scale the roots of p in and out of the unit circle. Plot the results.hold on

for sc = [1:-0.2:0.2 1.2 1.4];
b = polyscale(pp,sc);
plot(roots(b),'o')
end

axis([-1 1 -1 1]*1.5)

hold off

Bandwidth Expansion of LPC Speech SpectrumOpen This ExampleLoad a speech signal sampled at
. The file contains a recording of a female voice saying the word "MATLAB®."load mtlb
Model a 100-sample section of the signal using a 12th-order autoregressive polynomial.Ao = lpc(mtlb(1000:1100),12);
Ax = polyscale(Ao,0.85);
Perform bandwidth expansion of the signal by scaling the roots of the autoregressive polynomial by 0.85. Plot the zeros, poles, and frequency responses of the models.subplot(2,2,1)
zplane(1,Ao)
title('Original')

subplot(2,2,3)
zplane(1,Ax)
title('Flattened')

subplot(1,2,2)
[ho,w]=freqz(1,Ao);
[hx,w]=freqz(1,Ax);
plot(w/pi,abs([ho hx]))
legend('Original','Flattened')```