Frequency response of analog filters

`h = freqs(b,a,w)`

[h,w] = freqs(b,a,n)

freqs

`freqs`

returns the complex frequency response *H*(*j*ω)
(Laplace transform) of an analog filter

$$H(s)=\frac{B(s)}{A(s)}=\frac{b(1){s}^{n}+b(2){s}^{n-1}+\cdots +b(n+1)}{a(1){s}^{m}+a(2){s}^{m-1}+\cdots +a(m+1)}$$

given the numerator and denominator coefficients in vectors `b`

and `a`

.

`h = freqs(b,a,w)`

returns the
complex frequency response of the analog filter specified by coefficient
vectors `b`

and `a`

. `freqs`

evaluates
the frequency response along the imaginary axis in the complex plane
at the angular frequencies in rad/s specified in real vector `w`

,
where `w`

is a vector containing more than one frequency.

`[h,w] = freqs(b,a,n)`

uses `n`

frequency
points to compute the frequency response, `h`

, where
`n`

is a real, scalar value. The frequency vector
`w`

is auto-generated and has length `n`

. If you
omit `n`

as an input, 200 frequency points are used. If you do not need
the generated frequency vector returned, you can use the form ```
h =
freqs(b,a,n)
```

to return only the frequency response,
`h`

.

`freqs`

with no output arguments
plots the magnitude and phase response versus frequency in the current
figure window.

`freqs`

works only for real input systems and
positive frequencies.

`freqs`

evaluates the polynomials at each frequency
point, then divides the numerator response by the denominator response:

s = i*w; h = polyval(b,s)./polyval(a,s);